PASS 2021, v21.0.3	2024/10/30 20:23:24      1

Two-Sample T-Tests Assuming Equal Variance

Numeric Results for an Equal-Variance T-Test ─────────────────────────────────────────
δ = μ1 - μ2
Hypotheses:	H0: δ = 0   vs.   H1: δ ≠ 0

Target	Actual								
Power	Power	N1	N2	N	μ1	μ2	δ	σ	Alpha
0.8	1	2	2	4	78.22788	43.60184	34.62604	0.5	0.05

References
Chow, S.C., Shao, J., Wang, H., and Lokhnygina, Y. 2018. Sample Size Calculations in Clinical Research, Third
   Edition. Taylor & Francis/CRC. Boca Raton, Florida.
Julious, S. A. 2010. Sample Sizes for Clinical Trials. Chapman & Hall/CRC. Boca Raton, FL. 
Machin, D., Campbell, M., Fayers, P., and Pinol, A. 1997. Sample Size Tables for Clinical Studies, 2nd Edition.
   Blackwell Science. Malden, MA. 
Zar, Jerrold H. 1984. Biostatistical Analysis (Second Edition). Prentice-Hall. Englewood Cliffs, New Jersey. 

Report Definitions
Target Power is the desired power value (or values) entered in the procedure. Power is the probability of rejecting
   a false null hypothesis.
Actual Power is the power obtained in this scenario. Because N1 and N2 are discrete, this value is often (slightly)
   larger than the target power.
N1 and N2 are the number of items sampled from each population.
N = N1 + N2 is the total sample size.
μ1 and μ2 are the assumed population means.
δ = μ1 - μ2 is the difference between population means at which power and sample size calculations are made.
σ is the assumed population standard deviation for each of the two groups.
Alpha is the probability of rejecting a true null hypothesis.

Summary Statements ─────────────────────────────────────────────────────────
Group sample sizes of 2 and 2 achieve 100% power to reject the null hypothesis of equal means when the
population mean difference is μ1 - μ2 = 78.22788 - 43.60184 = 34.62604 with a standard deviation for both
groups of 0.5 and with a significance level (alpha) of 0.05 using a two-sided two-sample equal-variance t-test.

Dropout-Inflated Sample Size ────────────────────────────────────────────────────

						Dropout-Inflated		Expected
						Enrollment		Number of
		── Sample Size ──		── Sample Size ──		─── Dropouts ───
Dropout Rate		N1	N2	N		N1'	N2'	N'		D1	D2	D
0%		2	2	4		2	2	4		0	0	0

Definitions
Dropout Rate (DR) is the percentage of subjects (or items) that are expected to be lost at random during the
   course of the study and for whom no response data will be collected (i.e., will be treated as "missing").
N1, N2, and N are the evaluable sample sizes at which power is computed. If N1 and N2 subjects are evaluated
   out of the N1' and N2' subjects that are enrolled in the study, the design will achieve the stated power.
N1', N2', and N' are the number of subjects that should be enrolled in the study in order to end up with N1, N2,
   and N evaluable subjects, based on the assumed dropout rate. After solving for N1 and N2, N1' and N2' are
   calculated by inflating N1 and N2 using the formulas N1' = N1 / (1 - DR) and N2' = N2 / (1 - DR), with N1' and
   N2' always rounded up. (See Julious, S.A. (2010) pages 52-53, or Chow, S.C., Shao, J., Wang, H., and
   Lokhnygina, Y. (2018) pages 32-33.)
D1, D2, and D are the expected number of dropouts. D1 = N1' - N1, D2 = N2' - N2, and D = D1 + D2.

PASS 2021, v21.0.3	2024/10/30 20:23:24      2

Two-Sample T-Tests Assuming Equal Variance

Procedure Input Settings ──────────────────────────────────────────────────────

Autosaved Template File
C:\Users\zhangzhang\Documents\PASS 2021\Procedure Templates\Autosave\Two-Sample T-Tests Assuming Equal Variance - Autosaved 2024_10_30-20_23_24.t388

Design Tab
Solve For:	Sample Size
Alternative Hypothesis:	Two-Sided
Power:	0.8
Alpha:	0.05
Group Allocation:	Equal (N1 = N2)
Input Type:	Means
μ1:	78.2278807
μ2:	43.6018436
σ:	0.5