Supplementary material for the introductory paper on the multidimensional AIM-FAIR scale
Data from study 1,2,3 and 4
TL:DR - Important results
Comparison of fit indices across studies
| Fit_indices | optimal | Fit_S2_optimized | Fit_S3_optimized | Fit_S4_optimized |
|---|---|---|---|---|
| RMSEA | ≤ 0.06 | 0.067 (0.06,0.07) | 0.058 (0.05,0.07) | 0.055 (0.04,0.07) |
| SRMR | < 0.08 | 0.06 | 0.049 | 0.043 |
| TLI | ≥ 0.95 | 0.94 | 0.961 | 0.953 |
| CFI | ≥ 0.95 | 0.953 | 0.97 | 0.964 |
| χ² | < 0.05 | χ²(106, N=495)=340.86, p=0 | χ²(106, N=448)=264.45, p=0 | χ²(106, N=331)=210.2, p=0 |
| χ²/df ratio | < 3.00 | 3.22 | 2.49 | 1.98 |
Reliability of the items using Cronbach’s alpha and McDonald’s omega
| Scale component | alpha S3 | omega S3 | alpha S4 | omega S4 |
|---|---|---|---|---|
| Full Scale | 0.90 | 0.94 | 0.91 | 0.93 |
| F1 - Perceived Consistency | 0.75 | 0.76 | 0.75 | 0.76 |
| F2 - Perceived Equity | 0.80 | 0.84 | 0.82 | 0.84 |
| F3 - Perceived Group Bias | 0.75 | too few items to compute | 0.72 | too few items to compute |
| F4 - Perceived Manipulability | 0.92 | 0.92 | 0.81 | 0.82 |
| F5 - Perceived (Explanatory) Transparency | 0.95 | 0.95 | 0.92 | 0.93 |
Sup1: Overview of demographics of the participant pool for each study
| Demographic | S1_n= | S1_value | S2_n= | S2_value | S3_n= | S3_value | S4_n= | S4_value |
|---|---|---|---|---|---|---|---|---|
| Age | ||||||||
| Mean age | 503 | 40.79 ± 13.57 | 495 | 47.38 ± 15.26 | 448 | 42.68 ± 14.48 | 331 | 30-39 (5.8% 20-29; 75.2% 30-39; 18.8% 40-49; 0.3% >50) |
| Gender | ||||||||
| female | 251 | 49.9% | 255 | 51.5% | 218 | 48.7% | 234 | 70.7% |
| male | 250 | 49.7% | 236 | 47.7% | 220 | 49.1% | 90 | 27.2% |
| diverse | 2 | 0.4% | 4 | 0.8% | 4 | 0.9% | 2 | 0.6% |
| Professional status | ||||||||
| Employed - mostly desk work | 265 | 52.7% | 187 | 37.8% | 190 | 42.4% | ||
| Employed - mostly manual work | 63 | 12.5% | 93 | 18.8% | 73 | 16.3% | ||
| Free-lancer - mostly desk work | 32 | 6.4% | 27 | 5.5% | 35 | 7.8% | ||
| Free-lancer - mostly manual work | 7 | 1.4% | 10 | 2% | 8 | 1.8% | ||
| Student | 31 | 6.2% | 30 | 6.1% | 29 | 6.5% | ||
| Apprentice / Re-education | 1 | 0.2% | 3 | 0.6% | 1 | 0.2% | ||
| Stay-at-home parent | 25 | 5% | 13 | 2.6% | 23 | 5.1% | ||
| Retired | 39 | 7.8% | 107 | 21.6% | 54 | 12.1% | ||
| Unemployed | 37 | 7.4% | 25 | 5.1% | 17 | 3.8% | ||
| Level of education | ||||||||
| Doctorate or equivalent or above | 17 | 3.4% | 5 | 1% | 14 | 3.1% | ||
| Master’s Degree or equivalent | 84 | 16.7% | 87 | 17.6% | 87 | 19.4% | ||
| Bachelor’s Degree or equivalent | 222 | 44.1% | 80 | 16.2% | 161 | 35.9% | 269 | 81.27% finished uni |
| High School diploma or equivalent | 151 | 30% | 128 | 25.9% | 177 | 39.5% | 34 | 10.27% |
| Less than High School diploma | 11 | 2.2% | 171 | 34.5% | 9 | 2% | 25 | 7.55% |
| other: | 16 | 3.2% | 22 | 4.4% | ||||
| 2 | 0.4% | 2 | 0.4% | |||||
Sup2: Overview of all AI descriptions and scenarios
Study 1
Context:
A large company announced many new
vacant job positions. Applicants are required to hand in their CV and a
letter of motivation. Additionally, they are invited for an interview
and an assessment test. The company uses an artificial intelligence (AI)
to decide who to hire.
This AI focuses on a fair selection procedure.
It aims to ensure transparency in decision-making and follows
predefined criteria and guidelines. Its decision-making is based on
consistent and impartial criteria and was trained on how humans decided
in the past.
However, it doesn’t consider the impact of its decisions and communicates decisions to candidates using only one word.
Study 2
(same as in Study 1 but translated in German)
Kontext:
Ein großes Unternehmen hat viele neue freie
Stellen ausgeschrieben. Die Bewerber:innen werden aufgefordert, ihren
Lebenslauf und ein Motivationsschreiben einzureichen. Außerdem werden
sie zu einem Vorstellungsgespräch und einem Bewertungstest eingeladen.
Das Unternehmen setzt eine künstliche Intelligenz (KI) ein, um zu
entscheiden, wer eingestellt werden soll.
Diese KI konzentriert sich auf ein faires Auswahlverfahren,
das Transparenz bei der Entscheidungsfindung gewährleisten soll und
vordefinierten Kriterien und Richtlinien folgt. Sie trifft ihre
Entscheidungen auf der Grundlage einheitlicher und unparteiischer
Kriterien und wurde darauf trainiert, wie Menschen in der Vergangenheit
entschieden haben.
Allerdings berücksichtigt sie nicht die Auswirkungen ihrer Entscheidungen und teilt den Bewerber:innen ihre Entscheidungen nur mit einem Wort mit.
Study 3
Context stays the same across all
scenarios
Context:
A large company
announced many new vacant job positions. Applicants are required to hand
in their CV and a letter of motivation. Additionally, they are invited
for an interview and an assessment test. The company uses an artificial
intelligence (AI) to decide who to hire.
Scenario 1 - FAIR AI
Description 1
The AI focuses on
a fair selection procedure.
It aims to ensure
transparency in decision-making and follows predefined criteria and
guidelines. Its decision-making is based on consistent and impartial
criteria and has been thoroughly evaluated and approved by an
independent assessment.
Scenario 2 - DISCRIMINATORY AI
Description 2
The AI
exhibits discriminatory tendencies, disproportionately favoring certain
groups over others.
Its decision-making process
tends to reinforce biases present in the training data, often leading to
an acceptance of individuals mainly due to the fact, that they are
members of a certain groups.
Scenario 3 - HIGH ERROR AI
Description 3
The AI
depicts a high error rate in its decision-making process.
Despite efforts to follow predefined criteria and guidelines, it
frequently produces inaccurate and unreliable results thereby deciding
sometimes for individuals who did not deserve it or sometimes rejecting
individuals who would in reality deserve it.
Study 4
OSF link to supplementary material of study 4. Will be published once study 4 is published.
Sup3: Overview of used items
Item evolution across the four studies:
| Item no | Items S1 (English) |
|---|---|
| is fair. | |
| is just. | |
| 01 | evaluates situations according to the same factors. |
| 02 | evaluates according to criteria that are the same for all people. |
| 03 | considers a wide range of individual characteristics. |
| 04 | is designed to be equitable for all individuals. |
| 05 | is discriminatory against certain groups. |
| 06 | is favoring certain groups. |
| 07 | avoids perpetuating stereotypes. |
| 08 | avoids perpetuating bias. |
| 09 | ensures inclusivity in its outcomes. |
| 10 | is consistent throughout time. |
| 11 | produces similar results for similar people. |
| 12 | maintains reliability across different cases. |
| 13 | can be influenced. |
| 14 | is easy to manipulate. |
| 15 | is susceptible to external factors. |
| 16 | is vulnerable to external influence. |
| 17 | can be modified with intentional efforts. |
| 18 | provides clear explanations for its decisions. |
| 19 | allows users to understand the decision-making process. |
| 20 | makes the decision process transparent. |
| 21 | offers insights into the key factors influencing each decision. |
| 22 | helps users understand why a specific outcome was reached. |
| 23 | ensures there are mechanisms to find the source of errors. |
| 24 | is governed by established regulations. |
| 25 | discloses its limitations. |
| 26 | communicates what it cannot do. |
| Item no | Items S2 (German) | Corresponding factors |
|---|---|---|
| 01 | ist fair. | additional, optional item |
| 02 | ist gerecht. | additional, optional item |
| 03 | bewertet Situationen nach den gleichen Faktoren. | F1 (Perceived Consistency) |
| 04 | bewertet nach Kriterien, die für alle Menschen gleich sind. | F1 (Perceived Consistency) |
| 05 | ist über die Zeit hinweg konsistent. | F1 (Perceived Consistency) |
| 06 | liefert ähnliche Ergebnisse für ähnliche Personen. | discarded |
| 07 | bleibt über verschiedene Fälle hinweg zuverlässig. | discarded |
| 08 | ist so konzipiert, dass es für alle Menschen gleich ist. | F2 (Perceived Equity) |
| 09 | ist diskriminierend gegenüber bestimmten Gruppen. | F3 (Perceived Group Bias) |
| 10 | begünstigt bestimmte Gruppen. | F3 (Perceived Group Bias) |
| 11 | vermeidet die Aufrechterhaltung von Stereotypen. | F2 (Perceived Equity) |
| 12 | vermeidet die Aufrechterhaltung von Vorurteilen. | F2 (Perceived Equity) |
| 13 | gewährleistet Inklusivität in den Ergebnissen. | F2 (Perceived Equity) |
| 14 | kann beeinflusst werden. | F4 (Perceived Manipulability) |
| 15 | ist leicht zu manipulieren. | F4 (Perceived Manipulability) |
| 16 | ist anfällig für externe Faktoren. | discarded |
| 17 | ist anfällig für äußere Einflüsse. | F4 (Perceived Manipulability) |
| 18 | kann durch bewusste Anstrengungen verändert werden. | discarded |
| 19 | liefert klare Erklärungen für seine Entscheidungen. | F5 (Perceived (Explanatory) Transparency) |
| 20 | ermöglicht es den Entscheidungsprozess zu verstehen. | F5 (Perceived (Explanatory) Transparency) |
| 21 | macht den Entscheidungsprozess transparent. | F5 (Perceived (Explanatory) Transparency) |
| 22 | bietet Einblicke in die Schlüsselfaktoren, die jede Entscheidung beeinflussen. | F5 (Perceived (Explanatory) Transparency) |
| 23 | hilft den Nutzern zu verstehen, warum ein bestimmtes Ergebnis erzielt wurde. | F5 (Perceived (Explanatory) Transparency) |
| 24 | legt seine Grenzen offen. | discarded |
| 25 | kommuniziert, was es nicht tun kann. | discarded |
| Item no | Items S3 (English) | Items S4 (German) | Corresponding factors |
|---|---|---|---|
| is fair. | ist fair. | additional, optional item | |
| 01 | evaluates situations according to the same factors. | bewertet Situationen nach den gleichen Faktoren. | F1 (Perceived Consistency) |
| 02 | evaluates according to criteria that are the same for all people. | bewertet nach Kriterien, die für alle Menschen gleich sind. | F1 (Perceived Consistency) |
| 03 | is consistent throughout time. | bleibt immer gleich. | F1 (Perceived Consistency) |
| 04 | aims to be the same for all groups of people. | zielt darauf ab, für alle Gruppen von Menschen gleich zu sein. | F2 (Perceived Equity) |
| 05 | avoids spreading stereotypes. | vermeidet die Verbreitung von Vorurteilen. | F2 (Perceived Equity) |
| 06 | is unbiased. | ist unvoreingenommen. | F2 (Perceived Equity) |
| 07 | makes sure everyone is included in its results. | stellt sicher, dass alle Menschen gleichwertig berücksichtigt werden. | F2 (Perceived Equity) |
| 08 | discriminates against certain groups. | diskriminiert bestimmte Gruppen von Menschen. | F3 (Perceived Group Bias) |
| 09 | is favoring certain groups. | begünstigt bestimmte Gruppen von Menschen. | F3 (Perceived Group Bias) |
| 10 | can be influenced. | kann beeinflusst werden. | F4 (Perceived Manipulability) |
| 11 | is easy to manipulate. | ist leicht zu manipulieren. | F4 (Perceived Manipulability) |
| 12 | is vulnerable to external influence. | ist anfällig für äußere Einflüsse. | F4 (Perceived Manipulability) |
| 13 | provides clear explanations for its decisions. | liefert klare Erklärungen für seine Entscheidungen. | F5 (Perceived (Explanatory) Transparency) |
| 14 | helps users to understand how decisions are made. | hilft den Menschen zu verstehen, wie Entscheidungen getroffen werden. | F5 (Perceived (Explanatory) Transparency) |
| 15 | makes the decision process transparent. | ist transparent. | F5 (Perceived (Explanatory) Transparency) |
| 16 | shows the reasons behind each decision. | zeigt die Gründe für jede Entscheidung auf. | F5 (Perceived (Explanatory) Transparency) |
| 17 | helps users understand why a specific outcome was reached. | erklärt, warum ein bestimmtes Ergebnis erzielt wurde. | F5 (Perceived (Explanatory) Transparency) |
| item no | items S1 (English) | items S2 (German) | items S3 (English) | items S4 (German) | corresponding factors |
|---|---|---|---|---|---|
| is fair. | ist fair. | is fair. | ist fair. | additional, optional item | |
| is just. | ist gerecht. | additional, optional item | |||
| 01 | evaluates situations according to the same factors. | bewertet Situationen nach den gleichen Faktoren. | evaluates situations according to the same factors. | bewertet Situationen nach den gleichen Faktoren. | F1 (Perceived Consistency) |
| 02 | evaluates according to criteria that are the same for all people. | bewertet nach Kriterien, die für alle Menschen gleich sind. | evaluates according to criteria that are the same for all people. | bewertet nach Kriterien, die für alle Menschen gleich sind. | F1 (Perceived Consistency) |
| 03 | considers a wide range of individual characteristics. | ||||
| 04 | is designed to be equitable for all individuals. | ist so konzipiert, dass es für alle Menschen gleich ist. | aims to be the same for all groups of people. | zielt darauf ab, für alle Gruppen von Menschen gleich zu sein. | F2 (Perceived Equity) |
| 05 | is discriminatory against certain groups. | ist diskriminierend gegenüber bestimmten Gruppen. | discriminates against certain groups. | diskriminiert bestimmte Gruppen von Menschen. | F3 (Perceived Group Bias) |
| 06 | is favoring certain groups. | begünstigt bestimmte Gruppen. | is favoring certain groups. | begünstigt bestimmte Gruppen von Menschen. | F3 (Perceived Group Bias) |
| 07 | avoids perpetuating stereotypes. | vermeidet die Aufrechterhaltung von Stereotypen. | avoids spreading stereotypes. | vermeidet die Verbreitung von Vorurteilen. | F2 (Perceived Equity) |
| 08 | avoids perpetuating bias. | vermeidet die Aufrechterhaltung von Vorurteilen. | is unbiased. | ist unvoreingenommen. | F2 (Perceived Equity) |
| 09 | ensures inclusivity in its outcomes. | gewährleistet Inklusivität in den Ergebnissen. | makes sure everyone is included in its results. | stellt sicher, dass alle Menschen gleichwertig berücksichtigt werden. | F2 (Perceived Equity) |
| 10 | is consistent throughout time. | ist über die Zeit hinweg konsistent. | is consistent throughout time. | bleibt immer gleich. | F1 (Perceived Consistency) |
| 11 | produces similar results for similar people. | liefert ähnliche Ergebnisse für ähnliche Personen. | |||
| 12 | maintains reliability across different cases. | bleibt über verschiedene Fälle hinweg zuverlässig. | |||
| 13 | can be influenced. | kann beeinflusst werden. | can be influenced. | kann beeinflusst werden. | F4 (Perceived Manipulability) |
| 14 | is easy to manipulate. | ist leicht zu manipulieren. | is easy to manipulate. | ist leicht zu manipulieren. | F4 (Perceived Manipulability) |
| 15 | is susceptible to external factors. | ist anfällig für externe Faktoren. | |||
| 16 | is vulnerable to external influence. | ist anfällig für äußere Einflüsse. | is vulnerable to external influence. | ist anfällig für äußere Einflüsse. | F4 (Perceived Manipulability) |
| 17 | can be modified with intentional efforts. | kann durch bewusste Anstrengungen verändert werden. | |||
| 18 | provides clear explanations for its decisions. | liefert klare Erklärungen für seine Entscheidungen. | provides clear explanations for its decisions. | liefert klare Erklärungen für seine Entscheidungen. | F5 (Perceived (Explanatory) Transparency) |
| 19 | allows users to understand the decision-making process. | ermöglicht es den Entscheidungsprozess zu verstehen. | helps users to understand how decisions are made. | hilft den Menschen zu verstehen, wie Entscheidungen getroffen werden. | F5 (Perceived (Explanatory) Transparency) |
| 20 | makes the decision process transparent. | macht den Entscheidungsprozess transparent. | makes the decision process transparent. | ist transparent. | F5 (Perceived (Explanatory) Transparency) |
| 21 | offers insights into the key factors influencing each decision. | bietet Einblicke in die Schlüsselfaktoren, die jede Entscheidung beeinflussen. | shows the reasons behind each decision. | zeigt die Gründe für jede Entscheidung auf. | F5 (Perceived (Explanatory) Transparency) |
| 22 | helps users understand why a specific outcome was reached. | hilft den Nutzern zu verstehen, warum ein bestimmtes Ergebnis erzielt wurde. | helps users understand why a specific outcome was reached. | erklärt, warum ein bestimmtes Ergebnis erzielt wurde. | F5 (Perceived (Explanatory) Transparency) |
| 23 | ensures there are mechanisms to find the source of errors. | ||||
| 24 | is governed by established regulations. | ||||
| 25 | discloses its limitations. | legt seine Grenzen offen. | |||
| 26 | communicates what it cannot do. | kommuniziert, was es nicht tun kann. |
Note: As described in the paper, in study 3 all items that were used in study 2 were used as well. Only the items that made it into the final scale are listed for study 3 because analysis was only performed with them.
Final items table:
| item.no | final_ENG | final_GER |
|---|---|---|
| Optional | ||
| is fair. | ist fair. | |
| F1 (Perceived Consistency) | ||
| 01 | evaluates situations according to the same factors. | bewertet Situationen nach den gleichen Faktoren. |
| 02 | evaluates according to criteria that are the same for all people. | bewertet nach Kriterien, die für alle Menschen gleich sind. |
| 03 | is consistent throughout time. | bleibt immer gleich. |
| F2 (Perceived Equity) | ||
| 04 | aims to be the same for all groups of people. | zielt darauf ab, für alle Gruppen von Menschen gleich zu sein. |
| 05 | avoids spreading stereotypes. | vermeidet die Verbreitung von Vorurteilen. |
| 06 | is unbiased. | ist unvoreingenommen. |
| 07 | makes sure everyone is included in its results. | stellt sicher, dass alle Menschen gleichwertig berücksichtigt werden. |
| F3 (Perceived Group Bias) | ||
| 08 | discriminates against certain groups. | diskriminiert bestimmte Gruppen von Menschen. |
| 09 | is favoring certain groups. | begünstigt bestimmte Gruppen von Menschen. |
| F4 (Perceived Manipulability) | ||
| 10 | can be influenced. | kann beeinflusst werden. |
| 11 | is easy to manipulate. | ist leicht zu manipulieren. |
| 12 | is vulnerable to external influence. | ist anfällig für äußere Einflüsse. |
| F5 (Perceived (Explanatory) Transparency) | ||
| 13 | provides clear explanations for its decisions. | liefert klare Erklärungen für seine Entscheidungen. |
| 14 | helps users to understand how decisions are made. | hilft den Menschen zu verstehen, wie Entscheidungen getroffen werden. |
| 15 | makes the decision process transparent. | ist transparent. |
| 16 | shows the reasons behind each decision. | zeigt die Gründe für jede Entscheidung auf. |
| 17 | helps users understand why a specific outcome was reached. | erklärt, warum ein bestimmtes Ergebnis erzielt wurde. |
Sup4: Analysis of study 1
Sup4.1: Sampling adequacy and suitability of the data
Result: Data are not considered to be multivariate
normal
## $chisq
## [1] 1292.239
##
## $p.value
## [1] 2.824937e-100
##
## $df
## [1] 378## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = results_1.1_fair)
## Overall MSA = 0.91
## MSA for each item =
## AI1_fairness_scale_1 AI1_fairness_scale_2 AI1_fairness_scale_3
## 0.94 0.93 0.89
## AI1_fairness_scale_4 AI1_fairness_scale_5 AI1_fairness_scale_6
## 0.93 0.92 0.96
## AI1_fairness_scale_7 AI1_fairness_scale_8 AI1_fairness_scale_9
## 0.91 0.91 0.90
## AI1_fairness_scale_10 AI1_fairness_scale_11 AI1_fairness_scale_12
## 0.92 0.94 0.91
## AI1_fairness_scale_13 AI1_fairness_scale_14 AI1_fairness_scale_15
## 0.90 0.95 0.90
## AI1_fairness_scale_16 AI1_fairness_scale_17 AI1_fairness_scale_18
## 0.90 0.88 0.87
## AI1_fairness_scale_19 AI1_fairness_scale_20 AI1_fairness_scale_21
## 0.86 0.88 0.90
## AI1_fairness_scale_22 AI1_fairness_scale_23 AI1_fairness_scale_24
## 0.93 0.92 0.87
## AI1_fairness_scale_25 AI1_fairness_scale_26 AI1_fairness_scale_27
## 0.92 0.93 0.85
## AI1_fairness_scale_28
## 0.85## Test Statistic p value Result
## 1 Mardia Skewness 7658.03379612691 1.40025845895305e-224 NO
## 2 Mardia Kurtosis 40.8716813275392 0 NO
## 3 MVN <NA> <NA> NO## $multivariateNormality
## Test HZ p value MVN
## 1 Henze-Zirkler 1.023456 0 NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling AI1_fairness_scale_1 12.5976 <0.001 NO
## 2 Anderson-Darling AI1_fairness_scale_2 15.4786 <0.001 NO
## 3 Anderson-Darling AI1_fairness_scale_3 21.5632 <0.001 NO
## 4 Anderson-Darling AI1_fairness_scale_4 20.3548 <0.001 NO
## 5 Anderson-Darling AI1_fairness_scale_5 12.2921 <0.001 NO
## 6 Anderson-Darling AI1_fairness_scale_6 15.6173 <0.001 NO
## 7 Anderson-Darling AI1_fairness_scale_7 10.8542 <0.001 NO
## 8 Anderson-Darling AI1_fairness_scale_8 11.4510 <0.001 NO
## 9 Anderson-Darling AI1_fairness_scale_9 11.6256 <0.001 NO
## 10 Anderson-Darling AI1_fairness_scale_10 12.1523 <0.001 NO
## 11 Anderson-Darling AI1_fairness_scale_11 10.7553 <0.001 NO
## 12 Anderson-Darling AI1_fairness_scale_12 19.1032 <0.001 NO
## 13 Anderson-Darling AI1_fairness_scale_13 17.7778 <0.001 NO
## 14 Anderson-Darling AI1_fairness_scale_14 15.8358 <0.001 NO
## 15 Anderson-Darling AI1_fairness_scale_15 13.4588 <0.001 NO
## 16 Anderson-Darling AI1_fairness_scale_16 11.1946 <0.001 NO
## 17 Anderson-Darling AI1_fairness_scale_17 10.1579 <0.001 NO
## 18 Anderson-Darling AI1_fairness_scale_18 9.9319 <0.001 NO
## 19 Anderson-Darling AI1_fairness_scale_19 16.2800 <0.001 NO
## 20 Anderson-Darling AI1_fairness_scale_20 20.3069 <0.001 NO
## 21 Anderson-Darling AI1_fairness_scale_21 15.5587 <0.001 NO
## 22 Anderson-Darling AI1_fairness_scale_22 11.7826 <0.001 NO
## 23 Anderson-Darling AI1_fairness_scale_23 14.1768 <0.001 NO
## 24 Anderson-Darling AI1_fairness_scale_24 18.7389 <0.001 NO
## 25 Anderson-Darling AI1_fairness_scale_25 20.5880 <0.001 NO
## 26 Anderson-Darling AI1_fairness_scale_26 13.7119 <0.001 NO
## 27 Anderson-Darling AI1_fairness_scale_27 11.6744 <0.001 NO
## 28 Anderson-Darling AI1_fairness_scale_28 13.7542 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th
## AI1_fairness_scale_1 503 0.236580517 1.329145 0 -3 3 -1 1
## AI1_fairness_scale_2 503 0.027833002 1.218720 0 -3 3 -1 1
## AI1_fairness_scale_3 503 1.266401590 1.104412 1 -3 3 1 2
## AI1_fairness_scale_4 503 1.222664016 1.154466 1 -2 3 1 2
## AI1_fairness_scale_5 503 0.005964215 1.471497 0 -3 3 -1 1
## AI1_fairness_scale_6 503 0.681908549 1.360444 1 -3 3 0 2
## AI1_fairness_scale_7 503 -0.596421471 1.508986 0 -3 3 -2 0
## AI1_fairness_scale_8 503 -0.453280318 1.445319 0 -3 3 -2 0
## AI1_fairness_scale_9 503 0.244532803 1.466031 0 -3 3 -1 1
## AI1_fairness_scale_10 503 0.335984095 1.462832 0 -3 3 -1 1
## AI1_fairness_scale_11 503 -0.065606362 1.432989 0 -3 3 -1 1
## AI1_fairness_scale_12 503 1.047713718 1.161170 1 -2 3 0 2
## AI1_fairness_scale_13 503 1.071570577 1.146121 1 -3 3 0 2
## AI1_fairness_scale_14 503 0.781312127 1.268641 1 -3 3 0 2
## AI1_fairness_scale_15 503 0.013916501 1.572233 0 -3 3 -1 1
## AI1_fairness_scale_16 503 -0.041749503 1.428316 0 -3 3 -1 1
## AI1_fairness_scale_17 503 -0.033797217 1.515146 0 -3 3 -1 1
## AI1_fairness_scale_18 503 -0.049701789 1.577833 0 -3 3 -1 1
## AI1_fairness_scale_19 503 0.618290258 1.286392 1 -3 3 0 1
## AI1_fairness_scale_20 503 -1.141153082 1.677706 -2 -3 3 -3 0
## AI1_fairness_scale_21 503 -0.787276342 1.670126 -1 -3 3 -2 1
## AI1_fairness_scale_22 503 -0.069582505 1.652334 0 -3 3 -1 1
## AI1_fairness_scale_23 503 -0.844930417 1.589247 -1 -3 3 -2 0
## AI1_fairness_scale_24 503 -1.085487078 1.618693 -1 -3 3 -3 0
## AI1_fairness_scale_25 503 -0.216699801 1.166754 0 -3 3 -1 0
## AI1_fairness_scale_26 503 0.504970179 1.506783 1 -3 3 0 2
## AI1_fairness_scale_27 503 -0.578528827 1.463124 -1 -3 3 -2 0
## AI1_fairness_scale_28 503 -0.697813121 1.366990 -1 -3 3 -2 0
## Skew Kurtosis
## AI1_fairness_scale_1 -0.23460620 -0.43808455
## AI1_fairness_scale_2 -0.17821904 -0.09763277
## AI1_fairness_scale_3 -0.79527747 1.02357421
## AI1_fairness_scale_4 -0.62598641 0.07694560
## AI1_fairness_scale_5 -0.23488769 -0.76463022
## AI1_fairness_scale_6 -0.59311595 -0.04994298
## AI1_fairness_scale_7 0.15505040 -0.62194545
## AI1_fairness_scale_8 0.10459616 -0.59719737
## AI1_fairness_scale_9 -0.18414632 -0.78024701
## AI1_fairness_scale_10 -0.33333005 -0.61454579
## AI1_fairness_scale_11 -0.11618671 -0.50435548
## AI1_fairness_scale_12 -0.60309175 0.20570017
## AI1_fairness_scale_13 -0.53582296 0.25124695
## AI1_fairness_scale_14 -0.56149725 0.08423524
## AI1_fairness_scale_15 -0.24083815 -0.88198295
## AI1_fairness_scale_16 -0.13965718 -0.62875779
## AI1_fairness_scale_17 -0.11781986 -0.69990040
## AI1_fairness_scale_18 -0.03674023 -0.85021467
## AI1_fairness_scale_19 -0.54237972 0.06691924
## AI1_fairness_scale_20 0.59140431 -0.78194142
## AI1_fairness_scale_21 0.22813203 -1.17274923
## AI1_fairness_scale_22 -0.17483638 -0.99680233
## AI1_fairness_scale_23 0.28344539 -0.99241645
## AI1_fairness_scale_24 0.37717435 -1.10599453
## AI1_fairness_scale_25 -0.30242764 -0.08639146
## AI1_fairness_scale_26 -0.51336059 -0.38359657
## AI1_fairness_scale_27 0.21170816 -0.71793605
## AI1_fairness_scale_28 0.12740823 -0.59285646
## $multivariateNormality
## Test HZ p value MVN
## 1 Henze-Zirkler 1.023456 0 NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling AI1_fairness_scale_1 12.5976 <0.001 NO
## 2 Anderson-Darling AI1_fairness_scale_2 15.4786 <0.001 NO
## 3 Anderson-Darling AI1_fairness_scale_3 21.5632 <0.001 NO
## 4 Anderson-Darling AI1_fairness_scale_4 20.3548 <0.001 NO
## 5 Anderson-Darling AI1_fairness_scale_5 12.2921 <0.001 NO
## 6 Anderson-Darling AI1_fairness_scale_6 15.6173 <0.001 NO
## 7 Anderson-Darling AI1_fairness_scale_7 10.8542 <0.001 NO
## 8 Anderson-Darling AI1_fairness_scale_8 11.4510 <0.001 NO
## 9 Anderson-Darling AI1_fairness_scale_9 11.6256 <0.001 NO
## 10 Anderson-Darling AI1_fairness_scale_10 12.1523 <0.001 NO
## 11 Anderson-Darling AI1_fairness_scale_11 10.7553 <0.001 NO
## 12 Anderson-Darling AI1_fairness_scale_12 19.1032 <0.001 NO
## 13 Anderson-Darling AI1_fairness_scale_13 17.7778 <0.001 NO
## 14 Anderson-Darling AI1_fairness_scale_14 15.8358 <0.001 NO
## 15 Anderson-Darling AI1_fairness_scale_15 13.4588 <0.001 NO
## 16 Anderson-Darling AI1_fairness_scale_16 11.1946 <0.001 NO
## 17 Anderson-Darling AI1_fairness_scale_17 10.1579 <0.001 NO
## 18 Anderson-Darling AI1_fairness_scale_18 9.9319 <0.001 NO
## 19 Anderson-Darling AI1_fairness_scale_19 16.2800 <0.001 NO
## 20 Anderson-Darling AI1_fairness_scale_20 20.3069 <0.001 NO
## 21 Anderson-Darling AI1_fairness_scale_21 15.5587 <0.001 NO
## 22 Anderson-Darling AI1_fairness_scale_22 11.7826 <0.001 NO
## 23 Anderson-Darling AI1_fairness_scale_23 14.1768 <0.001 NO
## 24 Anderson-Darling AI1_fairness_scale_24 18.7389 <0.001 NO
## 25 Anderson-Darling AI1_fairness_scale_25 20.5880 <0.001 NO
## 26 Anderson-Darling AI1_fairness_scale_26 13.7119 <0.001 NO
## 27 Anderson-Darling AI1_fairness_scale_27 11.6744 <0.001 NO
## 28 Anderson-Darling AI1_fairness_scale_28 13.7542 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th
## AI1_fairness_scale_1 503 0.236580517 1.329145 0 -3 3 -1 1
## AI1_fairness_scale_2 503 0.027833002 1.218720 0 -3 3 -1 1
## AI1_fairness_scale_3 503 1.266401590 1.104412 1 -3 3 1 2
## AI1_fairness_scale_4 503 1.222664016 1.154466 1 -2 3 1 2
## AI1_fairness_scale_5 503 0.005964215 1.471497 0 -3 3 -1 1
## AI1_fairness_scale_6 503 0.681908549 1.360444 1 -3 3 0 2
## AI1_fairness_scale_7 503 -0.596421471 1.508986 0 -3 3 -2 0
## AI1_fairness_scale_8 503 -0.453280318 1.445319 0 -3 3 -2 0
## AI1_fairness_scale_9 503 0.244532803 1.466031 0 -3 3 -1 1
## AI1_fairness_scale_10 503 0.335984095 1.462832 0 -3 3 -1 1
## AI1_fairness_scale_11 503 -0.065606362 1.432989 0 -3 3 -1 1
## AI1_fairness_scale_12 503 1.047713718 1.161170 1 -2 3 0 2
## AI1_fairness_scale_13 503 1.071570577 1.146121 1 -3 3 0 2
## AI1_fairness_scale_14 503 0.781312127 1.268641 1 -3 3 0 2
## AI1_fairness_scale_15 503 0.013916501 1.572233 0 -3 3 -1 1
## AI1_fairness_scale_16 503 -0.041749503 1.428316 0 -3 3 -1 1
## AI1_fairness_scale_17 503 -0.033797217 1.515146 0 -3 3 -1 1
## AI1_fairness_scale_18 503 -0.049701789 1.577833 0 -3 3 -1 1
## AI1_fairness_scale_19 503 0.618290258 1.286392 1 -3 3 0 1
## AI1_fairness_scale_20 503 -1.141153082 1.677706 -2 -3 3 -3 0
## AI1_fairness_scale_21 503 -0.787276342 1.670126 -1 -3 3 -2 1
## AI1_fairness_scale_22 503 -0.069582505 1.652334 0 -3 3 -1 1
## AI1_fairness_scale_23 503 -0.844930417 1.589247 -1 -3 3 -2 0
## AI1_fairness_scale_24 503 -1.085487078 1.618693 -1 -3 3 -3 0
## AI1_fairness_scale_25 503 -0.216699801 1.166754 0 -3 3 -1 0
## AI1_fairness_scale_26 503 0.504970179 1.506783 1 -3 3 0 2
## AI1_fairness_scale_27 503 -0.578528827 1.463124 -1 -3 3 -2 0
## AI1_fairness_scale_28 503 -0.697813121 1.366990 -1 -3 3 -2 0
## Skew Kurtosis
## AI1_fairness_scale_1 -0.23460620 -0.43808455
## AI1_fairness_scale_2 -0.17821904 -0.09763277
## AI1_fairness_scale_3 -0.79527747 1.02357421
## AI1_fairness_scale_4 -0.62598641 0.07694560
## AI1_fairness_scale_5 -0.23488769 -0.76463022
## AI1_fairness_scale_6 -0.59311595 -0.04994298
## AI1_fairness_scale_7 0.15505040 -0.62194545
## AI1_fairness_scale_8 0.10459616 -0.59719737
## AI1_fairness_scale_9 -0.18414632 -0.78024701
## AI1_fairness_scale_10 -0.33333005 -0.61454579
## AI1_fairness_scale_11 -0.11618671 -0.50435548
## AI1_fairness_scale_12 -0.60309175 0.20570017
## AI1_fairness_scale_13 -0.53582296 0.25124695
## AI1_fairness_scale_14 -0.56149725 0.08423524
## AI1_fairness_scale_15 -0.24083815 -0.88198295
## AI1_fairness_scale_16 -0.13965718 -0.62875779
## AI1_fairness_scale_17 -0.11781986 -0.69990040
## AI1_fairness_scale_18 -0.03674023 -0.85021467
## AI1_fairness_scale_19 -0.54237972 0.06691924
## AI1_fairness_scale_20 0.59140431 -0.78194142
## AI1_fairness_scale_21 0.22813203 -1.17274923
## AI1_fairness_scale_22 -0.17483638 -0.99680233
## AI1_fairness_scale_23 0.28344539 -0.99241645
## AI1_fairness_scale_24 0.37717435 -1.10599453
## AI1_fairness_scale_25 -0.30242764 -0.08639146
## AI1_fairness_scale_26 -0.51336059 -0.38359657
## AI1_fairness_scale_27 0.21170816 -0.71793605
## AI1_fairness_scale_28 0.12740823 -0.59285646Sup4.2 = Fig4.2: Scree plot and EFA results
Result: 5 factor solution; item 5, 25 and 26 were
removed
## This is lavaan 0.6.17 -- running exploratory factor analysis
##
## Estimator ML
## Rotation method GEOMIN OBLIQUE
## Geomin epsilon 0.001
## Rotation algorithm (rstarts) GPA (30)
## Standardized metric TRUE
## Row weights None
##
## Number of observations 503
##
## Fit measures:
## aic bic sabic chisq df pvalue cfi rmsea
## nfactors = 5 43072.56 43739.41 43237.91 563.098 248 0 0.955 0.05
##
## Eigenvalues correlation matrix:
##
## ev1 ev2 ev3 ev4 ev5 ev6 ev7 ev8 ev9 ev10
## 7.572 4.757 2.217 1.586 1.020 0.968 0.848 0.776 0.676 0.661
## ev11 ev12 ev13 ev14 ev15 ev16 ev17 ev18 ev19 ev20
## 0.599 0.560 0.520 0.511 0.486 0.470 0.439 0.419 0.391 0.380
## ev21 ev22 ev23 ev24 ev25 ev26 ev27 ev28
## 0.339 0.324 0.286 0.279 0.261 0.238 0.223 0.195
##
## Standardized loadings: (* = significant at 1% level)
##
## f1 f2 f3 f4 f5 unique.var
## AI1_fairness_scale_1 0.531* . 0.325* 0.329
## AI1_fairness_scale_2 0.401* . 0.366* 0.471
## AI1_fairness_scale_3 0.740* 0.492
## AI1_fairness_scale_4 0.612* . 0.532
## AI1_fairness_scale_5 0.515* . . 0.629
## AI1_fairness_scale_6 .* .* 0.442* 0.457
## AI1_fairness_scale_7 -0.723* . 0.396
## AI1_fairness_scale_8 -0.676* .* 0.426
## AI1_fairness_scale_9 0.816* . 0.305
## AI1_fairness_scale_10 0.761* 0.353
## AI1_fairness_scale_11 0.374* 0.422* 0.552
## AI1_fairness_scale_12 0.687* . 0.421
## AI1_fairness_scale_13 . 0.576* . 0.648
## AI1_fairness_scale_14 0.326* 0.470* 0.453
## AI1_fairness_scale_15 0.787* 0.333
## AI1_fairness_scale_16 . 0.740* 0.372
## AI1_fairness_scale_17 . 0.673* 0.468
## AI1_fairness_scale_18 . 0.813* 0.257
## AI1_fairness_scale_19 . .* 0.690* 0.606
## AI1_fairness_scale_20 0.833* 0.267
## AI1_fairness_scale_21 . . 0.880* 0.295
## AI1_fairness_scale_22 .* .* 0.603* 0.547
## AI1_fairness_scale_23 0.816* 0.318
## AI1_fairness_scale_24 0.852* 0.267
## AI1_fairness_scale_25 . . 0.416* 0.726
## AI1_fairness_scale_26 0.330* .* 0.821
## AI1_fairness_scale_27 0.521* 0.712
## AI1_fairness_scale_28 . . 0.508* 0.665
## communalities
## AI1_fairness_scale_1 0.671
## AI1_fairness_scale_2 0.529
## AI1_fairness_scale_3 0.508
## AI1_fairness_scale_4 0.468
## AI1_fairness_scale_5 0.371
## AI1_fairness_scale_6 0.543
## AI1_fairness_scale_7 0.604
## AI1_fairness_scale_8 0.574
## AI1_fairness_scale_9 0.695
## AI1_fairness_scale_10 0.647
## AI1_fairness_scale_11 0.448
## AI1_fairness_scale_12 0.579
## AI1_fairness_scale_13 0.352
## AI1_fairness_scale_14 0.547
## AI1_fairness_scale_15 0.667
## AI1_fairness_scale_16 0.628
## AI1_fairness_scale_17 0.532
## AI1_fairness_scale_18 0.743
## AI1_fairness_scale_19 0.394
## AI1_fairness_scale_20 0.733
## AI1_fairness_scale_21 0.705
## AI1_fairness_scale_22 0.453
## AI1_fairness_scale_23 0.682
## AI1_fairness_scale_24 0.733
## AI1_fairness_scale_25 0.274
## AI1_fairness_scale_26 0.179
## AI1_fairness_scale_27 0.288
## AI1_fairness_scale_28 0.335
##
## f5 f3 f4 f2 f1 total
## Sum of sq (obliq) loadings 4.145 3.503 3.006 2.594 1.634 14.883
## Proportion of total 0.279 0.235 0.202 0.174 0.110 1.000
## Proportion var 0.148 0.125 0.107 0.093 0.058 0.532
## Cumulative var 0.148 0.273 0.381 0.473 0.532 0.532
##
## Factor correlations: (* = significant at 1% level)
##
## f1 f2 f3 f4 f5
## f1 1.000
## f2 0.311 1.000
## f3 0.390* 0.472* 1.000
## f4 -0.089 -0.366* -0.414* 1.000
## f5 0.327 -0.042 0.144 0.082 1.000| Item | f1 | f2 | f3 | f4 | f5 | unique.var | communalities |
|---|---|---|---|---|---|---|---|
| item01 | 0.74 | 0.492 | 0.508 | ||||
| item02 | 0.612 | 0.532 | 0.468 | ||||
| item03 | 0.515 | 0.629 | 0.371 | ||||
| item04 | 0.442 | 0.457 | 0.543 | ||||
| item05 | -0.723 | 0.396 | 0.604 | ||||
| item06 | -0.676 | 0.426 | 0.574 | ||||
| item07 | 0.816 | 0.305 | 0.695 | ||||
| item08 | 0.761 | 0.353 | 0.647 | ||||
| item09 | 0.374 | 0.422 | 0.552 | 0.448 | |||
| item10 | 0.687 | 0.421 | 0.579 | ||||
| item11 | 0.576 | 0.648 | 0.352 | ||||
| item12 | 0.326 | 0.47 | 0.453 | 0.547 | |||
| item13 | 0.787 | 0.333 | 0.667 | ||||
| item14 | 0.74 | 0.372 | 0.628 | ||||
| item15 | 0.673 | 0.468 | 0.532 | ||||
| item16 | 0.813 | 0.257 | 0.743 | ||||
| item17 | 0.69 | 0.606 | 0.394 | ||||
| item18 | 0.833 | 0.267 | 0.733 | ||||
| item19 | 0.88 | 0.295 | 0.705 | ||||
| item20 | 0.603 | 0.547 | 0.453 | ||||
| item21 | 0.816 | 0.318 | 0.682 | ||||
| item22 | 0.852 | 0.267 | 0.733 | ||||
| item23 | 0.416 | 0.726 | 0.274 | ||||
| item24 | 0.33 | 0.821 | 0.179 | ||||
| item25 | 0.521 | 0.712 | 0.288 | ||||
| item26 | 0.508 | 0.665 | 0.335 |
Sup4.3: CFA results
CFA check - performed only with items that are in the
final scale.
## lavaan 0.6.17 ended normally after 27 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 47
##
## Number of observations 503
##
## Model Test User Model:
##
## Test statistic 295.348
## Degrees of freedom 106
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## f1 =~
## fairness_scl_2 0.666 0.058 11.436 0.000
## fairness_scl_3 0.789 0.055 14.250 0.000
## fairness_scl_4 0.847 0.059 14.451 0.000
## f2 =~
## fairness_scl_5 0.925 0.056 16.574 0.000
## fairness_scl_6 1.226 0.056 22.037 0.000
## fairness_scl_7 1.204 0.056 21.529 0.000
## fairness_scl_8 0.843 0.061 13.736 0.000
## f3 =~
## fairness_scl_9 1.262 0.059 21.468 0.000
## fairnss_scl_10 1.187 0.057 20.969 0.000
## f4 =~
## fairnss_scl_11 1.311 0.061 21.523 0.000
## fairnss_scl_12 1.142 0.056 20.316 0.000
## fairnss_scl_13 1.278 0.062 20.665 0.000
## f5 =~
## fairnss_scl_14 1.351 0.065 20.764 0.000
## fairnss_scl_15 1.399 0.063 22.256 0.000
## fairnss_scl_16 0.978 0.070 13.929 0.000
## fairnss_scl_17 1.332 0.060 22.280 0.000
## fairnss_scl_18 1.334 0.062 21.530 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .fairness_scale_3 ~~
## .fairness_scl_5 0.116 0.045 2.604 0.009
## .fairness_scale_2 ~~
## .fairness_scl_4 0.105 0.058 1.803 0.071
## .fairness_scale_14 ~~
## .fairnss_scl_18 0.294 0.064 4.579 0.000
## f1 ~~
## f2 0.566 0.045 12.699 0.000
## f3 -0.556 0.047 -11.909 0.000
## f4 -0.515 0.047 -11.030 0.000
## f5 -0.052 0.056 -0.922 0.356
## f2 ~~
## f3 -0.814 0.026 -31.492 0.000
## f4 -0.432 0.044 -9.838 0.000
## f5 0.251 0.048 5.187 0.000
## f3 ~~
## f4 0.585 0.039 15.093 0.000
## f5 0.035 0.052 0.661 0.509
## f4 ~~
## f5 0.132 0.050 2.626 0.009
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .fairness_scl_2 0.774 0.070 11.068 0.000
## .fairness_scl_3 0.683 0.068 10.056 0.000
## .fairness_scl_4 0.628 0.076 8.248 0.000
## .fairness_scl_5 0.984 0.070 14.007 0.000
## .fairness_scl_6 0.643 0.060 10.750 0.000
## .fairness_scl_7 0.687 0.061 11.242 0.000
## .fairness_scl_8 1.339 0.091 14.741 0.000
## .fairness_scl_9 0.681 0.072 9.502 0.000
## .fairnss_scl_10 0.677 0.066 10.202 0.000
## .fairnss_scl_11 0.748 0.076 9.838 0.000
## .fairnss_scl_12 0.732 0.065 11.202 0.000
## .fairnss_scl_13 0.852 0.079 10.837 0.000
## .fairnss_scl_14 0.984 0.085 11.585 0.000
## .fairnss_scl_15 0.827 0.075 11.092 0.000
## .fairnss_scl_16 1.768 0.119 14.830 0.000
## .fairnss_scl_17 0.746 0.067 11.066 0.000
## .fairnss_scl_18 0.837 0.075 11.117 0.000
## f1 1.000
## f2 1.000
## f3 1.000
## f4 1.000
## f5 1.000Sup5: Analysis of study 2
Items used in S2
| Item no | Items S2 (German) | Corresponding factors |
|---|---|---|
| 01 | ist fair. | additional, optional item |
| 02 | ist gerecht. | additional, optional item |
| 03 | bewertet Situationen nach den gleichen Faktoren. | F1 (Perceived Consistency) |
| 04 | bewertet nach Kriterien, die für alle Menschen gleich sind. | F1 (Perceived Consistency) |
| 05 | ist über die Zeit hinweg konsistent. | F1 (Perceived Consistency) |
| 06 | liefert ähnliche Ergebnisse für ähnliche Personen. | discarded |
| 07 | bleibt über verschiedene Fälle hinweg zuverlässig. | discarded |
| 08 | ist so konzipiert, dass es für alle Menschen gleich ist. | F2 (Perceived Equity) |
| 09 | ist diskriminierend gegenüber bestimmten Gruppen. | F3 (Perceived Group Bias) |
| 10 | begünstigt bestimmte Gruppen. | F3 (Perceived Group Bias) |
| 11 | vermeidet die Aufrechterhaltung von Stereotypen. | F2 (Perceived Equity) |
| 12 | vermeidet die Aufrechterhaltung von Vorurteilen. | F2 (Perceived Equity) |
| 13 | gewährleistet Inklusivität in den Ergebnissen. | F2 (Perceived Equity) |
| 14 | kann beeinflusst werden. | F4 (Perceived Manipulability) |
| 15 | ist leicht zu manipulieren. | F4 (Perceived Manipulability) |
| 16 | ist anfällig für externe Faktoren. | discarded |
| 17 | ist anfällig für äußere Einflüsse. | F4 (Perceived Manipulability) |
| 18 | kann durch bewusste Anstrengungen verändert werden. | discarded |
| 19 | liefert klare Erklärungen für seine Entscheidungen. | F5 (Perceived (Explanatory) Transparency) |
| 20 | ermöglicht es den Entscheidungsprozess zu verstehen. | F5 (Perceived (Explanatory) Transparency) |
| 21 | macht den Entscheidungsprozess transparent. | F5 (Perceived (Explanatory) Transparency) |
| 22 | bietet Einblicke in die Schlüsselfaktoren, die jede Entscheidung beeinflussen. | F5 (Perceived (Explanatory) Transparency) |
| 23 | hilft den Nutzern zu verstehen, warum ein bestimmtes Ergebnis erzielt wurde. | F5 (Perceived (Explanatory) Transparency) |
| 24 | legt seine Grenzen offen. | discarded |
| 25 | kommuniziert, was es nicht tun kann. | discarded |
table 5.1 = Sup5.1: CFA results - original model
Result: unacceptable model fit
| Fit_indices | Optimal | Fit_values_original |
|---|---|---|
| RMSEA | ≤ 0.06 | 0.093 (0.09,0.1) |
| SRMR | < 0.08 | 0.116 |
| TLI | ≥ 0.95 | 0.845 |
| CFI | ≥ 0.95 | 0.865 |
| χ² | < 0.05 | χ²(220, N=495)=1156.27, p=0 |
| χ²/df ratio | < 3.00 | 5.26 |
## lavaan 0.6.17 ended normally after 33 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 56
##
## Number of observations 495
##
## Model Test User Model:
##
## Test statistic 1156.268
## Degrees of freedom 220
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## f1 =~
## frnss_scn1_s_3 1.238 0.056 21.931 0.000
## frnss_scn1_s_4 1.258 0.059 21.412 0.000
## frnss_scn1_s_5 1.207 0.055 21.795 0.000
## frnss_scn1_s_6 1.040 0.060 17.305 0.000
## frnss_scn1_s_7 1.141 0.055 20.620 0.000
## f2 =~
## frnss_scn1_s_8 1.277 0.062 20.709 0.000
## frnss_scn1_s_9 0.227 0.076 3.001 0.003
## frnss_scn1__10 0.020 0.075 0.267 0.789
## frnss_scn1__11 0.944 0.062 15.326 0.000
## frnss_scn1__12 1.174 0.062 19.048 0.000
## frnss_scn1__13 1.148 0.057 20.148 0.000
## f3 =~
## frnss_scn1__14 1.146 0.067 17.096 0.000
## frnss_scn1__15 1.179 0.067 17.578 0.000
## frnss_scn1__16 1.072 0.066 16.345 0.000
## frnss_scn1__17 1.171 0.067 17.402 0.000
## frnss_scn1__18 0.915 0.070 13.157 0.000
## f4 =~
## frnss_scn1__19 1.490 0.065 22.974 0.000
## frnss_scn1__20 1.400 0.057 24.365 0.000
## frnss_scn1__21 1.355 0.061 22.104 0.000
## frnss_scn1__22 1.283 0.061 20.977 0.000
## frnss_scn1__23 1.507 0.062 24.192 0.000
## f5 =~
## frnss_scn1__25 1.209 0.067 18.154 0.000
## frnss_scn1__26 1.077 0.065 16.480 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## f1 ~~
## f2 0.888 0.018 50.167 0.000
## f3 0.077 0.052 1.489 0.137
## f4 0.599 0.033 18.037 0.000
## f5 0.544 0.045 12.228 0.000
## f2 ~~
## f3 0.125 0.053 2.352 0.019
## f4 0.744 0.026 28.095 0.000
## f5 0.770 0.035 21.712 0.000
## f3 ~~
## f4 -0.041 0.051 -0.796 0.426
## f5 -0.196 0.057 -3.416 0.001
## f4 ~~
## f5 0.897 0.026 34.947 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .frnss_scn1_s_3 0.716 0.057 12.572 0.000
## .frnss_scn1_s_4 0.814 0.063 12.863 0.000
## .frnss_scn1_s_5 0.699 0.055 12.652 0.000
## .frnss_scn1_s_6 1.126 0.079 14.330 0.000
## .frnss_scn1_s_7 0.771 0.058 13.247 0.000
## .frnss_scn1_s_8 0.934 0.073 12.870 0.000
## .frnss_scn1_s_9 2.568 0.164 15.702 0.000
## .frnss_scn1__10 2.555 0.162 15.732 0.000
## .frnss_scn1__11 1.292 0.088 14.663 0.000
## .frnss_scn1__12 1.057 0.077 13.649 0.000
## .frnss_scn1__13 0.835 0.063 13.169 0.000
## .frnss_scn1__14 1.203 0.099 12.212 0.000
## .frnss_scn1__15 1.164 0.098 11.873 0.000
## .frnss_scn1__16 1.211 0.096 12.678 0.000
## .frnss_scn1__17 1.188 0.099 12.000 0.000
## .frnss_scn1__18 1.592 0.113 14.062 0.000
## .frnss_scn1__19 0.890 0.068 13.023 0.000
## .frnss_scn1__20 0.593 0.049 12.129 0.000
## .frnss_scn1__21 0.866 0.064 13.436 0.000
## .frnss_scn1__22 0.950 0.069 13.860 0.000
## .frnss_scn1__23 0.713 0.058 12.260 0.000
## .frnss_scn1__25 1.052 0.097 10.874 0.000
## .frnss_scn1__26 1.205 0.095 12.748 0.000
## f1 1.000
## f2 1.000
## f3 1.000
## f4 1.000
## f5 1.000Sup5.2: Sampling adequacy and suitability of the data
<br>Result: data are not considered to be multivariate normal
## $multivariateNormality
## Test HZ p value MVN
## 1 Henze-Zirkler 2.421199 0 NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling fairness_scen1_scale_1 13.0490 <0.001 NO
## 2 Anderson-Darling fairness_scen1_scale_3 14.3567 <0.001 NO
## 3 Anderson-Darling fairness_scen1_scale_4 11.4935 <0.001 NO
## 4 Anderson-Darling fairness_scen1_scale_5 13.2052 <0.001 NO
## 5 Anderson-Darling fairness_scen1_scale_6 14.3866 <0.001 NO
## 6 Anderson-Darling fairness_scen1_scale_7 14.0318 <0.001 NO
## 7 Anderson-Darling fairness_scen1_scale_8 11.9010 <0.001 NO
## 8 Anderson-Darling fairness_scen1_scale_9 10.6821 <0.001 NO
## 9 Anderson-Darling fairness_scen1_scale_10 9.0355 <0.001 NO
## 10 Anderson-Darling fairness_scen1_scale_11 12.8540 <0.001 NO
## 11 Anderson-Darling fairness_scen1_scale_12 11.5774 <0.001 NO
## 12 Anderson-Darling fairness_scen1_scale_13 14.8318 <0.001 NO
## 13 Anderson-Darling fairness_scen1_scale_14 10.1107 <0.001 NO
## 14 Anderson-Darling fairness_scen1_scale_15 9.6683 <0.001 NO
## 15 Anderson-Darling fairness_scen1_scale_16 10.6342 <0.001 NO
## 16 Anderson-Darling fairness_scen1_scale_17 9.1315 <0.001 NO
## 17 Anderson-Darling fairness_scen1_scale_18 11.2801 <0.001 NO
## 18 Anderson-Darling fairness_scen1_scale_19 12.3903 <0.001 NO
## 19 Anderson-Darling fairness_scen1_scale_20 12.3042 <0.001 NO
## 20 Anderson-Darling fairness_scen1_scale_21 10.4265 <0.001 NO
## 21 Anderson-Darling fairness_scen1_scale_22 11.3137 <0.001 NO
## 22 Anderson-Darling fairness_scen1_scale_23 10.7012 <0.001 NO
## 23 Anderson-Darling fairness_scen1_scale_25 11.4156 <0.001 NO
## 24 Anderson-Darling fairness_scen1_scale_26 13.3042 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th
## fairness_scen1_scale_1 495 4.218182 1.497931 4 1 7 4 5
## fairness_scen1_scale_3 495 4.795960 1.500602 5 1 7 4 6
## fairness_scen1_scale_4 495 4.622222 1.549687 5 1 7 4 6
## fairness_scen1_scale_5 495 4.569697 1.469904 5 1 7 4 6
## fairness_scen1_scale_6 495 4.751515 1.487081 5 1 7 4 6
## fairness_scen1_scale_7 495 4.438384 1.441063 4 1 7 4 5
## fairness_scen1_scale_8 495 4.408081 1.603114 5 1 7 4 5
## fairness_scen1_scale_9 495 4.381818 1.620239 4 1 7 3 5
## fairness_scen1_scale_10 495 4.149495 1.600188 4 1 7 3 5
## fairness_scen1_scale_11 495 4.022222 1.479109 4 1 7 3 5
## fairness_scen1_scale_12 495 4.317172 1.561949 4 1 7 4 5
## fairness_scen1_scale_13 495 4.139394 1.468551 4 1 7 3 5
## fairness_scen1_scale_14 495 3.612121 1.587863 3 1 7 3 5
## fairness_scen1_scale_15 495 3.727273 1.599710 4 1 7 3 5
## fairness_scen1_scale_16 495 3.634343 1.538189 4 1 7 3 4
## fairness_scen1_scale_17 495 3.826263 1.601529 4 1 7 3 5
## fairness_scen1_scale_18 495 3.553535 1.560086 3 1 7 3 4
## fairness_scen1_scale_19 495 3.896970 1.765473 4 1 7 3 5
## fairness_scen1_scale_20 495 3.876768 1.599268 4 1 7 3 5
## fairness_scen1_scale_21 495 4.022222 1.644987 4 1 7 3 5
## fairness_scen1_scale_22 495 3.882828 1.612956 4 1 7 3 5
## fairness_scen1_scale_23 495 3.836364 1.729563 4 1 7 3 5
## fairness_scen1_scale_25 495 4.026263 1.587310 4 1 7 3 5
## fairness_scen1_scale_26 495 3.802020 1.539361 4 1 7 3 5
## Skew Kurtosis
## fairness_scen1_scale_1 -0.28409972 -0.11461380
## fairness_scen1_scale_3 -0.71616073 0.31184900
## fairness_scen1_scale_4 -0.50362347 -0.07265981
## fairness_scen1_scale_5 -0.48961821 0.17267692
## fairness_scen1_scale_6 -0.69850284 0.34870004
## fairness_scen1_scale_7 -0.47651467 0.12811735
## fairness_scen1_scale_8 -0.46479654 -0.29212561
## fairness_scen1_scale_9 -0.15009724 -0.46409357
## fairness_scen1_scale_10 -0.01625011 -0.55670873
## fairness_scen1_scale_11 -0.26661135 -0.27516005
## fairness_scen1_scale_12 -0.39313604 -0.29578129
## fairness_scen1_scale_13 -0.33287767 0.02027805
## fairness_scen1_scale_14 0.33719376 -0.35812873
## fairness_scen1_scale_15 0.23853511 -0.50456816
## fairness_scen1_scale_16 0.31493572 -0.27961058
## fairness_scen1_scale_17 0.18344317 -0.60005922
## fairness_scen1_scale_18 0.38597119 -0.20523981
## fairness_scen1_scale_19 -0.22487665 -0.89258328
## fairness_scen1_scale_20 -0.26125253 -0.65571733
## fairness_scen1_scale_21 -0.25330090 -0.63208501
## fairness_scen1_scale_22 -0.15956054 -0.55410668
## fairness_scen1_scale_23 -0.13876946 -0.84339104
## fairness_scen1_scale_25 -0.24300814 -0.48136380
## fairness_scen1_scale_26 -0.18215044 -0.41195094## $multivariateNormality
## Test HZ p value MVN
## 1 Henze-Zirkler 2.421199 0 NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling fairness_scen1_scale_1 13.0490 <0.001 NO
## 2 Anderson-Darling fairness_scen1_scale_3 14.3567 <0.001 NO
## 3 Anderson-Darling fairness_scen1_scale_4 11.4935 <0.001 NO
## 4 Anderson-Darling fairness_scen1_scale_5 13.2052 <0.001 NO
## 5 Anderson-Darling fairness_scen1_scale_6 14.3866 <0.001 NO
## 6 Anderson-Darling fairness_scen1_scale_7 14.0318 <0.001 NO
## 7 Anderson-Darling fairness_scen1_scale_8 11.9010 <0.001 NO
## 8 Anderson-Darling fairness_scen1_scale_9 10.6821 <0.001 NO
## 9 Anderson-Darling fairness_scen1_scale_10 9.0355 <0.001 NO
## 10 Anderson-Darling fairness_scen1_scale_11 12.8540 <0.001 NO
## 11 Anderson-Darling fairness_scen1_scale_12 11.5774 <0.001 NO
## 12 Anderson-Darling fairness_scen1_scale_13 14.8318 <0.001 NO
## 13 Anderson-Darling fairness_scen1_scale_14 10.1107 <0.001 NO
## 14 Anderson-Darling fairness_scen1_scale_15 9.6683 <0.001 NO
## 15 Anderson-Darling fairness_scen1_scale_16 10.6342 <0.001 NO
## 16 Anderson-Darling fairness_scen1_scale_17 9.1315 <0.001 NO
## 17 Anderson-Darling fairness_scen1_scale_18 11.2801 <0.001 NO
## 18 Anderson-Darling fairness_scen1_scale_19 12.3903 <0.001 NO
## 19 Anderson-Darling fairness_scen1_scale_20 12.3042 <0.001 NO
## 20 Anderson-Darling fairness_scen1_scale_21 10.4265 <0.001 NO
## 21 Anderson-Darling fairness_scen1_scale_22 11.3137 <0.001 NO
## 22 Anderson-Darling fairness_scen1_scale_23 10.7012 <0.001 NO
## 23 Anderson-Darling fairness_scen1_scale_25 11.4156 <0.001 NO
## 24 Anderson-Darling fairness_scen1_scale_26 13.3042 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th
## fairness_scen1_scale_1 495 4.218182 1.497931 4 1 7 4 5
## fairness_scen1_scale_3 495 4.795960 1.500602 5 1 7 4 6
## fairness_scen1_scale_4 495 4.622222 1.549687 5 1 7 4 6
## fairness_scen1_scale_5 495 4.569697 1.469904 5 1 7 4 6
## fairness_scen1_scale_6 495 4.751515 1.487081 5 1 7 4 6
## fairness_scen1_scale_7 495 4.438384 1.441063 4 1 7 4 5
## fairness_scen1_scale_8 495 4.408081 1.603114 5 1 7 4 5
## fairness_scen1_scale_9 495 4.381818 1.620239 4 1 7 3 5
## fairness_scen1_scale_10 495 4.149495 1.600188 4 1 7 3 5
## fairness_scen1_scale_11 495 4.022222 1.479109 4 1 7 3 5
## fairness_scen1_scale_12 495 4.317172 1.561949 4 1 7 4 5
## fairness_scen1_scale_13 495 4.139394 1.468551 4 1 7 3 5
## fairness_scen1_scale_14 495 3.612121 1.587863 3 1 7 3 5
## fairness_scen1_scale_15 495 3.727273 1.599710 4 1 7 3 5
## fairness_scen1_scale_16 495 3.634343 1.538189 4 1 7 3 4
## fairness_scen1_scale_17 495 3.826263 1.601529 4 1 7 3 5
## fairness_scen1_scale_18 495 3.553535 1.560086 3 1 7 3 4
## fairness_scen1_scale_19 495 3.896970 1.765473 4 1 7 3 5
## fairness_scen1_scale_20 495 3.876768 1.599268 4 1 7 3 5
## fairness_scen1_scale_21 495 4.022222 1.644987 4 1 7 3 5
## fairness_scen1_scale_22 495 3.882828 1.612956 4 1 7 3 5
## fairness_scen1_scale_23 495 3.836364 1.729563 4 1 7 3 5
## fairness_scen1_scale_25 495 4.026263 1.587310 4 1 7 3 5
## fairness_scen1_scale_26 495 3.802020 1.539361 4 1 7 3 5
## Skew Kurtosis
## fairness_scen1_scale_1 -0.28409972 -0.11461380
## fairness_scen1_scale_3 -0.71616073 0.31184900
## fairness_scen1_scale_4 -0.50362347 -0.07265981
## fairness_scen1_scale_5 -0.48961821 0.17267692
## fairness_scen1_scale_6 -0.69850284 0.34870004
## fairness_scen1_scale_7 -0.47651467 0.12811735
## fairness_scen1_scale_8 -0.46479654 -0.29212561
## fairness_scen1_scale_9 -0.15009724 -0.46409357
## fairness_scen1_scale_10 -0.01625011 -0.55670873
## fairness_scen1_scale_11 -0.26661135 -0.27516005
## fairness_scen1_scale_12 -0.39313604 -0.29578129
## fairness_scen1_scale_13 -0.33287767 0.02027805
## fairness_scen1_scale_14 0.33719376 -0.35812873
## fairness_scen1_scale_15 0.23853511 -0.50456816
## fairness_scen1_scale_16 0.31493572 -0.27961058
## fairness_scen1_scale_17 0.18344317 -0.60005922
## fairness_scen1_scale_18 0.38597119 -0.20523981
## fairness_scen1_scale_19 -0.22487665 -0.89258328
## fairness_scen1_scale_20 -0.26125253 -0.65571733
## fairness_scen1_scale_21 -0.25330090 -0.63208501
## fairness_scen1_scale_22 -0.15956054 -0.55410668
## fairness_scen1_scale_23 -0.13876946 -0.84339104
## fairness_scen1_scale_25 -0.24300814 -0.48136380
## fairness_scen1_scale_26 -0.18215044 -0.41195094Sup5.3: Reliability of the items using Cronbach’s alpha and McDonald’s omega
<br>Result: items that were removed were: 6,7, 16,18, 22, 25,26
Note: f5 had only 2 items -> omega could not be
computed.
#for f1
f1_loadings## f1 f2 f3 f4 f5
## fairness_scen1_scale_3 1.237521 0 0 0 0
## fairness_scen1_scale_4 1.258134 0 0 0 0
## fairness_scen1_scale_5 1.207299 0 0 0 0
## fairness_scen1_scale_6 1.039711 0 0 0 0
## fairness_scen1_scale_7 1.140884 0 0 0 0f1_alpha## raw_alpha std.alpha G6(smc) average_r S/N alpha se
## fairness_scen1_scale_3 0.86 0.86 0.83 0.61 6.15 0.01
## fairness_scen1_scale_4 0.87 0.87 0.84 0.62 6.63 0.01
## fairness_scen1_scale_5 0.86 0.86 0.82 0.60 6.13 0.01
## fairness_scen1_scale_6 0.88 0.89 0.86 0.66 7.71 0.01
## fairness_scen1_scale_7 0.87 0.87 0.84 0.63 6.81 0.01
## var.r med.r
## fairness_scen1_scale_3 0 0.61
## fairness_scen1_scale_4 0 0.62
## fairness_scen1_scale_5 0 0.62
## fairness_scen1_scale_6 0 0.65
## fairness_scen1_scale_7 0 0.62f1_omega## [1] 0.91#for f2
f2_loadings## f1 f2 f3 f4 f5
## fairness_scen1_scale_8 0 1.27688743 0 0 0
## fairness_scen1_scale_9 0 0.22728960 0 0 0
## fairness_scen1_scale_10 0 0.02010091 0 0 0
## fairness_scen1_scale_11 0 0.94426223 0 0 0
## fairness_scen1_scale_12 0 1.17367840 0 0 0
## fairness_scen1_scale_13 0 1.14782757 0 0 0f2_alpha## raw_alpha std.alpha G6(smc) average_r S/N alpha se
## fairness_scen1_scale_8 0.60 0.61 0.70 0.24 1.55 0.03
## fairness_scen1_scale_9 0.71 0.71 0.74 0.33 2.49 0.02
## fairness_scen1_scale_10 0.75 0.75 0.75 0.38 3.03 0.02
## fairness_scen1_scale_11 0.68 0.68 0.75 0.30 2.12 0.02
## fairness_scen1_scale_12 0.63 0.63 0.71 0.25 1.69 0.03
## fairness_scen1_scale_13 0.64 0.64 0.72 0.26 1.79 0.03
## var.r med.r
## fairness_scen1_scale_8 0.09 0.12
## fairness_scen1_scale_9 0.09 0.51
## fairness_scen1_scale_10 0.06 0.51
## fairness_scen1_scale_11 0.07 0.16
## fairness_scen1_scale_12 0.08 0.16
## fairness_scen1_scale_13 0.08 0.16f2_omega## [1] 0.78#for f3
f3_loadings## f1 f2 f3 f4 f5
## fairness_scen1_scale_14 0 0 1.1458221 0 0
## fairness_scen1_scale_15 0 0 1.1790169 0 0
## fairness_scen1_scale_16 0 0 1.0723684 0 0
## fairness_scen1_scale_17 0 0 1.1714067 0 0
## fairness_scen1_scale_18 0 0 0.9145908 0 0f3_alpha## raw_alpha std.alpha G6(smc) average_r S/N alpha se
## fairness_scen1_scale_14 0.78 0.78 0.73 0.47 3.59 0.02
## fairness_scen1_scale_15 0.78 0.78 0.73 0.47 3.60 0.02
## fairness_scen1_scale_16 0.79 0.79 0.74 0.48 3.68 0.02
## fairness_scen1_scale_17 0.78 0.78 0.74 0.47 3.53 0.02
## fairness_scen1_scale_18 0.81 0.81 0.77 0.52 4.36 0.01
## var.r med.r
## fairness_scen1_scale_14 0.00 0.48
## fairness_scen1_scale_15 0.00 0.45
## fairness_scen1_scale_16 0.01 0.48
## fairness_scen1_scale_17 0.01 0.45
## fairness_scen1_scale_18 0.00 0.51f3_omega## [1] 0.86#for f4
f4_loadings## f1 f2 f3 f4 f5
## fairness_scen1_scale_19 0 0 0 1.490115 0
## fairness_scen1_scale_20 0 0 0 1.399831 0
## fairness_scen1_scale_21 0 0 0 1.354562 0
## fairness_scen1_scale_22 0 0 0 1.283171 0
## fairness_scen1_scale_23 0 0 0 1.507332 0f4_alpha## raw_alpha std.alpha G6(smc) average_r S/N alpha se
## fairness_scen1_scale_19 0.91 0.91 0.88 0.71 9.69 0.01
## fairness_scen1_scale_20 0.90 0.90 0.87 0.69 9.03 0.01
## fairness_scen1_scale_21 0.91 0.91 0.89 0.72 10.35 0.01
## fairness_scen1_scale_22 0.91 0.92 0.89 0.73 10.79 0.01
## fairness_scen1_scale_23 0.90 0.90 0.87 0.69 8.98 0.01
## var.r med.r
## fairness_scen1_scale_19 0 0.71
## fairness_scen1_scale_20 0 0.69
## fairness_scen1_scale_21 0 0.72
## fairness_scen1_scale_22 0 0.74
## fairness_scen1_scale_23 0 0.68f4_omega## [1] 0.93#for f5
f5_loadings## f1 f2 f3 f4 f5
## fairness_scen1_scale_25 0 0 0 0 1.209368
## fairness_scen1_scale_26 0 0 0 0 1.076740f5_alpha## raw_alpha std.alpha G6(smc) average_r S/N alpha se
## fairness_scen1_scale_25 0.55 0.53 0.29 0.53 1.15 NA
## fairness_scen1_scale_26 0.52 0.53 0.29 0.53 1.15 NA
## var.r med.r
## fairness_scen1_scale_25 0 0.53
## fairness_scen1_scale_26 0 0.53Sup5.4: Modification indices and optimized CFA model
new model BEFORE modification indices have been
investigated:
cfa_model_S2_mod_before <- ’
f1 =~ fairness_scen1_scale_3 +
fairness_scen1_scale_4 +
fairness_scen1_scale_5
f2 =~
fairness_scen1_scale_8 +
fairness_scen1_scale_11 +
fairness_scen1_scale_12 +
fairness_scen1_scale_13
f3 =~
fairness_scen1_scale_9 +
fairness_scen1_scale_10
f4 =~
fairness_scen1_scale_14 +
fairness_scen1_scale_15 +
fairness_scen1_scale_17
f5 =~ fairness_scen1_scale_19 +
fairness_scen1_scale_20 +
fairness_scen1_scale_21 +
fairness_scen1_scale_23
’
Factor loadings:
## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 f1 =~ fairness_scen1_scale_21 45.586 0.422 0.422 0.257 0.257
## 2 f2 =~ fairness_scen1_scale_21 43.531 0.532 0.532 0.324 0.324
## 3 f5 =~ fairness_scen1_scale_13 32.788 0.492 0.492 0.336 0.336
## 4 f3 =~ fairness_scen1_scale_8 23.972 0.287 0.287 0.179 0.179
## 5 f3 =~ fairness_scen1_scale_21 22.722 0.243 0.243 0.148 0.148
## 6 f3 =~ fairness_scen1_scale_11 22.610 -0.289 -0.289 -0.195 -0.195
## 7 f5 =~ fairness_scen1_scale_8 20.996 -0.426 -0.426 -0.266 -0.266
## 8 f1 =~ fairness_scen1_scale_8 19.512 0.765 0.765 0.478 0.478
## 9 f2 =~ fairness_scen1_scale_15 19.243 0.285 0.285 0.178 0.178
## 10 f4 =~ fairness_scen1_scale_21 18.634 0.220 0.220 0.134 0.134
## 11 f1 =~ fairness_scen1_scale_23 17.918 -0.253 -0.253 -0.146 -0.146
## 12 f5 =~ fairness_scen1_scale_15 16.031 0.247 0.247 0.155 0.155
## 13 f1 =~ fairness_scen1_scale_15 15.907 0.260 0.260 0.162 0.162
## 14 f2 =~ fairness_scen1_scale_9 14.309 0.234 0.234 0.145 0.145
## 15 f2 =~ fairness_scen1_scale_10 14.309 -0.270 -0.270 -0.169 -0.169
## 16 f2 =~ fairness_scen1_scale_23 14.165 -0.291 -0.291 -0.168 -0.168
## 17 f1 =~ fairness_scen1_scale_13 14.046 -0.599 -0.599 -0.408 -0.408
## 18 f4 =~ fairness_scen1_scale_22 13.235 -0.192 -0.192 -0.119 -0.119
## 19 f4 =~ fairness_scen1_scale_11 13.049 -0.227 -0.227 -0.154 -0.154
## 20 f2 =~ fairness_scen1_scale_4 12.820 0.637 0.637 0.412 0.412
## 21 f5 =~ fairness_scen1_scale_10 12.616 -0.252 -0.252 -0.158 -0.158
## 22 f5 =~ fairness_scen1_scale_9 12.616 0.219 0.219 0.135 0.135
## 23 f4 =~ fairness_scen1_scale_8 11.400 0.205 0.205 0.128 0.128
## 24 f4 =~ fairness_scen1_scale_20 11.390 0.150 0.150 0.094 0.094
## 25 f2 =~ fairness_scen1_scale_19 10.638 -0.274 -0.274 -0.156 -0.156
## 26 f1 =~ fairness_scen1_scale_10 10.638 -0.236 -0.236 -0.147 -0.147
## 27 f1 =~ fairness_scen1_scale_9 10.638 0.205 0.205 0.126 0.126
## 28 f5 =~ fairness_scen1_scale_12 10.629 -0.305 -0.305 -0.195 -0.195
## 29 f2 =~ fairness_scen1_scale_3 10.053 -0.550 -0.550 -0.367 -0.367
## 30 f1 =~ fairness_scen1_scale_14 9.336 -0.197 -0.197 -0.124 -0.124
## 31 f3 =~ fairness_scen1_scale_17 8.854 0.322 0.322 0.201 0.201
## 32 f4 =~ fairness_scen1_scale_23 8.804 -0.144 -0.144 -0.083 -0.083
## 33 f1 =~ fairness_scen1_scale_11 8.133 -0.498 -0.498 -0.337 -0.337
## 34 f5 =~ fairness_scen1_scale_11 7.554 0.260 0.260 0.176 0.176
## 35 f3 =~ fairness_scen1_scale_22 7.382 -0.143 -0.143 -0.089 -0.089
## 36 f1 =~ fairness_scen1_scale_19 7.373 -0.177 -0.177 -0.100 -0.100
## 37 f3 =~ fairness_scen1_scale_15 7.334 -0.312 -0.312 -0.195 -0.195
## 38 f5 =~ fairness_scen1_scale_17 6.672 -0.162 -0.162 -0.101 -0.101
## 39 f2 =~ fairness_scen1_scale_14 6.670 -0.166 -0.166 -0.104 -0.104
## 40 f4 =~ fairness_scen1_scale_9 5.553 0.594 0.594 0.367 0.367
## 41 f4 =~ fairness_scen1_scale_10 5.553 -0.684 -0.684 -0.428 -0.428
## 42 f3 =~ fairness_scen1_scale_5 4.973 -0.116 -0.116 -0.079 -0.079
## 43 f3 =~ fairness_scen1_scale_19 4.961 -0.118 -0.118 -0.067 -0.067
## 44 f3 =~ fairness_scen1_scale_13 4.948 -0.121 -0.121 -0.082 -0.082
## 45 f2 =~ fairness_scen1_scale_17 4.690 -0.142 -0.142 -0.089 -0.089
## 46 f5 =~ fairness_scen1_scale_3 4.146 -0.131 -0.131 -0.088 -0.088
## 47 f3 =~ fairness_scen1_scale_20 3.811 0.087 0.087 0.054 0.054
## 48 f3 =~ fairness_scen1_scale_4 3.754 0.105 0.105 0.068 0.068
## 49 f3 =~ fairness_scen1_scale_23 3.704 -0.093 -0.093 -0.054 -0.054
## 50 f5 =~ fairness_scen1_scale_14 3.336 -0.111 -0.111 -0.070 -0.070
## 51 f4 =~ fairness_scen1_scale_19 2.088 -0.077 -0.077 -0.044 -0.044
## 52 f1 =~ fairness_scen1_scale_12 2.016 0.246 0.246 0.158 0.158
## 53 f5 =~ fairness_scen1_scale_4 1.522 0.082 0.082 0.053 0.053
## 54 f1 =~ fairness_scen1_scale_17 1.385 -0.078 -0.078 -0.049 -0.049
## 55 f2 =~ fairness_scen1_scale_20 1.134 0.076 0.076 0.047 0.047
## 56 f4 =~ fairness_scen1_scale_4 0.845 0.051 0.051 0.033 0.033
## 57 f4 =~ fairness_scen1_scale_13 0.789 -0.050 -0.050 -0.034 -0.034
## 58 f5 =~ fairness_scen1_scale_5 0.739 0.055 0.055 0.037 0.037
## 59 f3 =~ fairness_scen1_scale_12 0.476 0.041 0.041 0.026 0.026
## 60 f1 =~ fairness_scen1_scale_20 0.375 0.034 0.034 0.021 0.021
## 61 f4 =~ fairness_scen1_scale_5 0.372 -0.033 -0.033 -0.022 -0.022
## 62 f2 =~ fairness_scen1_scale_5 0.165 -0.068 -0.068 -0.046 -0.046
## 63 f1 =~ fairness_scen1_scale_22 0.121 0.022 0.022 0.014 0.014
## 64 f4 =~ fairness_scen1_scale_3 0.112 -0.018 -0.018 -0.012 -0.012
## 65 f3 =~ fairness_scen1_scale_3 0.033 0.010 0.010 0.006 0.006
## 66 f3 =~ fairness_scen1_scale_14 0.005 -0.008 -0.008 -0.005 -0.005
## 67 f2 =~ fairness_scen1_scale_22 0.003 -0.004 -0.004 -0.003 -0.003
## 68 f4 =~ fairness_scen1_scale_12 0.002 0.003 0.003 0.002 0.002
Item–item correlations:
## lhs op rhs mi epc sepc.lv
## 1 fairness_scen1_scale_3 ~~ fairness_scen1_scale_5 18.704 0.243 0.243
## 2 fairness_scen1_scale_10 ~~ fairness_scen1_scale_15 14.743 -0.279 -0.279
## 3 fairness_scen1_scale_4 ~~ fairness_scen1_scale_8 13.100 0.181 0.181
## 4 fairness_scen1_scale_11 ~~ fairness_scen1_scale_10 12.119 -0.217 -0.217
## 5 fairness_scen1_scale_5 ~~ fairness_scen1_scale_20 10.387 0.124 0.124
## 6 fairness_scen1_scale_4 ~~ fairness_scen1_scale_5 10.340 -0.185 -0.185
## 7 fairness_scen1_scale_19 ~~ fairness_scen1_scale_21 9.502 -0.159 -0.159
## 8 fairness_scen1_scale_19 ~~ fairness_scen1_scale_23 9.082 0.154 0.154
## 9 fairness_scen1_scale_8 ~~ fairness_scen1_scale_13 8.811 -0.163 -0.163
## 10 fairness_scen1_scale_8 ~~ fairness_scen1_scale_21 8.576 0.139 0.139
## 11 fairness_scen1_scale_5 ~~ fairness_scen1_scale_23 8.244 -0.120 -0.120
## 12 fairness_scen1_scale_4 ~~ fairness_scen1_scale_22 8.207 0.134 0.134
## 13 fairness_scen1_scale_5 ~~ fairness_scen1_scale_15 8.047 0.152 0.152
## 14 fairness_scen1_scale_8 ~~ fairness_scen1_scale_10 7.865 0.161 0.161
## 15 fairness_scen1_scale_9 ~~ fairness_scen1_scale_14 7.253 -0.196 -0.196
## 16 fairness_scen1_scale_11 ~~ fairness_scen1_scale_12 7.222 0.164 0.164
## 17 fairness_scen1_scale_15 ~~ fairness_scen1_scale_20 7.170 0.126 0.126
## 18 fairness_scen1_scale_13 ~~ fairness_scen1_scale_10 6.989 -0.142 -0.142
## 19 fairness_scen1_scale_9 ~~ fairness_scen1_scale_15 6.867 0.193 0.193
## 20 fairness_scen1_scale_4 ~~ fairness_scen1_scale_9 6.182 0.139 0.139
## 21 fairness_scen1_scale_13 ~~ fairness_scen1_scale_22 5.946 0.114 0.114
## 22 fairness_scen1_scale_4 ~~ fairness_scen1_scale_23 5.805 -0.103 -0.103
## 23 fairness_scen1_scale_12 ~~ fairness_scen1_scale_19 5.681 -0.125 -0.125
## 24 fairness_scen1_scale_3 ~~ fairness_scen1_scale_17 5.268 0.128 0.128
## 25 fairness_scen1_scale_5 ~~ fairness_scen1_scale_13 5.217 -0.104 -0.104
## 26 fairness_scen1_scale_13 ~~ fairness_scen1_scale_21 5.026 -0.101 -0.101
## 27 fairness_scen1_scale_11 ~~ fairness_scen1_scale_23 4.990 0.112 0.112
## 28 fairness_scen1_scale_10 ~~ fairness_scen1_scale_21 4.962 0.118 0.118
## 29 fairness_scen1_scale_10 ~~ fairness_scen1_scale_17 4.895 0.160 0.160
## 30 fairness_scen1_scale_5 ~~ fairness_scen1_scale_14 4.831 -0.119 -0.119
## 31 fairness_scen1_scale_4 ~~ fairness_scen1_scale_21 4.273 0.094 0.094
## 32 fairness_scen1_scale_14 ~~ fairness_scen1_scale_15 4.056 0.254 0.254
## 33 fairness_scen1_scale_3 ~~ fairness_scen1_scale_20 3.955 -0.074 -0.074
## 34 fairness_scen1_scale_10 ~~ fairness_scen1_scale_14 3.841 0.140 0.140
## 35 fairness_scen1_scale_13 ~~ fairness_scen1_scale_9 3.572 0.105 0.105
## 36 fairness_scen1_scale_3 ~~ fairness_scen1_scale_11 3.349 -0.095 -0.095
## 37 fairness_scen1_scale_8 ~~ fairness_scen1_scale_12 3.302 0.107 0.107
## 38 fairness_scen1_scale_3 ~~ fairness_scen1_scale_15 3.259 -0.095 -0.095
## 39 fairness_scen1_scale_13 ~~ fairness_scen1_scale_23 3.253 0.077 0.077
## 40 fairness_scen1_scale_17 ~~ fairness_scen1_scale_22 3.036 -0.105 -0.105
## 41 fairness_scen1_scale_8 ~~ fairness_scen1_scale_23 2.942 -0.077 -0.077
## 42 fairness_scen1_scale_11 ~~ fairness_scen1_scale_13 2.748 0.091 0.091
## 43 fairness_scen1_scale_5 ~~ fairness_scen1_scale_22 2.701 -0.076 -0.076
## 44 fairness_scen1_scale_13 ~~ fairness_scen1_scale_19 2.323 0.071 0.071
## 45 fairness_scen1_scale_12 ~~ fairness_scen1_scale_17 2.271 -0.097 -0.097
## 46 fairness_scen1_scale_5 ~~ fairness_scen1_scale_21 2.254 0.067 0.067
## 47 fairness_scen1_scale_9 ~~ fairness_scen1_scale_22 2.198 -0.086 -0.086
## 48 fairness_scen1_scale_10 ~~ fairness_scen1_scale_19 2.144 -0.081 -0.081
## 49 fairness_scen1_scale_4 ~~ fairness_scen1_scale_20 2.085 -0.056 -0.056
## 50 fairness_scen1_scale_11 ~~ fairness_scen1_scale_19 2.015 -0.079 -0.079
## 51 fairness_scen1_scale_5 ~~ fairness_scen1_scale_9 1.993 -0.077 -0.077
## 52 fairness_scen1_scale_11 ~~ fairness_scen1_scale_17 1.959 -0.095 -0.095
## 53 fairness_scen1_scale_13 ~~ fairness_scen1_scale_15 1.767 0.072 0.072
## 54 fairness_scen1_scale_3 ~~ fairness_scen1_scale_23 1.686 0.053 0.053
## 55 fairness_scen1_scale_17 ~~ fairness_scen1_scale_19 1.656 0.078 0.078
## 56 fairness_scen1_scale_8 ~~ fairness_scen1_scale_11 1.597 -0.074 -0.074
## 57 fairness_scen1_scale_10 ~~ fairness_scen1_scale_20 1.500 -0.056 -0.056
## 58 fairness_scen1_scale_3 ~~ fairness_scen1_scale_21 1.391 0.051 0.051
## 59 fairness_scen1_scale_15 ~~ fairness_scen1_scale_23 1.373 -0.060 -0.060
## 60 fairness_scen1_scale_8 ~~ fairness_scen1_scale_19 1.331 -0.057 -0.057
## 61 fairness_scen1_scale_3 ~~ fairness_scen1_scale_10 1.274 0.058 0.058
## 62 fairness_scen1_scale_15 ~~ fairness_scen1_scale_22 1.252 -0.063 -0.063
## 63 fairness_scen1_scale_3 ~~ fairness_scen1_scale_4 1.243 -0.068 -0.068
## 64 fairness_scen1_scale_15 ~~ fairness_scen1_scale_17 1.222 -0.122 -0.122
## 65 fairness_scen1_scale_3 ~~ fairness_scen1_scale_12 1.212 -0.055 -0.055
## 66 fairness_scen1_scale_20 ~~ fairness_scen1_scale_23 1.196 -0.050 -0.050
## 67 fairness_scen1_scale_3 ~~ fairness_scen1_scale_9 1.164 -0.058 -0.058
## 68 fairness_scen1_scale_9 ~~ fairness_scen1_scale_23 1.151 0.057 0.057
## 69 fairness_scen1_scale_9 ~~ fairness_scen1_scale_20 1.040 0.049 0.049
## 70 fairness_scen1_scale_5 ~~ fairness_scen1_scale_10 1.032 -0.053 -0.053
## 71 fairness_scen1_scale_12 ~~ fairness_scen1_scale_14 1.013 0.062 0.062
## 72 fairness_scen1_scale_20 ~~ fairness_scen1_scale_22 0.955 -0.044 -0.044
## 73 fairness_scen1_scale_5 ~~ fairness_scen1_scale_12 0.862 0.047 0.047
## 74 fairness_scen1_scale_8 ~~ fairness_scen1_scale_22 0.824 -0.045 -0.045
## 75 fairness_scen1_scale_19 ~~ fairness_scen1_scale_20 0.819 0.043 0.043
## 76 fairness_scen1_scale_12 ~~ fairness_scen1_scale_13 0.747 -0.047 -0.047
## 77 fairness_scen1_scale_15 ~~ fairness_scen1_scale_21 0.719 0.046 0.046
## 78 fairness_scen1_scale_12 ~~ fairness_scen1_scale_22 0.688 -0.043 -0.043
## 79 fairness_scen1_scale_14 ~~ fairness_scen1_scale_17 0.659 -0.085 -0.085
## 80 fairness_scen1_scale_8 ~~ fairness_scen1_scale_17 0.629 -0.048 -0.048
## 81 fairness_scen1_scale_8 ~~ fairness_scen1_scale_20 0.627 -0.033 -0.033
## 82 fairness_scen1_scale_20 ~~ fairness_scen1_scale_21 0.621 0.035 0.035
## 83 fairness_scen1_scale_17 ~~ fairness_scen1_scale_23 0.618 -0.043 -0.043
## 84 fairness_scen1_scale_4 ~~ fairness_scen1_scale_17 0.602 -0.045 -0.045
## 85 fairness_scen1_scale_8 ~~ fairness_scen1_scale_14 0.565 0.044 0.044
## 86 fairness_scen1_scale_12 ~~ fairness_scen1_scale_20 0.516 0.031 0.031
## 87 fairness_scen1_scale_19 ~~ fairness_scen1_scale_22 0.481 0.036 0.036
## 88 fairness_scen1_scale_5 ~~ fairness_scen1_scale_17 0.432 0.038 0.038
## 89 fairness_scen1_scale_10 ~~ fairness_scen1_scale_22 0.431 0.036 0.036
## 90 fairness_scen1_scale_10 ~~ fairness_scen1_scale_23 0.396 -0.031 -0.031
## 91 fairness_scen1_scale_17 ~~ fairness_scen1_scale_21 0.379 0.036 0.036
## 92 fairness_scen1_scale_12 ~~ fairness_scen1_scale_10 0.372 0.036 0.036
## 93 fairness_scen1_scale_3 ~~ fairness_scen1_scale_22 0.365 -0.027 -0.027
## 94 fairness_scen1_scale_13 ~~ fairness_scen1_scale_20 0.365 0.024 0.024
## 95 fairness_scen1_scale_11 ~~ fairness_scen1_scale_9 0.361 0.039 0.039
## 96 fairness_scen1_scale_5 ~~ fairness_scen1_scale_11 0.340 -0.031 -0.031
## 97 fairness_scen1_scale_15 ~~ fairness_scen1_scale_19 0.325 -0.032 -0.032
## 98 fairness_scen1_scale_13 ~~ fairness_scen1_scale_14 0.317 -0.031 -0.031
## 99 fairness_scen1_scale_11 ~~ fairness_scen1_scale_21 0.310 -0.030 -0.030
## 100 fairness_scen1_scale_3 ~~ fairness_scen1_scale_19 0.297 -0.025 -0.025
## 101 fairness_scen1_scale_4 ~~ fairness_scen1_scale_11 0.295 -0.029 -0.029
## 102 fairness_scen1_scale_12 ~~ fairness_scen1_scale_23 0.288 -0.026 -0.026
## 103 fairness_scen1_scale_14 ~~ fairness_scen1_scale_20 0.283 0.025 0.025
## 104 fairness_scen1_scale_12 ~~ fairness_scen1_scale_9 0.273 -0.032 -0.032
## 105 fairness_scen1_scale_3 ~~ fairness_scen1_scale_14 0.252 -0.027 -0.027
## 106 fairness_scen1_scale_11 ~~ fairness_scen1_scale_22 0.189 -0.024 -0.024
## 107 fairness_scen1_scale_14 ~~ fairness_scen1_scale_22 0.188 -0.025 -0.025
## 108 fairness_scen1_scale_11 ~~ fairness_scen1_scale_20 0.176 0.019 0.019
## 109 fairness_scen1_scale_14 ~~ fairness_scen1_scale_23 0.155 -0.020 -0.020
## 110 fairness_scen1_scale_4 ~~ fairness_scen1_scale_13 0.109 0.015 0.015
## 111 fairness_scen1_scale_11 ~~ fairness_scen1_scale_15 0.106 0.021 0.021
## 112 fairness_scen1_scale_14 ~~ fairness_scen1_scale_21 0.091 -0.017 -0.017
## 113 fairness_scen1_scale_5 ~~ fairness_scen1_scale_19 0.088 0.014 0.014
## 114 fairness_scen1_scale_12 ~~ fairness_scen1_scale_15 0.087 -0.018 -0.018
## 115 fairness_scen1_scale_21 ~~ fairness_scen1_scale_23 0.071 -0.013 -0.013
## 116 fairness_scen1_scale_4 ~~ fairness_scen1_scale_10 0.061 -0.013 -0.013
## 117 fairness_scen1_scale_21 ~~ fairness_scen1_scale_22 0.057 -0.012 -0.012
## 118 fairness_scen1_scale_4 ~~ fairness_scen1_scale_12 0.050 0.012 0.012
## 119 fairness_scen1_scale_8 ~~ fairness_scen1_scale_15 0.048 0.013 0.013
## 120 fairness_scen1_scale_4 ~~ fairness_scen1_scale_14 0.026 -0.009 -0.009
## 121 fairness_scen1_scale_5 ~~ fairness_scen1_scale_8 0.012 0.005 0.005
## 122 fairness_scen1_scale_3 ~~ fairness_scen1_scale_13 0.008 0.004 0.004
## 123 fairness_scen1_scale_9 ~~ fairness_scen1_scale_21 0.007 -0.005 -0.005
## 124 fairness_scen1_scale_8 ~~ fairness_scen1_scale_9 0.004 0.004 0.004
## 125 fairness_scen1_scale_17 ~~ fairness_scen1_scale_20 0.004 -0.003 -0.003
## 126 fairness_scen1_scale_9 ~~ fairness_scen1_scale_19 0.004 0.004 0.004
## 127 fairness_scen1_scale_11 ~~ fairness_scen1_scale_14 0.004 0.004 0.004
## 128 fairness_scen1_scale_3 ~~ fairness_scen1_scale_8 0.003 -0.003 -0.003
## 129 fairness_scen1_scale_9 ~~ fairness_scen1_scale_17 0.002 -0.003 -0.003
## 130 fairness_scen1_scale_14 ~~ fairness_scen1_scale_19 0.002 -0.002 -0.002
## 131 fairness_scen1_scale_13 ~~ fairness_scen1_scale_17 0.001 -0.002 -0.002
## 132 fairness_scen1_scale_12 ~~ fairness_scen1_scale_21 0.001 0.001 0.001
## 133 fairness_scen1_scale_4 ~~ fairness_scen1_scale_15 0.000 -0.001 -0.001
## 134 fairness_scen1_scale_22 ~~ fairness_scen1_scale_23 0.000 -0.001 -0.001
## 135 fairness_scen1_scale_4 ~~ fairness_scen1_scale_19 0.000 0.000 0.000
## sepc.all sepc.nox
## 1 0.330 0.330
## 2 -0.337 -0.337
## 3 0.216 0.216
## 4 -0.234 -0.234
## 5 0.184 0.184
## 6 -0.239 -0.239
## 7 -0.178 -0.178
## 8 0.193 0.193
## 9 -0.187 -0.187
## 10 0.157 0.157
## 11 -0.163 -0.163
## 12 0.156 0.156
## 13 0.170 0.170
## 14 0.206 0.206
## 15 -0.170 -0.170
## 16 0.138 0.138
## 17 0.163 0.163
## 18 -0.190 -0.190
## 19 0.174 0.174
## 20 0.145 0.145
## 21 0.127 0.127
## 22 -0.140 -0.140
## 23 -0.125 -0.125
## 24 0.131 0.131
## 25 -0.129 -0.129
## 26 -0.118 -0.118
## 27 0.118 0.118
## 28 0.155 0.155
## 29 0.167 0.167
## 30 -0.128 -0.128
## 31 0.115 0.115
## 32 0.238 0.238
## 33 -0.118 -0.118
## 34 0.163 0.163
## 35 0.105 0.105
## 36 -0.100 -0.100
## 37 0.107 0.107
## 38 -0.112 -0.112
## 39 0.100 0.100
## 40 -0.091 -0.091
## 41 -0.097 -0.097
## 42 0.088 0.088
## 43 -0.087 -0.087
## 44 0.081 0.081
## 45 -0.079 -0.079
## 46 0.081 0.081
## 47 -0.080 -0.080
## 48 -0.103 -0.103
## 49 -0.085 -0.085
## 50 -0.072 -0.072
## 51 -0.080 -0.080
## 52 -0.071 -0.071
## 53 0.078 0.078
## 54 0.076 0.076
## 55 0.069 0.069
## 56 -0.069 -0.069
## 57 -0.090 -0.090
## 58 0.066 0.066
## 59 -0.071 -0.071
## 60 -0.063 -0.063
## 61 0.086 0.086
## 62 -0.063 -0.063
## 63 -0.094 -0.094
## 64 -0.102 -0.102
## 65 -0.063 -0.063
## 66 -0.078 -0.078
## 67 -0.063 -0.063
## 68 0.062 0.062
## 69 0.059 0.059
## 70 -0.074 -0.074
## 71 0.056 0.056
## 72 -0.059 -0.059
## 73 0.051 0.051
## 74 -0.048 -0.048
## 75 0.059 0.059
## 76 -0.049 -0.049
## 77 0.049 0.049
## 78 -0.042 -0.042
## 79 -0.069 -0.069
## 80 -0.043 -0.043
## 81 -0.045 -0.045
## 82 0.050 0.050
## 83 -0.044 -0.044
## 84 -0.044 -0.044
## 85 0.043 0.043
## 86 0.039 0.039
## 87 0.039 0.039
## 88 0.036 0.036
## 89 0.045 0.045
## 90 -0.046 -0.046
## 91 0.033 0.033
## 92 0.043 0.043
## 93 -0.033 -0.033
## 94 0.034 0.034
## 95 0.032 0.032
## 96 -0.031 -0.031
## 97 -0.033 -0.033
## 98 -0.032 -0.032
## 99 -0.028 -0.028
## 100 -0.031 -0.031
## 101 -0.029 -0.029
## 102 -0.029 -0.029
## 103 0.031 0.031
## 104 -0.028 -0.028
## 105 -0.030 -0.030
## 106 -0.022 -0.022
## 107 -0.024 -0.024
## 108 0.022 0.022
## 109 -0.023 -0.023
## 110 0.019 0.019
## 111 0.018 0.018
## 112 -0.017 -0.017
## 113 0.016 0.016
## 114 -0.017 -0.017
## 115 -0.017 -0.017
## 116 -0.019 -0.019
## 117 -0.013 -0.013
## 118 0.013 0.013
## 119 0.013 0.013
## 120 -0.010 -0.010
## 121 0.006 0.006
## 122 0.005 0.005
## 123 -0.005 -0.005
## 124 0.004 0.004
## 125 -0.004 -0.004
## 126 0.003 0.003
## 127 0.003 0.003
## 128 -0.004 -0.004
## 129 -0.003 -0.003
## 130 -0.002 -0.002
## 131 -0.002 -0.002
## 132 0.001 0.001
## 133 -0.001 -0.001
## 134 -0.001 -0.001
## 135 -0.001 -0.001Rational
lhs op rhs mod epc sepc.lv sepc.all sepc.nox
1 fairness_scen1_scale_3 ~~ fairness_scen1_scale_5 18.704 0.243 0.243 0.330 0.330
2 fairness_scen1_scale_10 ~~ fairness_scen1_scale_15 14.743 -0.279 -0.279 -0.337 -0.337
3 fairness_scen1_scale_4 ~~ fairness_scen1_scale_8 13.100 0.181 0.181 0.216 0.216
4 fairness_scen1_scale_11 ~~ fairness_scen1_scale_10 12.119 -0.217 -0.217 -0.234 -0.234
5 fairness_scen1_scale_5 ~~ fairness_scen1_scale_20 10.387 0.124 0.124 0.184 0.184
6 fairness_scen1_scale_4 ~~ fairness_scen1_scale_5 10.340 -0.185 -0.185 -0.239 -0.239
7 fairness_scen1_scale_19 ~~ fairness_scen1_scale_21 9.502 -0.159 -0.159 -0.178 -0.178
8 fairness_scen1_scale_19 ~~ fairness_scen1_scale_23 9.082 0.154 0.154 0.193 0.193
9 fairness_scen1_scale_8 ~~ fairness_scen1_scale_13 8.811 -0.163 -0.163 -0.187 -0.187we used mod values as an initial guide (Kline, 2016), looking at
indices > 10 as a possible threshold. However, our final decisions
were not based solely on these numerical values. Instead, we correlated
residuals only when there was clear semantic and conceptual overlap, and
we sought to minimize multiple correlations involving the same item to
avoid overfitting and ensure parsimony. (also see paper results
S2).
fairness_scen1_scale_3 ~~ fairness_scen1_scale_5: mod: 18.7
Participants may view these two statements as tapping into a similar
idea of consistent/stable underlying logic, hence shared residual
variance.
fairness_scen1_scale_4 ~~ fairness_scen1_scale_8: mod: 13.1
both
address a uniform application of rules for all individuals. This
conceptual overlap (i.e., “the same for everyone”) can produce shared
residual variance.
fairness_scen1_scale_19 ~~ fairness_scen1_scale_23: mod: 9.1
direct semantic similarity justifies correlating these two
residuals
Rest:
fairness_scen1_scale_10 ~~ fairness_scen1_scale_15: mod = 14.7
Although the mod is >10 items address different conceptual domains
(i.e., favoring certain groups versus susceptibility to manipulation).
-> no compelling theoretical rationale / no strong semantic
overlap that would justify residual correlation.
fairness_scen1_scale_11 ~~ fairness_scen1_scale_10: mod = 12.1
Both items concern group-related outcomes (stereotypes vs. favoring
certain groups), but they capture sufficiently distinct aspects—one
focuses on stereotype prevention, the other on explicit group
favoritism.
-> no compelling theoretical rationale / no strong
semantic overlap that would justify residual correlation.
fairness_scen1_scale_5 ~~ fairness_scen1_scale_20: mod = 10.4
These items measure disparate facets (consistency vs. process
understanding).
-> no compelling theoretical rationale / no
strong semantic overlap that would justify residual
correlation.
fairness_scen1_scale_4 ~~ fairness_scen1_scale_5: mod = 10.3
Both
reference consistency, yet item #4 emphasizes the sameness of criteria
for all people, whereas item #5 focuses on consistency over time. We
opted for correlating #3 and #5 instead, to avoid adding multiple
correlations within the same factor and to maintain model
parsimony.
fairness_scen1_scale_19 ~~ fairness_scen1_scale_21: mod = 9.5
Although both deal with transparency, item #21 is broader (“makes the
decision process transparent”), while item #19 highlights “clear
explanations.” We identified a more direct semantic connection between
#19 and #23, and limited extra correlations to avoid
overfitting.
fairness_scen1_scale_8 ~~ fairness_scen1_scale_13: mod = 8.8
Both
items refer to equity and inclusivity, but the overlap is less
pronounced than in the chosen pairs (e.g., #4~~#8). Moreover, the mod is
below our initial threshold, and adding multiple residual correlations
within the same factor risks reducing model parsimony.
new model AFTER modification indices have been
investigated:
cfa_model_S2_mod <- ’
f1 =~ fairness_scen1_scale_3 +
fairness_scen1_scale_4 +
fairness_scen1_scale_5
f2 =~
fairness_scen1_scale_8 +
fairness_scen1_scale_11 +
fairness_scen1_scale_12 +
fairness_scen1_scale_13
f3 =~
fairness_scen1_scale_9 +
fairness_scen1_scale_10
f4 =~
fairness_scen1_scale_14 +
fairness_scen1_scale_15 +
fairness_scen1_scale_17
f5 =~ fairness_scen1_scale_19 +
fairness_scen1_scale_20 +
fairness_scen1_scale_21 +
fairness_scen1_scale_23
.#Allowing specific item residuals to correlate:
fairness_scen1_scale_4 ~~ fairness_scen1_scale_8
fairness_scen1_scale_3 ~~ fairness_scen1_scale_5
fairness_scen1_scale_19 ~~ fairness_scen1_scale_23
’
Factor
loadings:
## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 f3 =~ fairness_scen1_scale_10 135.194 0.923 0.923 0.577 0.577
## 2 f3 =~ fairness_scen1_scale_9 92.386 0.766 0.766 0.473 0.473
## 3 f2 =~ fairness_scen1_scale_18 73.348 -0.543 -0.543 -0.348 -0.348
## 4 f5 =~ fairness_scen1_scale_10 65.743 -1.059 -1.059 -0.663 -0.663
## 5 f1 =~ fairness_scen1_scale_18 64.192 -0.505 -0.505 -0.324 -0.324
## 6 f5 =~ fairness_scen1_scale_18 60.434 -0.509 -0.509 -0.327 -0.327
## 7 f4 =~ fairness_scen1_scale_18 55.680 -0.463 -0.463 -0.297 -0.297
## 8 f5 =~ fairness_scen1_scale_9 46.220 -0.892 -0.892 -0.551 -0.551
## 9 f1 =~ fairness_scen1_scale_21 44.973 0.423 0.423 0.257 0.257
## 10 f2 =~ fairness_scen1_scale_15 42.472 0.383 0.383 0.240 0.240
## 11 f2 =~ fairness_scen1_scale_21 41.078 0.516 0.516 0.314 0.314
## 12 f1 =~ fairness_scen1_scale_15 36.031 0.351 0.351 0.220 0.220
## 13 f5 =~ fairness_scen1_scale_15 34.156 0.356 0.356 0.223 0.223
## 14 f4 =~ fairness_scen1_scale_13 33.683 0.497 0.497 0.339 0.339
## 15 f4 =~ fairness_scen1_scale_15 32.350 0.328 0.328 0.205 0.205
## 16 f4 =~ fairness_scen1_scale_7 31.102 0.335 0.335 0.233 0.233
## 17 f4 =~ fairness_scen1_scale_10 30.780 -0.680 -0.680 -0.426 -0.426
## 18 f3 =~ fairness_scen1_scale_6 23.333 -0.268 -0.268 -0.181 -0.181
## 19 f5 =~ fairness_scen1_scale_13 23.110 0.429 0.429 0.293 0.293
## 20 f5 =~ fairness_scen1_scale_8 22.892 -0.462 -0.462 -0.289 -0.289
## 21 f1 =~ fairness_scen1_scale_25 21.301 0.456 0.456 0.287 0.287
## 22 f1 =~ fairness_scen1_scale_26 21.301 -0.406 -0.406 -0.264 -0.264
## 23 f5 =~ fairness_scen1_scale_7 20.306 0.275 0.275 0.191 0.191
## 24 f2 =~ fairness_scen1_scale_26 18.758 -0.504 -0.504 -0.328 -0.328
## 25 f2 =~ fairness_scen1_scale_25 18.758 0.566 0.566 0.357 0.357
## 26 f1 =~ fairness_scen1_scale_8 17.294 0.665 0.665 0.415 0.415
## 27 f1 =~ fairness_scen1_scale_23 17.175 -0.251 -0.251 -0.145 -0.145
## 28 f4 =~ fairness_scen1_scale_9 15.982 -0.493 -0.493 -0.304 -0.304
## 29 f5 =~ fairness_scen1_scale_11 15.117 0.388 0.388 0.262 0.262
## 30 f4 =~ fairness_scen1_scale_8 14.984 -0.359 -0.359 -0.224 -0.224
## 31 f2 =~ fairness_scen1_scale_23 14.704 -0.298 -0.298 -0.173 -0.173
## 32 f2 =~ fairness_scen1_scale_7 13.367 0.485 0.485 0.337 0.337
## 33 f3 =~ fairness_scen1_scale_11 12.790 -0.216 -0.216 -0.146 -0.146
## 34 f3 =~ fairness_scen1_scale_20 12.513 0.156 0.156 0.097 0.097
## 35 f3 =~ fairness_scen1_scale_21 11.873 0.173 0.173 0.105 0.105
## 36 f4 =~ fairness_scen1_scale_12 11.720 -0.317 -0.317 -0.203 -0.203
## 37 f2 =~ fairness_scen1_scale_19 10.431 -0.269 -0.269 -0.153 -0.153
## 38 f3 =~ fairness_scen1_scale_22 10.351 -0.166 -0.166 -0.103 -0.103
## 39 f3 =~ fairness_scen1_scale_23 9.677 -0.149 -0.149 -0.086 -0.086
## 40 f4 =~ fairness_scen1_scale_3 9.636 -0.186 -0.186 -0.124 -0.124
## 41 f1 =~ fairness_scen1_scale_19 9.236 -0.198 -0.198 -0.112 -0.112
## 42 f5 =~ fairness_scen1_scale_3 8.489 -0.178 -0.178 -0.119 -0.119
## 43 f2 =~ fairness_scen1_scale_4 7.944 0.394 0.394 0.254 0.254
## 44 f4 =~ fairness_scen1_scale_11 7.345 0.256 0.256 0.173 0.173
## 45 f1 =~ fairness_scen1_scale_11 7.125 -0.430 -0.430 -0.291 -0.291
## 46 f3 =~ fairness_scen1_scale_25 6.448 0.205 0.205 0.129 0.129
## 47 f3 =~ fairness_scen1_scale_26 6.447 -0.182 -0.182 -0.118 -0.118
## 48 f2 =~ fairness_scen1_scale_3 6.351 -0.337 -0.337 -0.225 -0.225
## 49 f1 =~ fairness_scen1_scale_13 6.005 -0.361 -0.361 -0.246 -0.246
## 50 f3 =~ fairness_scen1_scale_8 5.454 0.137 0.137 0.085 0.085
## 51 f5 =~ fairness_scen1_scale_22 5.431 0.388 0.388 0.241 0.241
## 52 f5 =~ fairness_scen1_scale_20 5.255 -0.331 -0.331 -0.207 -0.207
## 53 f4 =~ fairness_scen1_scale_26 4.882 -0.574 -0.574 -0.373 -0.373
## 54 f4 =~ fairness_scen1_scale_25 4.882 0.644 0.644 0.406 0.406
## 55 f2 =~ fairness_scen1_scale_5 4.590 -0.281 -0.281 -0.192 -0.192
## 56 f2 =~ fairness_scen1_scale_6 3.962 -0.298 -0.298 -0.200 -0.200
## 57 f5 =~ fairness_scen1_scale_12 3.421 -0.179 -0.179 -0.115 -0.115
## 58 f5 =~ fairness_scen1_scale_5 3.292 -0.109 -0.109 -0.074 -0.074
## 59 f3 =~ fairness_scen1_scale_4 2.865 0.085 0.085 0.055 0.055
## 60 f3 =~ fairness_scen1_scale_13 2.091 -0.078 -0.078 -0.053 -0.053
## 61 f4 =~ fairness_scen1_scale_5 1.969 -0.083 -0.083 -0.056 -0.056
## 62 f2 =~ fairness_scen1_scale_20 1.582 0.090 0.090 0.056 0.056
## 63 f5 =~ fairness_scen1_scale_14 1.448 0.073 0.073 0.046 0.046
## 64 f5 =~ fairness_scen1_scale_21 1.404 -0.192 -0.192 -0.117 -0.117
## 65 f5 =~ fairness_scen1_scale_23 1.306 0.180 0.180 0.104 0.104
## 66 f5 =~ fairness_scen1_scale_17 1.259 -0.069 -0.069 -0.043 -0.043
## 67 f3 =~ fairness_scen1_scale_19 0.936 -0.050 -0.050 -0.028 -0.028
## 68 f1 =~ fairness_scen1_scale_17 0.923 0.056 0.056 0.035 0.035
## 69 f1 =~ fairness_scen1_scale_20 0.816 0.050 0.050 0.031 0.031
## 70 f4 =~ fairness_scen1_scale_6 0.801 -0.062 -0.062 -0.041 -0.041
## 71 f3 =~ fairness_scen1_scale_7 0.713 0.041 0.041 0.028 0.028
## 72 f3 =~ fairness_scen1_scale_5 0.650 0.038 0.038 0.026 0.026
## 73 f2 =~ fairness_scen1_scale_16 0.452 -0.039 -0.039 -0.025 -0.025
## 74 f1 =~ fairness_scen1_scale_14 0.452 -0.039 -0.039 -0.025 -0.025
## 75 f4 =~ fairness_scen1_scale_14 0.446 0.039 0.039 0.024 0.024
## 76 f4 =~ fairness_scen1_scale_17 0.397 -0.036 -0.036 -0.023 -0.023
## 77 f1 =~ fairness_scen1_scale_16 0.328 -0.033 -0.033 -0.022 -0.022
## 78 f5 =~ fairness_scen1_scale_4 0.176 0.027 0.027 0.017 0.017
## 79 f2 =~ fairness_scen1_scale_14 0.149 0.023 0.023 0.014 0.014
## 80 f4 =~ fairness_scen1_scale_16 0.134 -0.021 -0.021 -0.014 -0.014
## 81 f5 =~ fairness_scen1_scale_19 0.128 0.060 0.060 0.034 0.034
## 82 f5 =~ fairness_scen1_scale_16 0.106 -0.020 -0.020 -0.013 -0.013
## 83 f3 =~ fairness_scen1_scale_3 0.089 0.014 0.014 0.010 0.010
## 84 f1 =~ fairness_scen1_scale_22 0.082 0.019 0.019 0.012 0.012
## 85 f3 =~ fairness_scen1_scale_12 0.068 0.015 0.015 0.010 0.010
## 86 f1 =~ fairness_scen1_scale_10 0.066 -0.053 -0.053 -0.033 -0.033
## 87 f5 =~ fairness_scen1_scale_6 0.040 0.014 0.014 0.009 0.009
## 88 f1 =~ fairness_scen1_scale_12 0.034 0.029 0.029 0.019 0.019
## 89 f1 =~ fairness_scen1_scale_9 0.030 0.036 0.036 0.022 0.022
## 90 f2 =~ fairness_scen1_scale_17 0.011 -0.006 -0.006 -0.004 -0.004
## 91 f2 =~ fairness_scen1_scale_22 0.001 -0.003 -0.003 -0.002 -0.002
## 92 f4 =~ fairness_scen1_scale_4 0.000 0.001 0.001 0.001 0.001
Item–item correlations:
## lhs op rhs mi epc sepc.lv
## 1 fairness_scen1_scale_9 ~~ fairness_scen1_scale_10 202.128 1.638 1.638
## 2 fairness_scen1_scale_8 ~~ fairness_scen1_scale_10 23.792 0.371 0.371
## 3 fairness_scen1_scale_10 ~~ fairness_scen1_scale_11 19.619 -0.374 -0.374
## 4 fairness_scen1_scale_14 ~~ fairness_scen1_scale_15 18.691 0.354 0.354
## 5 fairness_scen1_scale_4 ~~ fairness_scen1_scale_8 18.014 0.203 0.203
## 6 fairness_scen1_scale_6 ~~ fairness_scen1_scale_10 16.806 -0.326 -0.326
## 7 fairness_scen1_scale_10 ~~ fairness_scen1_scale_21 16.360 0.291 0.291
## 8 fairness_scen1_scale_6 ~~ fairness_scen1_scale_14 16.300 -0.244 -0.244
## 9 fairness_scen1_scale_9 ~~ fairness_scen1_scale_26 14.708 -0.324 -0.324
## 10 fairness_scen1_scale_4 ~~ fairness_scen1_scale_26 14.131 -0.198 -0.198
## 11 fairness_scen1_scale_12 ~~ fairness_scen1_scale_26 12.984 0.215 0.215
## 12 fairness_scen1_scale_4 ~~ fairness_scen1_scale_5 12.764 -0.164 -0.164
## 13 fairness_scen1_scale_19 ~~ fairness_scen1_scale_21 12.202 -0.174 -0.174
## 14 fairness_scen1_scale_8 ~~ fairness_scen1_scale_9 12.095 0.266 0.266
## 15 fairness_scen1_scale_16 ~~ fairness_scen1_scale_17 10.995 0.260 0.260
## 16 fairness_scen1_scale_14 ~~ fairness_scen1_scale_16 10.708 -0.254 -0.254
## 17 fairness_scen1_scale_10 ~~ fairness_scen1_scale_17 10.678 0.285 0.285
## 18 fairness_scen1_scale_15 ~~ fairness_scen1_scale_18 10.649 -0.260 -0.260
## 19 fairness_scen1_scale_5 ~~ fairness_scen1_scale_13 9.737 -0.130 -0.130
## 20 fairness_scen1_scale_5 ~~ fairness_scen1_scale_23 9.332 -0.120 -0.120
## 21 fairness_scen1_scale_8 ~~ fairness_scen1_scale_21 9.288 0.144 0.144
## 22 fairness_scen1_scale_5 ~~ fairness_scen1_scale_7 9.122 0.131 0.131
## 23 fairness_scen1_scale_10 ~~ fairness_scen1_scale_14 9.034 0.262 0.262
## 24 fairness_scen1_scale_8 ~~ fairness_scen1_scale_26 8.305 -0.168 -0.168
## 25 fairness_scen1_scale_12 ~~ fairness_scen1_scale_19 8.302 -0.146 -0.146
## 26 fairness_scen1_scale_4 ~~ fairness_scen1_scale_9 8.255 0.205 0.205
## 27 fairness_scen1_scale_9 ~~ fairness_scen1_scale_22 7.944 -0.210 -0.210
## 28 fairness_scen1_scale_10 ~~ fairness_scen1_scale_16 7.825 0.241 0.241
## 29 fairness_scen1_scale_19 ~~ fairness_scen1_scale_26 7.724 0.154 0.154
## 30 fairness_scen1_scale_5 ~~ fairness_scen1_scale_20 7.720 0.100 0.100
## 31 fairness_scen1_scale_19 ~~ fairness_scen1_scale_23 7.305 0.133 0.133
## 32 fairness_scen1_scale_9 ~~ fairness_scen1_scale_17 7.262 0.236 0.236
## 33 fairness_scen1_scale_9 ~~ fairness_scen1_scale_15 7.074 0.231 0.231
## 34 fairness_scen1_scale_21 ~~ fairness_scen1_scale_26 7.014 -0.142 -0.142
## 35 fairness_scen1_scale_3 ~~ fairness_scen1_scale_17 6.948 0.134 0.134
## 36 fairness_scen1_scale_7 ~~ fairness_scen1_scale_8 6.695 -0.118 -0.118
## 37 fairness_scen1_scale_10 ~~ fairness_scen1_scale_26 6.604 -0.217 -0.217
## 38 fairness_scen1_scale_10 ~~ fairness_scen1_scale_19 6.501 -0.188 -0.188
## 39 fairness_scen1_scale_11 ~~ fairness_scen1_scale_23 6.427 0.127 0.127
## 40 fairness_scen1_scale_4 ~~ fairness_scen1_scale_22 6.402 0.116 0.116
## 41 fairness_scen1_scale_8 ~~ fairness_scen1_scale_13 6.398 -0.136 -0.136
## 42 fairness_scen1_scale_3 ~~ fairness_scen1_scale_7 6.369 -0.111 -0.111
## 43 fairness_scen1_scale_7 ~~ fairness_scen1_scale_20 6.208 0.092 0.092
## 44 fairness_scen1_scale_9 ~~ fairness_scen1_scale_21 6.006 0.177 0.177
## 45 fairness_scen1_scale_11 ~~ fairness_scen1_scale_16 5.963 -0.155 -0.155
## 46 fairness_scen1_scale_7 ~~ fairness_scen1_scale_13 5.894 0.104 0.104
## 47 fairness_scen1_scale_9 ~~ fairness_scen1_scale_11 5.829 -0.205 -0.205
## 48 fairness_scen1_scale_11 ~~ fairness_scen1_scale_12 5.787 0.144 0.144
## 49 fairness_scen1_scale_4 ~~ fairness_scen1_scale_23 5.747 -0.101 -0.101
## 50 fairness_scen1_scale_13 ~~ fairness_scen1_scale_22 5.687 0.109 0.109
## 51 fairness_scen1_scale_15 ~~ fairness_scen1_scale_20 5.583 0.111 0.111
## 52 fairness_scen1_scale_3 ~~ fairness_scen1_scale_20 5.552 -0.086 -0.086
## 53 fairness_scen1_scale_23 ~~ fairness_scen1_scale_25 5.500 -0.117 -0.117
## 54 fairness_scen1_scale_18 ~~ fairness_scen1_scale_25 5.457 -0.158 -0.158
## 55 fairness_scen1_scale_3 ~~ fairness_scen1_scale_5 5.212 0.100 0.100
## 56 fairness_scen1_scale_14 ~~ fairness_scen1_scale_17 5.178 -0.186 -0.186
## 57 fairness_scen1_scale_13 ~~ fairness_scen1_scale_16 5.075 -0.120 -0.120
## 58 fairness_scen1_scale_4 ~~ fairness_scen1_scale_10 4.551 0.151 0.151
## 59 fairness_scen1_scale_10 ~~ fairness_scen1_scale_22 4.519 -0.158 -0.158
## 60 fairness_scen1_scale_13 ~~ fairness_scen1_scale_23 4.470 0.089 0.089
## 61 fairness_scen1_scale_15 ~~ fairness_scen1_scale_17 4.448 -0.175 -0.175
## 62 fairness_scen1_scale_10 ~~ fairness_scen1_scale_23 4.222 -0.140 -0.140
## 63 fairness_scen1_scale_13 ~~ fairness_scen1_scale_21 4.145 -0.090 -0.090
## 64 fairness_scen1_scale_12 ~~ fairness_scen1_scale_17 4.140 -0.122 -0.122
## 65 fairness_scen1_scale_6 ~~ fairness_scen1_scale_18 4.068 -0.133 -0.133
## 66 fairness_scen1_scale_17 ~~ fairness_scen1_scale_26 4.022 -0.130 -0.130
## 67 fairness_scen1_scale_4 ~~ fairness_scen1_scale_21 3.955 0.088 0.088
## 68 fairness_scen1_scale_9 ~~ fairness_scen1_scale_16 3.903 0.171 0.171
## 69 fairness_scen1_scale_16 ~~ fairness_scen1_scale_25 3.902 0.122 0.122
## 70 fairness_scen1_scale_5 ~~ fairness_scen1_scale_9 3.900 -0.131 -0.131
## 71 fairness_scen1_scale_15 ~~ fairness_scen1_scale_21 3.865 0.107 0.107
## 72 fairness_scen1_scale_3 ~~ fairness_scen1_scale_6 3.823 0.096 0.096
## 73 fairness_scen1_scale_5 ~~ fairness_scen1_scale_22 3.815 -0.084 -0.084
## 74 fairness_scen1_scale_10 ~~ fairness_scen1_scale_13 3.716 -0.137 -0.137
## 75 fairness_scen1_scale_6 ~~ fairness_scen1_scale_9 3.709 -0.154 -0.154
## 76 fairness_scen1_scale_17 ~~ fairness_scen1_scale_22 3.586 -0.107 -0.107
## 77 fairness_scen1_scale_16 ~~ fairness_scen1_scale_22 3.554 0.105 0.105
## 78 fairness_scen1_scale_4 ~~ fairness_scen1_scale_25 3.540 0.096 0.096
## 79 fairness_scen1_scale_6 ~~ fairness_scen1_scale_7 3.353 -0.090 -0.090
## 80 fairness_scen1_scale_16 ~~ fairness_scen1_scale_23 3.304 -0.093 -0.093
## 81 fairness_scen1_scale_8 ~~ fairness_scen1_scale_18 3.137 -0.111 -0.111
## 82 fairness_scen1_scale_6 ~~ fairness_scen1_scale_20 3.127 -0.076 -0.076
## 83 fairness_scen1_scale_5 ~~ fairness_scen1_scale_14 3.086 -0.088 -0.088
## 84 fairness_scen1_scale_8 ~~ fairness_scen1_scale_14 2.890 0.098 0.098
## 85 fairness_scen1_scale_7 ~~ fairness_scen1_scale_16 2.869 0.087 0.087
## 86 fairness_scen1_scale_4 ~~ fairness_scen1_scale_20 2.766 -0.064 -0.064
## 87 fairness_scen1_scale_3 ~~ fairness_scen1_scale_16 2.743 -0.084 -0.084
## 88 fairness_scen1_scale_5 ~~ fairness_scen1_scale_15 2.635 0.081 0.081
## 89 fairness_scen1_scale_11 ~~ fairness_scen1_scale_13 2.604 0.088 0.088
## 90 fairness_scen1_scale_18 ~~ fairness_scen1_scale_21 2.578 -0.095 -0.095
## 91 fairness_scen1_scale_13 ~~ fairness_scen1_scale_15 2.494 0.085 0.085
## 92 fairness_scen1_scale_9 ~~ fairness_scen1_scale_20 2.471 0.098 0.098
## 93 fairness_scen1_scale_6 ~~ fairness_scen1_scale_13 2.463 -0.078 -0.078
## 94 fairness_scen1_scale_12 ~~ fairness_scen1_scale_18 2.402 0.101 0.101
## 95 fairness_scen1_scale_8 ~~ fairness_scen1_scale_12 2.329 0.088 0.088
## 96 fairness_scen1_scale_15 ~~ fairness_scen1_scale_22 2.293 -0.085 -0.085
## 97 fairness_scen1_scale_12 ~~ fairness_scen1_scale_13 2.234 -0.080 -0.080
## 98 fairness_scen1_scale_3 ~~ fairness_scen1_scale_10 2.201 0.100 0.100
## 99 fairness_scen1_scale_14 ~~ fairness_scen1_scale_18 2.157 0.116 0.116
## 100 fairness_scen1_scale_18 ~~ fairness_scen1_scale_20 2.147 0.075 0.075
## 101 fairness_scen1_scale_5 ~~ fairness_scen1_scale_6 2.134 0.071 0.071
## 102 fairness_scen1_scale_11 ~~ fairness_scen1_scale_19 2.132 -0.079 -0.079
## 103 fairness_scen1_scale_21 ~~ fairness_scen1_scale_25 2.093 0.075 0.075
## 104 fairness_scen1_scale_8 ~~ fairness_scen1_scale_19 2.005 -0.069 -0.069
## 105 fairness_scen1_scale_6 ~~ fairness_scen1_scale_17 1.918 0.084 0.084
## 106 fairness_scen1_scale_8 ~~ fairness_scen1_scale_23 1.904 -0.062 -0.062
## 107 fairness_scen1_scale_17 ~~ fairness_scen1_scale_21 1.858 0.074 0.074
## 108 fairness_scen1_scale_9 ~~ fairness_scen1_scale_19 1.796 -0.099 -0.099
## 109 fairness_scen1_scale_6 ~~ fairness_scen1_scale_16 1.727 -0.078 -0.078
## 110 fairness_scen1_scale_3 ~~ fairness_scen1_scale_11 1.702 -0.065 -0.065
## 111 fairness_scen1_scale_13 ~~ fairness_scen1_scale_19 1.701 0.060 0.060
## 112 fairness_scen1_scale_3 ~~ fairness_scen1_scale_18 1.684 -0.072 -0.072
## 113 fairness_scen1_scale_9 ~~ fairness_scen1_scale_14 1.658 0.113 0.113
## 114 fairness_scen1_scale_16 ~~ fairness_scen1_scale_19 1.645 0.071 0.071
## 115 fairness_scen1_scale_11 ~~ fairness_scen1_scale_25 1.621 -0.078 -0.078
## 116 fairness_scen1_scale_12 ~~ fairness_scen1_scale_16 1.561 0.074 0.074
## 117 fairness_scen1_scale_5 ~~ fairness_scen1_scale_21 1.517 0.051 0.051
## 118 fairness_scen1_scale_10 ~~ fairness_scen1_scale_12 1.496 0.097 0.097
## 119 fairness_scen1_scale_17 ~~ fairness_scen1_scale_19 1.488 0.068 0.068
## 120 fairness_scen1_scale_11 ~~ fairness_scen1_scale_17 1.460 -0.077 -0.077
## 121 fairness_scen1_scale_11 ~~ fairness_scen1_scale_26 1.460 0.076 0.076
## 122 fairness_scen1_scale_8 ~~ fairness_scen1_scale_25 1.458 0.069 0.069
## 123 fairness_scen1_scale_7 ~~ fairness_scen1_scale_12 1.456 -0.057 -0.057
## 124 fairness_scen1_scale_5 ~~ fairness_scen1_scale_16 1.443 0.060 0.060
## 125 fairness_scen1_scale_5 ~~ fairness_scen1_scale_10 1.305 -0.076 -0.076
## 126 fairness_scen1_scale_4 ~~ fairness_scen1_scale_7 1.301 -0.053 -0.053
## 127 fairness_scen1_scale_8 ~~ fairness_scen1_scale_15 1.285 0.065 0.065
## 128 fairness_scen1_scale_6 ~~ fairness_scen1_scale_8 1.277 0.060 0.060
## 129 fairness_scen1_scale_12 ~~ fairness_scen1_scale_22 1.231 -0.056 -0.056
## 130 fairness_scen1_scale_3 ~~ fairness_scen1_scale_15 1.229 -0.056 -0.056
## 131 fairness_scen1_scale_13 ~~ fairness_scen1_scale_25 1.215 -0.059 -0.059
## 132 fairness_scen1_scale_17 ~~ fairness_scen1_scale_18 1.136 0.085 0.085
## 133 fairness_scen1_scale_3 ~~ fairness_scen1_scale_21 1.066 0.043 0.043
## 134 fairness_scen1_scale_15 ~~ fairness_scen1_scale_19 1.048 -0.057 -0.057
## 135 fairness_scen1_scale_6 ~~ fairness_scen1_scale_22 1.046 0.053 0.053
## 136 fairness_scen1_scale_7 ~~ fairness_scen1_scale_25 0.992 0.049 0.049
## 137 fairness_scen1_scale_20 ~~ fairness_scen1_scale_21 0.980 0.043 0.043
## 138 fairness_scen1_scale_8 ~~ fairness_scen1_scale_11 0.970 -0.058 -0.058
## 139 fairness_scen1_scale_8 ~~ fairness_scen1_scale_22 0.935 -0.047 -0.047
## 140 fairness_scen1_scale_4 ~~ fairness_scen1_scale_17 0.904 -0.051 -0.051
## 141 fairness_scen1_scale_3 ~~ fairness_scen1_scale_14 0.863 0.047 0.047
## 142 fairness_scen1_scale_23 ~~ fairness_scen1_scale_26 0.840 0.047 0.047
## 143 fairness_scen1_scale_13 ~~ fairness_scen1_scale_18 0.815 -0.053 -0.053
## 144 fairness_scen1_scale_4 ~~ fairness_scen1_scale_12 0.781 0.044 0.044
## 145 fairness_scen1_scale_14 ~~ fairness_scen1_scale_22 0.779 -0.050 -0.050
## 146 fairness_scen1_scale_20 ~~ fairness_scen1_scale_22 0.767 -0.038 -0.038
## 147 fairness_scen1_scale_3 ~~ fairness_scen1_scale_23 0.766 0.035 0.035
## 148 fairness_scen1_scale_3 ~~ fairness_scen1_scale_8 0.750 0.039 0.039
## 149 fairness_scen1_scale_4 ~~ fairness_scen1_scale_14 0.733 0.046 0.046
## 150 fairness_scen1_scale_20 ~~ fairness_scen1_scale_25 0.729 -0.039 -0.039
## 151 fairness_scen1_scale_9 ~~ fairness_scen1_scale_18 0.695 -0.079 -0.079
## 152 fairness_scen1_scale_16 ~~ fairness_scen1_scale_18 0.688 0.064 0.064
## 153 fairness_scen1_scale_16 ~~ fairness_scen1_scale_21 0.674 -0.044 -0.044
## 154 fairness_scen1_scale_22 ~~ fairness_scen1_scale_25 0.672 0.044 0.044
## 155 fairness_scen1_scale_4 ~~ fairness_scen1_scale_16 0.659 0.043 0.043
## 156 fairness_scen1_scale_3 ~~ fairness_scen1_scale_22 0.648 -0.035 -0.035
## 157 fairness_scen1_scale_13 ~~ fairness_scen1_scale_26 0.640 0.043 0.043
## 158 fairness_scen1_scale_5 ~~ fairness_scen1_scale_25 0.636 0.038 0.038
## 159 fairness_scen1_scale_5 ~~ fairness_scen1_scale_12 0.617 0.036 0.036
## 160 fairness_scen1_scale_6 ~~ fairness_scen1_scale_15 0.605 0.047 0.047
## 161 fairness_scen1_scale_20 ~~ fairness_scen1_scale_26 0.588 -0.036 -0.036
## 162 fairness_scen1_scale_10 ~~ fairness_scen1_scale_18 0.585 0.073 0.073
## 163 fairness_scen1_scale_14 ~~ fairness_scen1_scale_21 0.582 0.042 0.042
## 164 fairness_scen1_scale_12 ~~ fairness_scen1_scale_14 0.581 0.046 0.046
## 165 fairness_scen1_scale_7 ~~ fairness_scen1_scale_11 0.580 -0.038 -0.038
## 166 fairness_scen1_scale_19 ~~ fairness_scen1_scale_25 0.573 0.041 0.041
## 167 fairness_scen1_scale_14 ~~ fairness_scen1_scale_26 0.561 0.048 0.048
## 168 fairness_scen1_scale_12 ~~ fairness_scen1_scale_15 0.560 -0.044 -0.044
## 169 fairness_scen1_scale_3 ~~ fairness_scen1_scale_19 0.553 -0.032 -0.032
## 170 fairness_scen1_scale_15 ~~ fairness_scen1_scale_23 0.537 -0.038 -0.038
## 171 fairness_scen1_scale_13 ~~ fairness_scen1_scale_20 0.530 0.028 0.028
## 172 fairness_scen1_scale_19 ~~ fairness_scen1_scale_20 0.496 0.032 0.032
## 173 fairness_scen1_scale_8 ~~ fairness_scen1_scale_20 0.494 -0.029 -0.029
## 174 fairness_scen1_scale_5 ~~ fairness_scen1_scale_11 0.485 -0.034 -0.034
## 175 fairness_scen1_scale_10 ~~ fairness_scen1_scale_15 0.475 0.060 0.060
## 176 fairness_scen1_scale_7 ~~ fairness_scen1_scale_23 0.443 0.027 0.027
## 177 fairness_scen1_scale_6 ~~ fairness_scen1_scale_11 0.439 -0.039 -0.039
## 178 fairness_scen1_scale_11 ~~ fairness_scen1_scale_20 0.405 0.029 0.029
## 179 fairness_scen1_scale_16 ~~ fairness_scen1_scale_20 0.366 -0.028 -0.028
## 180 fairness_scen1_scale_7 ~~ fairness_scen1_scale_26 0.366 -0.030 -0.030
## 181 fairness_scen1_scale_18 ~~ fairness_scen1_scale_19 0.360 -0.037 -0.037
## 182 fairness_scen1_scale_15 ~~ fairness_scen1_scale_25 0.338 0.036 0.036
## 183 fairness_scen1_scale_6 ~~ fairness_scen1_scale_26 0.331 0.034 0.034
## 184 fairness_scen1_scale_3 ~~ fairness_scen1_scale_4 0.327 0.027 0.027
## 185 fairness_scen1_scale_10 ~~ fairness_scen1_scale_25 0.326 0.046 0.046
## 186 fairness_scen1_scale_12 ~~ fairness_scen1_scale_23 0.308 -0.026 -0.026
## 187 fairness_scen1_scale_12 ~~ fairness_scen1_scale_25 0.306 -0.032 -0.032
## 188 fairness_scen1_scale_10 ~~ fairness_scen1_scale_20 0.300 0.034 0.034
## 189 fairness_scen1_scale_14 ~~ fairness_scen1_scale_19 0.277 -0.030 -0.030
## 190 fairness_scen1_scale_13 ~~ fairness_scen1_scale_17 0.266 0.028 0.028
## 191 fairness_scen1_scale_9 ~~ fairness_scen1_scale_12 0.247 0.039 0.039
## 192 fairness_scen1_scale_7 ~~ fairness_scen1_scale_21 0.246 0.021 0.021
## 193 fairness_scen1_scale_6 ~~ fairness_scen1_scale_23 0.234 -0.023 -0.023
## 194 fairness_scen1_scale_9 ~~ fairness_scen1_scale_23 0.224 -0.032 -0.032
## 195 fairness_scen1_scale_3 ~~ fairness_scen1_scale_25 0.215 -0.022 -0.022
## 196 fairness_scen1_scale_4 ~~ fairness_scen1_scale_13 0.205 0.020 0.020
## 197 fairness_scen1_scale_15 ~~ fairness_scen1_scale_26 0.202 -0.029 -0.029
## 198 fairness_scen1_scale_12 ~~ fairness_scen1_scale_20 0.195 0.019 0.019
## 199 fairness_scen1_scale_3 ~~ fairness_scen1_scale_12 0.194 -0.021 -0.021
## 200 fairness_scen1_scale_18 ~~ fairness_scen1_scale_22 0.183 -0.026 -0.026
## 201 fairness_scen1_scale_17 ~~ fairness_scen1_scale_20 0.180 -0.020 -0.020
## 202 fairness_scen1_scale_21 ~~ fairness_scen1_scale_22 0.177 -0.021 -0.021
## 203 fairness_scen1_scale_7 ~~ fairness_scen1_scale_9 0.175 -0.029 -0.029
## 204 fairness_scen1_scale_17 ~~ fairness_scen1_scale_25 0.161 0.025 0.025
## 205 fairness_scen1_scale_22 ~~ fairness_scen1_scale_26 0.150 0.021 0.021
## 206 fairness_scen1_scale_14 ~~ fairness_scen1_scale_25 0.141 0.023 0.023
## 207 fairness_scen1_scale_14 ~~ fairness_scen1_scale_20 0.137 0.018 0.018
## 208 fairness_scen1_scale_11 ~~ fairness_scen1_scale_22 0.136 -0.020 -0.020
## 209 fairness_scen1_scale_7 ~~ fairness_scen1_scale_19 0.133 0.016 0.016
## 210 fairness_scen1_scale_7 ~~ fairness_scen1_scale_22 0.109 0.015 0.015
## 211 fairness_scen1_scale_8 ~~ fairness_scen1_scale_17 0.109 -0.019 -0.019
## 212 fairness_scen1_scale_11 ~~ fairness_scen1_scale_21 0.102 -0.017 -0.017
## 213 fairness_scen1_scale_9 ~~ fairness_scen1_scale_25 0.086 -0.024 -0.024
## 214 fairness_scen1_scale_3 ~~ fairness_scen1_scale_26 0.085 0.015 0.015
## 215 fairness_scen1_scale_7 ~~ fairness_scen1_scale_10 0.065 -0.017 -0.017
## 216 fairness_scen1_scale_9 ~~ fairness_scen1_scale_13 0.063 0.018 0.018
## 217 fairness_scen1_scale_20 ~~ fairness_scen1_scale_23 0.062 -0.011 -0.011
## 218 fairness_scen1_scale_6 ~~ fairness_scen1_scale_19 0.058 0.012 0.012
## 219 fairness_scen1_scale_7 ~~ fairness_scen1_scale_18 0.055 -0.013 -0.013
## 220 fairness_scen1_scale_6 ~~ fairness_scen1_scale_12 0.051 0.012 0.012
## 221 fairness_scen1_scale_18 ~~ fairness_scen1_scale_26 0.048 0.015 0.015
## 222 fairness_scen1_scale_5 ~~ fairness_scen1_scale_19 0.048 0.009 0.009
## 223 fairness_scen1_scale_19 ~~ fairness_scen1_scale_22 0.045 0.011 0.011
## 224 fairness_scen1_scale_8 ~~ fairness_scen1_scale_16 0.044 0.012 0.012
## 225 fairness_scen1_scale_5 ~~ fairness_scen1_scale_26 0.037 -0.009 -0.009
## 226 fairness_scen1_scale_16 ~~ fairness_scen1_scale_26 0.033 -0.012 -0.012
## 227 fairness_scen1_scale_18 ~~ fairness_scen1_scale_23 0.032 -0.010 -0.010
## 228 fairness_scen1_scale_17 ~~ fairness_scen1_scale_23 0.031 -0.009 -0.009
## 229 fairness_scen1_scale_6 ~~ fairness_scen1_scale_25 0.026 0.009 0.009
## 230 fairness_scen1_scale_4 ~~ fairness_scen1_scale_19 0.025 -0.007 -0.007
## 231 fairness_scen1_scale_7 ~~ fairness_scen1_scale_15 0.025 0.008 0.008
## 232 fairness_scen1_scale_7 ~~ fairness_scen1_scale_17 0.025 0.008 0.008
## 233 fairness_scen1_scale_14 ~~ fairness_scen1_scale_23 0.025 -0.008 -0.008
## 234 fairness_scen1_scale_11 ~~ fairness_scen1_scale_15 0.023 0.010 0.010
## 235 fairness_scen1_scale_12 ~~ fairness_scen1_scale_21 0.014 -0.006 -0.006
## 236 fairness_scen1_scale_4 ~~ fairness_scen1_scale_15 0.013 0.006 0.006
## 237 fairness_scen1_scale_13 ~~ fairness_scen1_scale_14 0.013 0.006 0.006
## 238 fairness_scen1_scale_4 ~~ fairness_scen1_scale_6 0.012 -0.006 -0.006
## 239 fairness_scen1_scale_6 ~~ fairness_scen1_scale_21 0.012 0.005 0.005
## 240 fairness_scen1_scale_11 ~~ fairness_scen1_scale_14 0.011 0.007 0.007
## 241 fairness_scen1_scale_3 ~~ fairness_scen1_scale_13 0.009 0.004 0.004
## 242 fairness_scen1_scale_3 ~~ fairness_scen1_scale_9 0.007 0.006 0.006
## 243 fairness_scen1_scale_7 ~~ fairness_scen1_scale_14 0.006 -0.004 -0.004
## 244 fairness_scen1_scale_21 ~~ fairness_scen1_scale_23 0.004 -0.003 -0.003
## 245 fairness_scen1_scale_4 ~~ fairness_scen1_scale_18 0.004 -0.004 -0.004
## 246 fairness_scen1_scale_5 ~~ fairness_scen1_scale_8 0.001 0.002 0.002
## 247 fairness_scen1_scale_4 ~~ fairness_scen1_scale_11 0.001 -0.002 -0.002
## 248 fairness_scen1_scale_5 ~~ fairness_scen1_scale_18 0.001 0.001 0.001
## 249 fairness_scen1_scale_5 ~~ fairness_scen1_scale_17 0.000 -0.001 -0.001
## 250 fairness_scen1_scale_15 ~~ fairness_scen1_scale_16 0.000 -0.001 -0.001
## 251 fairness_scen1_scale_11 ~~ fairness_scen1_scale_18 0.000 -0.001 -0.001
## 252 fairness_scen1_scale_22 ~~ fairness_scen1_scale_23 0.000 0.000 0.000
## sepc.all sepc.nox
## 1 0.640 0.640
## 2 0.240 0.240
## 3 -0.206 -0.206
## 4 0.299 0.299
## 5 0.232 0.232
## 6 -0.192 -0.192
## 7 0.195 0.195
## 8 -0.209 -0.209
## 9 -0.184 -0.184
## 10 -0.200 -0.200
## 11 0.191 0.191
## 12 -0.217 -0.217
## 13 -0.198 -0.198
## 14 0.172 0.172
## 15 0.217 0.217
## 16 -0.210 -0.210
## 17 0.163 0.163
## 18 -0.191 -0.191
## 19 -0.170 -0.170
## 20 -0.170 -0.170
## 21 0.161 0.161
## 22 0.178 0.178
## 23 0.149 0.149
## 24 -0.158 -0.158
## 25 -0.151 -0.151
## 26 0.142 0.142
## 27 -0.134 -0.134
## 28 0.137 0.137
## 29 0.148 0.148
## 30 0.155 0.155
## 31 0.167 0.167
## 32 0.135 0.135
## 33 0.134 0.134
## 34 -0.139 -0.139
## 35 0.146 0.146
## 36 -0.139 -0.139
## 37 -0.123 -0.123
## 38 -0.125 -0.125
## 39 0.132 0.132
## 40 0.132 0.132
## 41 -0.154 -0.154
## 42 -0.150 -0.150
## 43 0.136 0.136
## 44 0.119 0.119
## 45 -0.124 -0.124
## 46 0.129 0.129
## 47 -0.112 -0.112
## 48 0.123 0.123
## 49 -0.132 -0.132
## 50 0.123 0.123
## 51 0.134 0.134
## 52 -0.132 -0.132
## 53 -0.135 -0.135
## 54 -0.122 -0.122
## 55 0.142 0.142
## 56 -0.156 -0.156
## 57 -0.119 -0.119
## 58 0.105 0.105
## 59 -0.101 -0.101
## 60 0.115 0.115
## 61 -0.149 -0.149
## 62 -0.103 -0.103
## 63 -0.106 -0.106
## 64 -0.109 -0.109
## 65 -0.099 -0.099
## 66 -0.108 -0.108
## 67 0.105 0.105
## 68 0.097 0.097
## 69 0.108 0.108
## 70 -0.098 -0.098
## 71 0.106 0.106
## 72 0.107 0.107
## 73 -0.103 -0.103
## 74 -0.094 -0.094
## 75 -0.090 -0.090
## 76 -0.100 -0.100
## 77 0.098 0.098
## 78 0.104 0.104
## 79 -0.097 -0.097
## 80 -0.100 -0.100
## 81 -0.091 -0.091
## 82 -0.093 -0.093
## 83 -0.096 -0.096
## 84 0.092 0.092
## 85 0.090 0.090
## 86 -0.092 -0.092
## 87 -0.090 -0.090
## 88 0.090 0.090
## 89 0.085 0.085
## 90 -0.081 -0.081
## 91 0.086 0.086
## 92 0.080 0.080
## 93 -0.080 -0.080
## 94 0.078 0.078
## 95 0.089 0.089
## 96 -0.081 -0.081
## 97 -0.085 -0.085
## 98 0.074 0.074
## 99 0.084 0.084
## 100 0.078 0.078
## 101 0.080 0.080
## 102 -0.074 -0.074
## 103 0.079 0.079
## 104 -0.076 -0.076
## 105 0.072 0.072
## 106 -0.076 -0.076
## 107 0.073 0.073
## 108 -0.066 -0.066
## 109 -0.067 -0.067
## 110 -0.068 -0.068
## 111 0.069 0.069
## 112 -0.067 -0.067
## 113 0.064 0.064
## 114 0.069 0.069
## 115 -0.067 -0.067
## 116 0.065 0.065
## 117 0.066 0.066
## 118 0.059 0.059
## 119 0.067 0.067
## 120 -0.062 -0.062
## 121 0.061 0.061
## 122 0.070 0.070
## 123 -0.063 -0.063
## 124 0.065 0.065
## 125 -0.057 -0.057
## 126 -0.066 -0.066
## 127 0.062 0.062
## 128 0.058 0.058
## 129 -0.056 -0.056
## 130 -0.062 -0.062
## 131 -0.063 -0.063
## 132 0.062 0.062
## 133 0.055 0.055
## 134 -0.056 -0.056
## 135 0.051 0.051
## 136 0.054 0.054
## 137 0.060 0.060
## 138 -0.052 -0.052
## 139 -0.050 -0.050
## 140 -0.052 -0.052
## 141 0.051 0.051
## 142 0.051 0.051
## 143 -0.046 -0.046
## 144 0.047 0.047
## 145 -0.046 -0.046
## 146 -0.051 -0.051
## 147 0.049 0.049
## 148 0.048 0.048
## 149 0.047 0.047
## 150 -0.049 -0.049
## 151 -0.039 -0.039
## 152 0.046 0.046
## 153 -0.043 -0.043
## 154 0.044 0.044
## 155 0.044 0.044
## 156 -0.042 -0.042
## 157 0.043 0.043
## 158 0.044 0.044
## 159 0.042 0.042
## 160 0.041 0.041
## 161 -0.043 -0.043
## 162 0.036 0.036
## 163 0.041 0.041
## 164 0.040 0.040
## 165 -0.038 -0.038
## 166 0.042 0.042
## 167 0.040 0.040
## 168 -0.040 -0.040
## 169 -0.040 -0.040
## 170 -0.041 -0.041
## 171 0.040 0.040
## 172 0.044 0.044
## 173 -0.039 -0.039
## 174 -0.036 -0.036
## 175 0.035 0.035
## 176 0.036 0.036
## 177 -0.032 -0.032
## 178 0.033 0.033
## 179 -0.033 -0.033
## 180 -0.032 -0.032
## 181 -0.031 -0.031
## 182 0.033 0.033
## 183 0.029 0.029
## 184 0.035 0.035
## 185 0.028 0.028
## 186 -0.030 -0.030
## 187 -0.031 -0.031
## 188 0.028 0.028
## 189 -0.029 -0.029
## 190 0.028 0.028
## 191 0.024 0.024
## 192 0.026 0.026
## 193 -0.025 -0.025
## 194 -0.024 -0.024
## 195 -0.026 -0.026
## 196 0.025 0.025
## 197 -0.024 -0.024
## 198 0.024 0.024
## 199 -0.024 -0.024
## 200 -0.021 -0.021
## 201 -0.024 -0.024
## 202 -0.023 -0.023
## 203 -0.020 -0.020
## 204 0.022 0.022
## 205 0.020 0.020
## 206 0.021 0.021
## 207 0.021 0.021
## 208 -0.018 -0.018
## 209 0.019 0.019
## 210 0.017 0.017
## 211 -0.018 -0.018
## 212 -0.016 -0.016
## 213 -0.015 -0.015
## 214 0.016 0.016
## 215 -0.012 -0.012
## 216 0.012 0.012
## 217 -0.017 -0.017
## 218 0.012 0.012
## 219 -0.012 -0.012
## 220 0.011 0.011
## 221 0.011 0.011
## 222 0.012 0.012
## 223 0.012 0.012
## 224 0.011 0.011
## 225 -0.010 -0.010
## 226 -0.010 -0.010
## 227 -0.009 -0.009
## 228 -0.010 -0.010
## 229 0.008 0.008
## 230 -0.008 -0.008
## 231 0.009 0.009
## 232 0.009 0.009
## 233 -0.009 -0.009
## 234 0.008 0.008
## 235 -0.006 -0.006
## 236 0.006 0.006
## 237 0.006 0.006
## 238 -0.006 -0.006
## 239 0.005 0.005
## 240 0.005 0.005
## 241 0.005 0.005
## 242 0.004 0.004
## 243 -0.004 -0.004
## 244 -0.004 -0.004
## 245 -0.003 -0.003
## 246 0.002 0.002
## 247 -0.002 -0.002
## 248 0.001 0.001
## 249 -0.001 -0.001
## 250 -0.001 -0.001
## 251 0.000 0.000
## 252 0.000 0.000Sup5.5: CFA results - optimized model + comparison of fit indices
| Fit_indices | Optimal | Fit_values_original | Fit_values_mod_V1 |
|---|---|---|---|
| RMSEA | ≤ 0.06 | 0.093 (0.09,0.1) | 0.067 (0.06,0.07) |
| SRMR | < 0.08 | 0.116 | 0.06 |
| TLI | ≥ 0.95 | 0.845 | 0.94 |
| CFI | ≥ 0.95 | 0.865 | 0.953 |
| χ² | < 0.05 | χ²(220, N=495)=1156.27, p=0 | χ²(106, N=495)=340.86, p=0 |
| χ²/df ratio | < 3.00 | 5.26 | 3.22 |
## lavaan 0.6.17 ended normally after 33 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 47
##
## Number of observations 495
##
## Model Test User Model:
##
## Test statistic 340.863
## Degrees of freedom 106
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## f1 =~
## frnss_scn1_s_3 1.196 0.061 19.737 0.000
## frnss_scn1_s_4 1.286 0.060 21.280 0.000
## frnss_scn1_s_5 1.118 0.061 18.411 0.000
## f2 =~
## frnss_scn1_s_8 1.269 0.062 20.338 0.000
## frnss_scn1__11 0.954 0.062 15.428 0.000
## frnss_scn1__12 1.161 0.062 18.642 0.000
## frnss_scn1__13 1.156 0.057 20.214 0.000
## f3 =~
## frnss_scn1_s_9 1.194 0.075 15.940 0.000
## frnss_scn1__10 1.373 0.075 18.372 0.000
## f4 =~
## frnss_scn1__14 1.186 0.069 17.231 0.000
## frnss_scn1__15 1.235 0.069 17.917 0.000
## frnss_scn1__17 1.084 0.071 15.321 0.000
## f5 =~
## frnss_scn1__19 1.453 0.067 21.824 0.000
## frnss_scn1__20 1.412 0.057 24.582 0.000
## frnss_scn1__21 1.364 0.061 22.247 0.000
## frnss_scn1__22 1.281 0.061 20.836 0.000
## frnss_scn1__23 1.488 0.063 23.472 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .fairness_scen1_scale_4 ~~
## .frnss_scn1_s_8 0.145 0.055 2.632 0.008
## .fairness_scen1_scale_3 ~~
## .frnss_scn1_s_5 0.209 0.062 3.358 0.001
## .fairness_scen1_scale_19 ~~
## .frnss_scn1__23 0.154 0.055 2.791 0.005
## f1 ~~
## f2 0.904 0.020 45.228 0.000
## f3 0.087 0.055 1.577 0.115
## f4 0.186 0.054 3.420 0.001
## f5 0.597 0.036 16.648 0.000
## f2 ~~
## f3 0.082 0.054 1.507 0.132
## f4 0.211 0.053 3.942 0.000
## f5 0.760 0.026 29.540 0.000
## f3 ~~
## f4 0.650 0.040 16.144 0.000
## f5 -0.114 0.052 -2.204 0.028
## f4 ~~
## f5 0.050 0.053 0.948 0.343
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .frnss_scn1_s_3 0.817 0.077 10.555 0.000
## .frnss_scn1_s_4 0.730 0.075 9.783 0.000
## .frnss_scn1_s_5 0.906 0.079 11.421 0.000
## .frnss_scn1_s_8 0.953 0.077 12.464 0.000
## .frnss_scn1__11 1.274 0.088 14.465 0.000
## .frnss_scn1__12 1.087 0.081 13.480 0.000
## .frnss_scn1__13 0.817 0.064 12.702 0.000
## .frnss_scn1_s_9 1.194 0.126 9.494 0.000
## .frnss_scn1__10 0.670 0.139 4.813 0.000
## .frnss_scn1__14 1.110 0.105 10.575 0.000
## .frnss_scn1__15 1.030 0.106 9.748 0.000
## .frnss_scn1__17 1.384 0.112 12.353 0.000
## .frnss_scn1__19 1.000 0.080 12.500 0.000
## .frnss_scn1__20 0.558 0.050 11.087 0.000
## .frnss_scn1__21 0.839 0.065 12.905 0.000
## .frnss_scn1__22 0.955 0.070 13.560 0.000
## .frnss_scn1__23 0.770 0.066 11.597 0.000
## f1 1.000
## f2 1.000
## f3 1.000
## f4 1.000
## f5 1.000- Chi-square ratio (χ²/df): ideally < 2.00, acceptable 2-5 [Alavi et al. 2020]
- Comparative Fit Index (CFI): >.90 [Bentler, 1990, Hooper et al. 2008]
- Root Mean Square Error of Approximation (RMSEA): ideally <.05, acceptable 0.05 - 0.08 [Fabrigar et al. 1999] [see also Browne & Cudeck, 1992; Steiger, 1989]
- Standardized Root Mean Residual (SRMR): <.08 [Hu and Bentler, 1999]
- Tucker-Lewis-Index (TLI): >0.90 [Bentler, 1990]
Sup5.5.1: CFA result - all loadings
Table shows Unstandardized Factor Loadings, Unstandardized Standard Error, Unstandardized Error Variance, Standardized Factor Loadings and Standardized Error Variance for S2
| Factor | Indicator | Unstd_Fa_loading | Unstd_SE | Unstd_Error_Var | Std_Fa_loading | Std_Error_Var |
|---|---|---|---|---|---|---|
| f1 | fairness_scen1_scale_3 | 1.1958907 | 0.0605916 | 0.8171037 | 0.7977467 | 0.3636003 |
| f1 | fairness_scen1_scale_4 | 1.2856622 | 0.0604160 | 0.7300401 | 0.8328520 | 0.3063576 |
| f1 | fairness_scen1_scale_5 | 1.1181403 | 0.0607315 | 0.9060200 | 0.7614580 | 0.4201817 |
| f2 | fairness_scen1_scale_8 | 1.2688942 | 0.0623903 | 0.9534944 | 0.7925039 | 0.3719376 |
| f2 | fairness_scen1_scale_11 | 0.9537117 | 0.0618177 | 1.2737828 | 0.6454395 | 0.5834078 |
| f2 | fairness_scen1_scale_12 | 1.1608980 | 0.0622747 | 1.0870757 | 0.7439881 | 0.4464817 |
| f2 | fairness_scen1_scale_13 | 1.1556556 | 0.0571706 | 0.8167502 | 0.7877312 | 0.3794796 |
| f3 | fairness_scen1_scale_9 | 1.1942707 | 0.0749219 | 1.1935866 | 0.7378413 | 0.4555902 |
| f3 | fairness_scen1_scale_10 | 1.3731292 | 0.0747417 | 0.6699417 | 0.8589736 | 0.2621644 |
| f4 | fairness_scen1_scale_14 | 1.1858387 | 0.0688215 | 1.1099996 | 0.7475701 | 0.4411389 |
| f4 | fairness_scen1_scale_15 | 1.2345662 | 0.0689033 | 1.0297449 | 0.7725250 | 0.4032051 |
| f4 | fairness_scen1_scale_17 | 1.0841801 | 0.0707650 | 1.3842634 | 0.6776510 | 0.5407892 |
| f5 | fairness_scen1_scale_19 | 1.4528171 | 0.0665696 | 0.9999241 | 0.8237373 | 0.3214568 |
| f5 | fairness_scen1_scale_20 | 1.4123805 | 0.0574560 | 0.5576755 | 0.8840347 | 0.2184826 |
| f5 | fairness_scen1_scale_21 | 1.3643647 | 0.0613268 | 0.8390287 | 0.8302460 | 0.3106916 |
| f5 | fairness_scen1_scale_22 | 1.2812272 | 0.0614911 | 0.9548328 | 0.7951377 | 0.3677560 |
| f5 | fairness_scen1_scale_23 | 1.4883460 | 0.0634096 | 0.7701757 | 0.8614029 | 0.2579851 |
Sup6: Analysis of study 3
Sup6.1: CFA result - original scale
| Fit_indices | optimal | Fit_values_S3 |
|---|---|---|
| RMSEA | ≤ 0.06 | 0.073 (0.07,0.08) |
| SRMR | < 0.08 | 0.075 |
| TLI | ≥ 0.95 | 0.914 |
| CFI | ≥ 0.95 | 0.926 |
| χ² | < 0.05 | χ²(220, N=448)=746.43, p=0 |
| χ²/df ratio | < 3.00 | 3.39 |
## lavaan 0.6.17 ended normally after 42 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 56
##
## Number of observations 448
##
## Model Test User Model:
##
## Test statistic 746.426
## Degrees of freedom 220
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## f1 =~
## fairness_scl_3 0.704 0.044 16.150 0.000
## fairness_scl_4 0.690 0.041 16.677 0.000
## fairness_scl_5 0.641 0.041 15.770 0.000
## fairness_scl_6 0.545 0.045 12.218 0.000
## fairness_scl_7 0.700 0.041 17.217 0.000
## f2 =~
## fairness_scl_8 0.678 0.040 17.024 0.000
## fairness_scl_9 0.529 0.041 12.983 0.000
## fairnss_scl_10 0.404 0.039 10.250 0.000
## fairnss_scl_11 0.682 0.037 18.190 0.000
## fairnss_scl_12 0.709 0.036 19.682 0.000
## fairnss_scl_13 0.612 0.048 12.818 0.000
## f3 =~
## fairnss_scl_14 1.045 0.041 25.643 0.000
## fairnss_scl_15 1.014 0.044 23.186 0.000
## fairnss_scl_16 0.925 0.043 21.297 0.000
## fairnss_scl_17 1.062 0.044 23.964 0.000
## fairnss_scl_18 0.976 0.047 20.690 0.000
## f4 =~
## fairnss_scl_19 0.949 0.038 24.854 0.000
## fairnss_scl_20 0.905 0.036 24.946 0.000
## fairnss_scl_21 0.809 0.039 20.576 0.000
## fairnss_scl_22 0.936 0.039 24.037 0.000
## fairnss_scl_23 0.955 0.038 24.929 0.000
## f5 =~
## fairnss_scl_25 0.497 0.060 8.222 0.000
## fairnss_scl_26 0.926 0.059 15.710 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## f1 ~~
## f2 0.858 0.024 36.452 0.000
## f3 0.339 0.048 7.022 0.000
## f4 0.586 0.037 15.685 0.000
## f5 0.355 0.055 6.459 0.000
## f2 ~~
## f3 0.370 0.046 8.008 0.000
## f4 0.550 0.038 14.337 0.000
## f5 0.366 0.054 6.805 0.000
## f3 ~~
## f4 0.061 0.050 1.226 0.220
## f5 -0.120 0.054 -2.221 0.026
## f4 ~~
## f5 0.813 0.043 18.859 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .fairness_scl_3 0.506 0.040 12.753 0.000
## .fairness_scl_4 0.441 0.035 12.522 0.000
## .fairness_scl_5 0.449 0.035 12.906 0.000
## .fairness_scl_6 0.637 0.046 13.926 0.000
## .fairness_scl_7 0.411 0.033 12.259 0.000
## .fairness_scl_8 0.410 0.032 12.712 0.000
## .fairness_scl_9 0.525 0.038 13.907 0.000
## .fairnss_scl_10 0.538 0.037 14.366 0.000
## .fairnss_scl_11 0.335 0.028 12.163 0.000
## .fairnss_scl_12 0.273 0.024 11.225 0.000
## .fairnss_scl_13 0.726 0.052 13.941 0.000
## .fairnss_scl_14 0.177 0.019 9.527 0.000
## .fairnss_scl_15 0.317 0.026 12.112 0.000
## .fairnss_scl_16 0.390 0.030 13.059 0.000
## .fairnss_scl_17 0.290 0.025 11.521 0.000
## .fairnss_scl_18 0.487 0.037 13.272 0.000
## .fairnss_scl_19 0.190 0.016 11.659 0.000
## .fairnss_scl_20 0.168 0.015 11.575 0.000
## .fairnss_scl_21 0.347 0.025 13.671 0.000
## .fairnss_scl_22 0.227 0.018 12.285 0.000
## .fairnss_scl_23 0.188 0.016 11.591 0.000
## .fairnss_scl_25 1.257 0.087 14.399 0.000
## .fairnss_scl_26 0.237 0.084 2.812 0.005
## f1 1.000
## f2 1.000
## f3 1.000
## f4 1.000
## f5 1.000table 6.2 = Sup6.2: CFA result - optimized scale and comparison of fit indices
| Fit_indices | optimal | Fit_values_S2_original | Fit_values_S3_original. | Fit_values_S2_optimized | Fit_values_S3_optimized. |
|---|---|---|---|---|---|
| RMSEA | ≤ 0.06 | 0.093 (0.09,0.1) | 0.073 (0.07,0.08) | 0.067 (0.06,0.07) | 0.058 (0.05,0.07) |
| SRMR | < 0.08 | 0.116 | 0.075 | 0.06 | 0.049 |
| TLI | ≥ 0.95 | 0.845 | 0.914 | 0.94 | 0.961 |
| CFI | ≥ 0.95 | 0.865 | 0.926 | 0.953 | 0.97 |
| χ² | < 0.05 | χ²(220, N=495)=1156.27, p=0 | χ²(220, N=448)=746.43, p=0 | χ²(106, N=495)=340.86, p=0 | χ²(106, N=448)=264.45, p=0 |
| χ²/df ratio | < 3.00 | 5.26 | 3.39 | 3.22 | 2.49 |
## lavaan 0.6.17 ended normally after 37 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 47
##
## Number of observations 448
##
## Model Test User Model:
##
## Test statistic 264.452
## Degrees of freedom 106
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## f1 =~
## fairness_scl_2 0.705 0.047 15.038 0.000
## fairness_scl_3 0.662 0.043 15.566 0.000
## fairness_scl_4 0.631 0.044 14.399 0.000
## f2 =~
## fairness_scl_5 0.669 0.040 16.777 0.000
## fairness_scl_6 0.673 0.038 17.845 0.000
## fairness_scl_7 0.697 0.036 19.119 0.000
## fairness_scl_8 0.624 0.048 13.129 0.000
## f3 =~
## fairness_scl_9 0.749 0.041 18.079 0.000
## fairnss_scl_10 0.608 0.039 15.647 0.000
## f4 =~
## fairnss_scl_11 1.061 0.041 25.891 0.000
## fairnss_scl_12 1.008 0.044 22.716 0.000
## fairnss_scl_13 1.039 0.045 22.878 0.000
## f5 =~
## fairnss_scl_14 0.945 0.039 24.533 0.000
## fairnss_scl_15 0.905 0.036 24.907 0.000
## fairnss_scl_16 0.810 0.039 20.566 0.000
## fairnss_scl_17 0.939 0.039 24.120 0.000
## fairnss_scl_18 0.956 0.039 24.812 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .fairness_scale_3 ~~
## .fairness_scl_5 0.134 0.027 5.007 0.000
## .fairness_scale_2 ~~
## .fairness_scl_4 0.012 0.033 0.362 0.717
## .fairness_scale_14 ~~
## .fairnss_scl_18 -0.003 0.014 -0.247 0.805
## f1 ~~
## f2 0.890 0.028 31.788 0.000
## f3 0.425 0.055 7.714 0.000
## f4 0.353 0.051 6.867 0.000
## f5 0.599 0.041 14.733 0.000
## f2 ~~
## f3 0.683 0.039 17.286 0.000
## f4 0.319 0.049 6.502 0.000
## f5 0.599 0.037 16.352 0.000
## f3 ~~
## f4 0.474 0.046 10.371 0.000
## f5 0.232 0.053 4.415 0.000
## f4 ~~
## f5 0.056 0.050 1.130 0.259
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .fairness_scl_2 0.506 0.046 10.892 0.000
## .fairness_scl_3 0.460 0.039 11.930 0.000
## .fairness_scl_4 0.461 0.041 11.306 0.000
## .fairness_scl_5 0.417 0.033 12.736 0.000
## .fairness_scl_6 0.346 0.028 12.267 0.000
## .fairness_scl_7 0.291 0.025 11.471 0.000
## .fairness_scl_8 0.711 0.051 13.870 0.000
## .fairness_scl_9 0.245 0.039 6.356 0.000
## .fairnss_scl_10 0.331 0.032 10.376 0.000
## .fairnss_scl_11 0.143 0.024 6.057 0.000
## .fairnss_scl_12 0.330 0.030 11.128 0.000
## .fairnss_scl_13 0.338 0.031 10.945 0.000
## .fairnss_scl_14 0.196 0.019 10.412 0.000
## .fairnss_scl_15 0.168 0.015 11.079 0.000
## .fairnss_scl_16 0.347 0.026 13.565 0.000
## .fairnss_scl_17 0.221 0.019 11.875 0.000
## .fairnss_scl_18 0.186 0.018 10.167 0.000
## f1 1.000
## f2 1.000
## f3 1.000
## f4 1.000
## f5 1.000table 6.2.1 = Sup6.2.1: CFA result - all loadings
Table shows Unstandardized Factor Loadings, Unstandardized Standard Error, Unstandardized Error Variance, Standardized Factor Loadings and Standardized Error Variance for S3
| Factor | Indicator | Unstd_Fa_loading | Unstd_SE | Unstd_Error_Var | Std_Fa_loading | Std_Error_Var |
|---|---|---|---|---|---|---|
| f1 | fairness_scale_2 | 0.7045412 | 0.0468518 | 0.5060990 | 0.7036702 | 0.5048483 |
| f1 | fairness_scale_3 | 0.6620944 | 0.0425348 | 0.4602935 | 0.6984279 | 0.5121984 |
| f1 | fairness_scale_4 | 0.6312865 | 0.0438429 | 0.4611480 | 0.6808641 | 0.5364241 |
| f2 | fairness_scale_5 | 0.6688081 | 0.0398636 | 0.4166362 | 0.7195478 | 0.4822510 |
| f2 | fairness_scale_6 | 0.6733478 | 0.0377321 | 0.3464509 | 0.7528972 | 0.4331458 |
| f2 | fairness_scale_7 | 0.6965561 | 0.0364327 | 0.2908306 | 0.7907139 | 0.3747715 |
| f2 | fairness_scale_8 | 0.6239809 | 0.0475282 | 0.7107256 | 0.5949214 | 0.6460686 |
| f3 | fairness_scale_9 | 0.7485729 | 0.0414066 | 0.2448209 | 0.8342323 | 0.3040565 |
| f3 | fairness_scale_10 | 0.6078708 | 0.0388495 | 0.3311028 | 0.7262284 | 0.4725923 |
| f4 | fairness_scale_11 | 1.0612257 | 0.0409890 | 0.1431391 | 0.9419306 | 0.1127667 |
| f4 | fairness_scale_12 | 1.0075075 | 0.0443517 | 0.3302606 | 0.8686275 | 0.2454863 |
| f4 | fairness_scale_13 | 1.0393095 | 0.0454277 | 0.3383510 | 0.8726255 | 0.2385248 |
| f5 | fairness_scale_14 | 0.9454113 | 0.0385370 | 0.1956017 | 0.9057874 | 0.1795492 |
| f5 | fairness_scale_15 | 0.9052189 | 0.0363437 | 0.1678566 | 0.9110326 | 0.1700196 |
| f5 | fairness_scale_16 | 0.8098653 | 0.0393782 | 0.3468174 | 0.8087745 | 0.3458838 |
| f5 | fairness_scale_17 | 0.9385535 | 0.0389115 | 0.2214888 | 0.8939126 | 0.2009203 |
| f5 | fairness_scale_18 | 0.9560652 | 0.0385331 | 0.1860591 | 0.9115228 | 0.1691262 |
Sup6.3: Pathplot CFA results optimized scale
Study 3
Sup6.4: Evaluate the reliability of the items using Cronbach’s alpha and McDonald’s omega
| Scale component | alpha S3 | omega S3 | alpha S4 | omega S4 |
|---|---|---|---|---|
| Full Scale | 0.90 | 0.94 | 0.91 | 0.93 |
| F1 - Perceived Consistency | 0.75 | 0.76 | 0.75 | 0.76 |
| F2 - Perceived Equity | 0.80 | 0.84 | 0.82 | 0.84 |
| F3 - Perceived Group Bias | 0.75 | too few items to compute | 0.72 | too few items to compute |
| F4 - Perceived Manipulability | 0.92 | 0.92 | 0.81 | 0.82 |
| F5 - Perceived (Explanatory) Transparency | 0.95 | 0.95 | 0.92 | 0.93 |
Sup7: Analysis of study 4
Sup7.1: CFA result - optimized scale and comparison of fit indices
| Fit_indices | optimal | Fit_S2_original | Fit_S2_optimized | Fit_S3_optimized | Fit_S4_optimized |
|---|---|---|---|---|---|
| RMSEA | ≤ 0.06 | 0.093 (0.09,0.1) | 0.067 (0.06,0.07) | 0.058 (0.05,0.07) | 0.055 (0.04,0.07) |
| SRMR | < 0.08 | 0.116 | 0.06 | 0.049 | 0.043 |
| TLI | ≥ 0.95 | 0.845 | 0.94 | 0.961 | 0.953 |
| CFI | ≥ 0.95 | 0.865 | 0.953 | 0.97 | 0.964 |
| χ² | < 0.05 | χ²(220, N=495)=1156.27, p=0 | χ²(106, N=495)=340.86, p=0 | χ²(106, N=448)=264.45, p=0 | χ²(106, N=331)=210.2, p=0 |
| χ²/df ratio | < 3.00 | 5.26 | 3.22 | 2.49 | 1.98 |
## lavaan 0.6.17 ended normally after 28 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 47
##
## Used Total
## Number of observations 328 331
##
## Model Test User Model:
##
## Test statistic 210.202
## Degrees of freedom 106
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## f1 =~
## fairness_scl_2 0.810 0.058 14.018 0.000
## fairness_scl_3 0.984 0.064 15.367 0.000
## fairness_scl_4 0.616 0.062 9.973 0.000
## f2 =~
## fairness_scl_5 0.835 0.061 13.792 0.000
## fairness_scl_6 0.850 0.060 14.073 0.000
## fairness_scl_7 0.789 0.059 13.470 0.000
## fairness_scl_8 0.984 0.059 16.545 0.000
## f3 =~
## fairness_scl_9 0.977 0.070 13.910 0.000
## fairnss_scl_10 0.870 0.068 12.763 0.000
## f4 =~
## fairnss_scl_11 0.952 0.061 15.646 0.000
## fairnss_scl_12 0.908 0.058 15.562 0.000
## fairnss_scl_13 0.806 0.060 13.363 0.000
## f5 =~
## fairnss_scl_14 1.048 0.060 17.561 0.000
## fairnss_scl_15 1.116 0.055 20.235 0.000
## fairnss_scl_16 1.013 0.062 16.232 0.000
## fairnss_scl_17 0.988 0.057 17.268 0.000
## fairnss_scl_18 1.049 0.059 17.817 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .fairness_scale_3 ~~
## .fairness_scl_5 0.072 0.048 1.496 0.135
## .fairness_scale_2 ~~
## .fairness_scl_4 0.037 0.048 0.767 0.443
## .fairness_scale_14 ~~
## .fairnss_scl_18 0.104 0.040 2.597 0.009
## f1 ~~
## f2 0.866 0.033 26.097 0.000
## f3 0.538 0.060 8.956 0.000
## f4 0.363 0.063 5.766 0.000
## f5 0.649 0.044 14.643 0.000
## f2 ~~
## f3 0.732 0.045 16.156 0.000
## f4 0.460 0.056 8.219 0.000
## f5 0.634 0.042 15.101 0.000
## f3 ~~
## f4 0.431 0.062 6.954 0.000
## f5 0.318 0.062 5.095 0.000
## f4 ~~
## f5 0.326 0.058 5.631 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .fairness_scl_2 0.553 0.060 9.243 0.000
## .fairness_scl_3 0.609 0.072 8.394 0.000
## .fairness_scl_4 0.801 0.072 11.198 0.000
## .fairness_scl_5 0.723 0.066 11.024 0.000
## .fairness_scl_6 0.711 0.065 11.004 0.000
## .fairness_scl_7 0.697 0.062 11.229 0.000
## .fairness_scl_8 0.553 0.058 9.602 0.000
## .fairness_scl_9 0.590 0.092 6.376 0.000
## .fairnss_scl_10 0.708 0.084 8.406 0.000
## .fairnss_scl_11 0.496 0.067 7.448 0.000
## .fairnss_scl_12 0.462 0.061 7.566 0.000
## .fairnss_scl_13 0.658 0.066 10.039 0.000
## .fairnss_scl_14 0.537 0.053 10.048 0.000
## .fairnss_scl_15 0.316 0.039 8.128 0.000
## .fairnss_scl_16 0.687 0.062 11.091 0.000
## .fairnss_scl_17 0.523 0.049 10.644 0.000
## .fairnss_scl_18 0.509 0.051 9.916 0.000
## f1 1.000
## f2 1.000
## f3 1.000
## f4 1.000
## f5 1.000table 7.1.1 = Sup7.1.1: CFA result - all loadings
Table shows Unstandardized Factor Loadings, Unstandardized Standard Error, Unstandardized Error Variance, Standardized Factor Loadings and Standardized Error Variance for S4
| Factor | Indicator | Unstd_Fa_loading | Unstd_SE | Unstd_Error_Var | Std_Fa_loading | Std_Error_Var |
|---|---|---|---|---|---|---|
| f1 | fairness_scale_2 | 0.8103472 | 0.0578087 | 0.5533967 | 0.7366612 | 0.4573302 |
| f1 | fairness_scale_3 | 0.9835118 | 0.0640030 | 0.6085038 | 0.7834822 | 0.3861557 |
| f1 | fairness_scale_4 | 0.6160430 | 0.0617684 | 0.8012985 | 0.5669196 | 0.6786021 |
| f2 | fairness_scale_5 | 0.8350751 | 0.0605476 | 0.7230109 | 0.7006903 | 0.5090331 |
| f2 | fairness_scale_6 | 0.8497557 | 0.0603819 | 0.7108326 | 0.7098777 | 0.4960737 |
| f2 | fairness_scale_7 | 0.7889565 | 0.0585694 | 0.6966934 | 0.6869208 | 0.5281398 |
| f2 | fairness_scale_8 | 0.9837918 | 0.0594619 | 0.5528257 | 0.7977842 | 0.3635404 |
| f3 | fairness_scale_9 | 0.9773755 | 0.0702658 | 0.5896137 | 0.7863476 | 0.3816575 |
| f3 | fairness_scale_10 | 0.8699000 | 0.0681563 | 0.7078690 | 0.7188041 | 0.4833206 |
| f4 | fairness_scale_11 | 0.9517472 | 0.0608299 | 0.4955664 | 0.8039744 | 0.3536252 |
| f4 | fairness_scale_12 | 0.9075324 | 0.0583164 | 0.4619946 | 0.8004009 | 0.3593583 |
| f4 | fairness_scale_13 | 0.8057551 | 0.0602977 | 0.6584534 | 0.7046117 | 0.5035223 |
| f5 | fairness_scale_14 | 1.0483742 | 0.0597000 | 0.5374377 | 0.8195111 | 0.3284015 |
| f5 | fairness_scale_15 | 1.1160285 | 0.0551530 | 0.3156694 | 0.8931976 | 0.2021981 |
| f5 | fairness_scale_16 | 1.0126282 | 0.0623831 | 0.6870690 | 0.7738141 | 0.4012117 |
| f5 | fairness_scale_17 | 0.9876407 | 0.0571956 | 0.5226230 | 0.8069280 | 0.3488672 |
| f5 | fairness_scale_18 | 1.0493756 | 0.0588966 | 0.5087146 | 0.8270486 | 0.3159907 |
Sup7.2: Pathplot CFA results optimized scale
Study 4
Sup7.3 = Sup6.4: Evaluate the reliability of the items using Cronbach’s alpha and McDonald’s omega
| Scale component | alpha S3 | omega S3 | alpha S4 | omega S4 |
|---|---|---|---|---|
| Full Scale | 0.90 | 0.94 | 0.91 | 0.93 |
| F1 - Perceived Consistency | 0.75 | 0.76 | 0.75 | 0.76 |
| F2 - Perceived Equity | 0.80 | 0.84 | 0.82 | 0.84 |
| F3 - Perceived Group Bias | 0.75 | too few items to compute | 0.72 | too few items to compute |
| F4 - Perceived Manipulability | 0.92 | 0.92 | 0.81 | 0.82 |
| F5 - Perceived (Explanatory) Transparency | 0.95 | 0.95 | 0.92 | 0.93 |
Note on item numbering
see also uploaded excel file
Sup8: Overview of measurement invariance indices
| MI indice | Cut off | MI across scenarios S3 | MI across conditions S4 | MI across S1 and S3 (ENG) | MI across S2 and S4 (GER) | MI across S3 and S4 | MI across S1,S2,S3 and S4 |
|---|---|---|---|---|---|---|---|
| Configural | |||||||
| CFI | > .95 | 0.989 | 1.000 | 0.985 | 0.999 | 1.000 | 0.992 |
| TLI | > .95 | 0.987 | 1.054 | 0.981 | 0.999 | 1.006 | 0.990 |
| RMSEA | < .06 | 0.034 | 0.000 | 0.042 | 0.012 | 0.000 | 0.032 |
| Metric | |||||||
| ΔCFI | < .01 | 0.007 | 0.000 | 0.005 | 0.002 | 0.000 | 0.007 |
| Δχ2 | Δχ²(24)=81.69, p<.001 | Δχ²(36)=28.97, p=0.791 | Δχ²(12)=54.59, p<.001 | Δχ²(12)=28.45, p=0.005 | Δχ²(12)=16.74, p=0.16 | Δχ²(36)=143.71, p<.001 | |
| Scalar | |||||||
| ΔCFI | < .01 | 0.018 | 0.000 | 0.010 | 0.001 | 0.009 | 0.010 |
| Δχ2 | Δχ²(24)=403.15, p<.001 | Δχ²(36)=26.75, p=0.869 | Δχ²(12)=142.02, p<.001 | Δχ²(12)=48.5, p<.001 | Δχ²(12)=266.8, p<.001 | Δχ²(36)=453.65, p<.001 |
Sup9: Quantitative analysis
Sup9.1: Fairness subscales in correlation with other scales in study 2
Note: The analysis results presented below have been conducted
using the optimized scale (17 items) in Study 2. And correlated the
individual subscales with attitudes to AI, propensity to trust and
justice sensitivity.
Sup9.2: subscale performance in scenarios of study 3
Note: The analysis results presented below have been conducted using the optimized scale (17 items) in Study 3.
Here you find mean scores for the individual subscales in each scenario in S3.
| Subscales | Scenario_1_FAIR | Scenario_2_DISCRIMNATORY | Scenario_3_HIGH.ERROR |
|---|---|---|---|
| Provided scenario | The AI focuses on a fair selection procedure. It aims to ensure transparency in decision-making and follows predefined criteria and guidelines. Its decision-making is based on consistent and impartial criteria and has been thoroughly evaluated and approved by an independent assessment. | The AI exhibits discriminatory tendencies, disproportionately favoring certain groups over others. Its decision-making process tends to reinforce biases present in the training data, often leading to an acceptance of individuals mainly due to the fact, that they are members of a certain groups. | The AI depicts a high error rate in its decision-making process. Despite efforts to follow predefined criteria and guidelines, it frequently produces inaccurate and unreliable results thereby deciding sometimes for individuals who did not deserve it or sometimes rejecting individuals who would in reality deserve it. |
| F1 (Perceived Consistency) | 5.38 ± 0.98 | 3.48 ± 1.26 | 2.54 ± 1.21 |
| F2 (Perceived Equity) | 4.97 ± 1.07 | 2.37 ± 1.08 | 2.84 ± 1.14 |
| F3 (Perceived Group Bias Assessment) | 3.13 ± 1.35 | 1.76 ± 1.05 | 3.54 ± 1.41 |
| F2+F3 (Perceived Group discrimination) | 4.05 ± 1.3 | 2.07 ± 0.43 | 3.19 ± 0.49 |
| F4 (Perceived Influence Vulnerability) | 3.93 ± 1.38 | 3 ± 1.28 | 3.23 ± 1.3 |
| F5 (Perceived Explanatory Transparency) | 4.57 ± 1.25 | 3.39 ± 1.2 | 2.78 ± 1.15 |
Note for the graphic below:
Fig3. Mean subscale scores
in S2’s mostly fair scenario and S3’s fair, discriminatory, and
high‐error scenarios. Error bars represent standard deviations. Note:
The dot plot is presented as a descriptive summary only. Formal
inferential comparisons were conducted via separate one‐sided t-tests
comparing each S3 condition against the S2 baseline. Significance
brackets denote p-values; “ns” indicates non-significant
differences.
One-sided t-test comparisons of mean subscale scores for S3
conditions against the S2 baseline.
One-way ANOVA results for mean
subscale scores among the three S3 conditions
| Subscale | S3_Condition | estimate | statistic | parameter | mean_diff | p.value | conf.low | conf.high |
|---|---|---|---|---|---|---|---|---|
| F1 - Perceived Consistency | 2 FAIR AI scen. S3 | 0.7146059 | 9.4461364 | 904.9218 | NA | 1.0000000 | -Inf | 0.8391676 |
| F1 - Perceived Consistency | 3 DISCRIMNATORY AI scen. | -1.1864358 | -14.0744996 | 939.1998 | NA | 0.0000000 | -Inf | -1.0476429 |
| F1 - Perceived Consistency | 4 HIGH ERROR AI scen. | -2.1239358 | -25.6669448 | 940.9688 | NA | 0.0000000 | -Inf | -1.9876903 |
| F2 - Perceived Equity | 2 FAIR AI scen. S3 | 0.7481489 | 9.9170889 | 938.0258 | NA | 1.0000000 | -Inf | 0.8723599 |
| F2 - Perceived Equity | 3 DISCRIMNATORY AI scen. | -1.8534136 | -24.4301983 | 939.1879 | NA | 0.0000000 | -Inf | -1.7285025 |
| F2 - Perceived Equity | 4 HIGH ERROR AI scen. | -1.3824315 | -17.8017505 | 940.9659 | NA | 0.0000000 | -Inf | -1.2545711 |
| F3 - Perceived Group Bias | 2 FAIR AI scen. S3 | -0.6037631 | -6.6174952 | 940.5480 | NA | 0.0000000 | -Inf | -0.4535429 |
| F3 - Perceived Group Bias | 3 DISCRIMNATORY AI scen. | 2.5033798 | 30.4411625 | 899.1546 | NA | 1.0000000 | -Inf | 2.6387866 |
| F3 - Perceived Group Bias | 4 HIGH ERROR AI scen. | 0.7265941 | 7.7727221 | 936.3175 | NA | 1.0000000 | -Inf | 0.8805073 |
| F4 - Perceived Manipulability | 2 FAIR AI scen. S3 | -0.3495430 | -3.9546883 | 922.4524 | NA | 0.0000413 | -Inf | -0.2040132 |
| F4 - Perceived Manipulability | 3 DISCRIMNATORY AI scen. | 0.7248617 | 8.5432293 | 937.1242 | NA | 1.0000000 | -Inf | 0.8645596 |
| F4 - Perceived Manipulability | 4 HIGH ERROR AI scen. | 0.4882546 | 5.6964870 | 934.3858 | NA | 1.0000000 | -Inf | 0.6293774 |
| F5 - Perceived (Explanatory) Transparency | 2 FAIR AI scen. S3 | 0.6657197 | 7.5283628 | 937.9806 | NA | 1.0000000 | -Inf | 0.8113150 |
| F5 - Perceived (Explanatory) Transparency | 3 DISCRIMNATORY AI scen. | -0.5101732 | -5.8661715 | 932.7166 | NA | 0.0000000 | -Inf | -0.3669802 |
| F5 - Perceived (Explanatory) Transparency | 4 HIGH ERROR AI scen. | -1.1208874 | -13.1189165 | 924.0148 | NA | 0.0000000 | -Inf | -0.9802092 |
| Overall Fairness Score | 2 FAIR AI scen. S3 | 0.2669416 | 5.5177817 | 759.5529 | NA | 1.0000000 | -Inf | 0.3466143 |
| Overall Fairness Score | 3 DISCRIMNATORY AI scen. | -0.0324482 | -0.6613034 | 784.9723 | NA | 0.2543059 | -Inf | 0.0483553 |
| Overall Fairness Score | 4 HIGH ERROR AI scen. | -0.6505732 | -12.2885736 | 891.8565 | NA | 0.0000000 | -Inf | -0.5634020 |
| Subscale | df | denom_df | sumsq | meansq | statistic | p.value |
|---|---|---|---|---|---|---|
| F1 - Perceived Consistency | 2 | 1341 | 1874.1609 | 937.08044 | 701.0282 | 0 |
| F2 - Perceived Equity | 2 | 1341 | 1721.7124 | 860.85621 | 717.5243 | 0 |
| F3 - Perceived Group Bias | 2 | 1341 | 2177.4524 | 1088.72619 | 663.4442 | 0 |
| F4 - Perceived Manipulability | 2 | 1341 | 285.5602 | 142.78009 | 81.6251 | 0 |
| F5 - Perceived (Explanatory) Transparency | 2 | 1341 | 738.8507 | 369.42536 | 254.9457 | 0 |
| Overall Fairness Score | 2 | 1341 | 196.1563 | 98.07813 | 305.3305 | 0 |
Below you find the full ANOVA results for each subscale of S3
## [1] "ANOVA results and Tukey's HSD test - Scenario 1 FAIR AI"## Df Sum Sq Mean Sq F value Pr(>F)
## Subscale 4 1408 351.9 238.1 <2e-16 ***
## Residuals 2235 3303 1.5
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = mean_values ~ Subscale, data = df_scn1)
##
## $Subscale
## diff
## F2 - Perceived Equity-F1 - Perceived Consistency -0.4073661
## F3 - Perceived Group Bias Assessment-F1 - Perceived Consistency -2.2466518
## F4 - Perceived Influence Vulnerability-F1 - Perceived Consistency -1.4486607
## F5 - Perceived Explanatory Transparency-F1 - Perceived Consistency -0.8084821
## F3 - Perceived Group Bias Assessment-F2 - Perceived Equity -1.8392857
## F4 - Perceived Influence Vulnerability-F2 - Perceived Equity -1.0412946
## F5 - Perceived Explanatory Transparency-F2 - Perceived Equity -0.4011161
## F4 - Perceived Influence Vulnerability-F3 - Perceived Group Bias Assessment 0.7979911
## F5 - Perceived Explanatory Transparency-F3 - Perceived Group Bias Assessment 1.4381696
## F5 - Perceived Explanatory Transparency-F4 - Perceived Influence Vulnerability 0.6401786
## lwr
## F2 - Perceived Equity-F1 - Perceived Consistency -0.6291119
## F3 - Perceived Group Bias Assessment-F1 - Perceived Consistency -2.4683976
## F4 - Perceived Influence Vulnerability-F1 - Perceived Consistency -1.6704065
## F5 - Perceived Explanatory Transparency-F1 - Perceived Consistency -1.0302280
## F3 - Perceived Group Bias Assessment-F2 - Perceived Equity -2.0610315
## F4 - Perceived Influence Vulnerability-F2 - Perceived Equity -1.2630405
## F5 - Perceived Explanatory Transparency-F2 - Perceived Equity -0.6228619
## F4 - Perceived Influence Vulnerability-F3 - Perceived Group Bias Assessment 0.5762453
## F5 - Perceived Explanatory Transparency-F3 - Perceived Group Bias Assessment 1.2164238
## F5 - Perceived Explanatory Transparency-F4 - Perceived Influence Vulnerability 0.4184328
## upr
## F2 - Perceived Equity-F1 - Perceived Consistency -0.1856203
## F3 - Perceived Group Bias Assessment-F1 - Perceived Consistency -2.0249060
## F4 - Perceived Influence Vulnerability-F1 - Perceived Consistency -1.2269149
## F5 - Perceived Explanatory Transparency-F1 - Perceived Consistency -0.5867363
## F3 - Perceived Group Bias Assessment-F2 - Perceived Equity -1.6175399
## F4 - Perceived Influence Vulnerability-F2 - Perceived Equity -0.8195488
## F5 - Perceived Explanatory Transparency-F2 - Perceived Equity -0.1793703
## F4 - Perceived Influence Vulnerability-F3 - Perceived Group Bias Assessment 1.0197369
## F5 - Perceived Explanatory Transparency-F3 - Perceived Group Bias Assessment 1.6599155
## F5 - Perceived Explanatory Transparency-F4 - Perceived Influence Vulnerability 0.8619244
## p adj
## F2 - Perceived Equity-F1 - Perceived Consistency 5.7e-06
## F3 - Perceived Group Bias Assessment-F1 - Perceived Consistency 0.0e+00
## F4 - Perceived Influence Vulnerability-F1 - Perceived Consistency 0.0e+00
## F5 - Perceived Explanatory Transparency-F1 - Perceived Consistency 0.0e+00
## F3 - Perceived Group Bias Assessment-F2 - Perceived Equity 0.0e+00
## F4 - Perceived Influence Vulnerability-F2 - Perceived Equity 0.0e+00
## F5 - Perceived Explanatory Transparency-F2 - Perceived Equity 8.4e-06
## F4 - Perceived Influence Vulnerability-F3 - Perceived Group Bias Assessment 0.0e+00
## F5 - Perceived Explanatory Transparency-F3 - Perceived Group Bias Assessment 0.0e+00
## F5 - Perceived Explanatory Transparency-F4 - Perceived Influence Vulnerability 0.0e+00## [1] "ANOVA results and Tukey's HSD test - Scenario 2 DISCRIMINATORY AI"## Df Sum Sq Mean Sq F value Pr(>F)
## Subscale 4 4154 1038.6 747.3 <2e-16 ***
## Residuals 2235 3106 1.4
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = mean_values ~ Subscale, data = df_scn2)
##
## $Subscale
## diff
## F2 - Perceived Equity-F1 - Perceived Consistency -1.10788690
## F3 - Perceived Group Bias Assessment-F1 - Perceived Consistency 2.76153274
## F4 - Perceived Influence Vulnerability-F1 - Perceived Consistency 1.52678571
## F5 - Perceived Explanatory Transparency-F1 - Perceived Consistency -0.08333333
## F3 - Perceived Group Bias Assessment-F2 - Perceived Equity 3.86941964
## F4 - Perceived Influence Vulnerability-F2 - Perceived Equity 2.63467262
## F5 - Perceived Explanatory Transparency-F2 - Perceived Equity 1.02455357
## F4 - Perceived Influence Vulnerability-F3 - Perceived Group Bias Assessment -1.23474702
## F5 - Perceived Explanatory Transparency-F3 - Perceived Group Bias Assessment -2.84486607
## F5 - Perceived Explanatory Transparency-F4 - Perceived Influence Vulnerability -1.61011905
## lwr
## F2 - Perceived Equity-F1 - Perceived Consistency -1.3229203
## F3 - Perceived Group Bias Assessment-F1 - Perceived Consistency 2.5464994
## F4 - Perceived Influence Vulnerability-F1 - Perceived Consistency 1.3117524
## F5 - Perceived Explanatory Transparency-F1 - Perceived Consistency -0.2983667
## F3 - Perceived Group Bias Assessment-F2 - Perceived Equity 3.6543863
## F4 - Perceived Influence Vulnerability-F2 - Perceived Equity 2.4196393
## F5 - Perceived Explanatory Transparency-F2 - Perceived Equity 0.8095202
## F4 - Perceived Influence Vulnerability-F3 - Perceived Group Bias Assessment -1.4497804
## F5 - Perceived Explanatory Transparency-F3 - Perceived Group Bias Assessment -3.0598994
## F5 - Perceived Explanatory Transparency-F4 - Perceived Influence Vulnerability -1.8251524
## upr
## F2 - Perceived Equity-F1 - Perceived Consistency -0.8928536
## F3 - Perceived Group Bias Assessment-F1 - Perceived Consistency 2.9765661
## F4 - Perceived Influence Vulnerability-F1 - Perceived Consistency 1.7418191
## F5 - Perceived Explanatory Transparency-F1 - Perceived Consistency 0.1317000
## F3 - Perceived Group Bias Assessment-F2 - Perceived Equity 4.0844530
## F4 - Perceived Influence Vulnerability-F2 - Perceived Equity 2.8497060
## F5 - Perceived Explanatory Transparency-F2 - Perceived Equity 1.2395869
## F4 - Perceived Influence Vulnerability-F3 - Perceived Group Bias Assessment -1.0197137
## F5 - Perceived Explanatory Transparency-F3 - Perceived Group Bias Assessment -2.6298327
## F5 - Perceived Explanatory Transparency-F4 - Perceived Influence Vulnerability -1.3950857
## p adj
## F2 - Perceived Equity-F1 - Perceived Consistency 0.0000000
## F3 - Perceived Group Bias Assessment-F1 - Perceived Consistency 0.0000000
## F4 - Perceived Influence Vulnerability-F1 - Perceived Consistency 0.0000000
## F5 - Perceived Explanatory Transparency-F1 - Perceived Consistency 0.8279664
## F3 - Perceived Group Bias Assessment-F2 - Perceived Equity 0.0000000
## F4 - Perceived Influence Vulnerability-F2 - Perceived Equity 0.0000000
## F5 - Perceived Explanatory Transparency-F2 - Perceived Equity 0.0000000
## F4 - Perceived Influence Vulnerability-F3 - Perceived Group Bias Assessment 0.0000000
## F5 - Perceived Explanatory Transparency-F3 - Perceived Group Bias Assessment 0.0000000
## F5 - Perceived Explanatory Transparency-F4 - Perceived Influence Vulnerability 0.0000000## [1] "ANOVA results and Tukey's HSD test - Scenario 3 HIGH ERROR AI"## Df Sum Sq Mean Sq F value Pr(>F)
## Subscale 4 1971 492.9 316.4 <2e-16 ***
## Residuals 2235 3482 1.6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = mean_values ~ Subscale, data = df_scn3)
##
## $Subscale
## diff
## F2 - Perceived Equity-F1 - Perceived Consistency 0.30059524
## F3 - Perceived Group Bias Assessment-F1 - Perceived Consistency 1.92224702
## F4 - Perceived Influence Vulnerability-F1 - Perceived Consistency 2.22767857
## F5 - Perceived Explanatory Transparency-F1 - Perceived Consistency 0.24345238
## F3 - Perceived Group Bias Assessment-F2 - Perceived Equity 1.62165179
## F4 - Perceived Influence Vulnerability-F2 - Perceived Equity 1.92708333
## F5 - Perceived Explanatory Transparency-F2 - Perceived Equity -0.05714286
## F4 - Perceived Influence Vulnerability-F3 - Perceived Group Bias Assessment 0.30543155
## F5 - Perceived Explanatory Transparency-F3 - Perceived Group Bias Assessment -1.67879464
## F5 - Perceived Explanatory Transparency-F4 - Perceived Influence Vulnerability -1.98422619
## lwr
## F2 - Perceived Equity-F1 - Perceived Consistency 0.07292656
## F3 - Perceived Group Bias Assessment-F1 - Perceived Consistency 1.69457835
## F4 - Perceived Influence Vulnerability-F1 - Perceived Consistency 2.00000990
## F5 - Perceived Explanatory Transparency-F1 - Perceived Consistency 0.01578371
## F3 - Perceived Group Bias Assessment-F2 - Perceived Equity 1.39398311
## F4 - Perceived Influence Vulnerability-F2 - Perceived Equity 1.69941466
## F5 - Perceived Explanatory Transparency-F2 - Perceived Equity -0.28481153
## F4 - Perceived Influence Vulnerability-F3 - Perceived Group Bias Assessment 0.07776287
## F5 - Perceived Explanatory Transparency-F3 - Perceived Group Bias Assessment -1.90646332
## F5 - Perceived Explanatory Transparency-F4 - Perceived Influence Vulnerability -2.21189487
## upr
## F2 - Perceived Equity-F1 - Perceived Consistency 0.5282639
## F3 - Perceived Group Bias Assessment-F1 - Perceived Consistency 2.1499157
## F4 - Perceived Influence Vulnerability-F1 - Perceived Consistency 2.4553472
## F5 - Perceived Explanatory Transparency-F1 - Perceived Consistency 0.4711211
## F3 - Perceived Group Bias Assessment-F2 - Perceived Equity 1.8493205
## F4 - Perceived Influence Vulnerability-F2 - Perceived Equity 2.1547520
## F5 - Perceived Explanatory Transparency-F2 - Perceived Equity 0.1705258
## F4 - Perceived Influence Vulnerability-F3 - Perceived Group Bias Assessment 0.5331002
## F5 - Perceived Explanatory Transparency-F3 - Perceived Group Bias Assessment -1.4511260
## F5 - Perceived Explanatory Transparency-F4 - Perceived Influence Vulnerability -1.7565575
## p adj
## F2 - Perceived Equity-F1 - Perceived Consistency 0.0029488
## F3 - Perceived Group Bias Assessment-F1 - Perceived Consistency 0.0000000
## F4 - Perceived Influence Vulnerability-F1 - Perceived Consistency 0.0000000
## F5 - Perceived Explanatory Transparency-F1 - Perceived Consistency 0.0291545
## F3 - Perceived Group Bias Assessment-F2 - Perceived Equity 0.0000000
## F4 - Perceived Influence Vulnerability-F2 - Perceived Equity 0.0000000
## F5 - Perceived Explanatory Transparency-F2 - Perceived Equity 0.9597107
## F4 - Perceived Influence Vulnerability-F3 - Perceived Group Bias Assessment 0.0023729
## F5 - Perceived Explanatory Transparency-F3 - Perceived Group Bias Assessment 0.0000000
## F5 - Perceived Explanatory Transparency-F4 - Perceived Influence Vulnerability 0.0000000Sup9.3: correlation of subscales with optional item in study 3
Note: The analysis results presented below have been conducted using the optimized scale (17 items) in Study 3.
| factors | Scen1_FAIR | Scen2_DISCRIMINATORY | Scen3_HIGH_ERROR |
|---|---|---|---|
| F1 - Perceived Consistency | 0.54, p=0.0000 | 0.43, p=0.0000 | 0.62, p=0.0000 |
| F2 - Perceived Equity | 0.66, p=0.0000 | 0.79, p=0.0000 | 0.53, p=0.0000 |
| F3 - Perceived Group Bias | -0.51, p=0.0000 | -0.63, p=0.0000 | -0.16, p=0.0010 |
| F4 - Perceived Manipulability | -0.34, p=0.0000 | -0.14, p=0.0035 | -0.15, p=0.0011 |
| F5 - Perceived Explanatory Transparency | 0.49, p=0.0000 | 0.44, p=0.0000 | 0.53, p=0.0000 |
| Full scale | 0.67, p=0.0000 | 0.68, p=0.0000 | 0.62, p=0.0000 |