Ziegenbalg et al: EMF distracts zebrafish. Tables 2/3/4 - Statistical Treatment

Table 2, group A: p values CPR(LM:M)>FPR

m13=binom.test(4,13,p=0.27,alternative='greater')
m14=binom.test(2,12,p=0.19,alternative='greater')
m11=binom.test(3,12,p=0.33,alternative='greater')

cbind(lapply(list(m13,m14,m11),function(x) return(x$p.value) ))

     [,1]     
[1,] 0.4825762
[2,] 0.6957058
[3,] 0.8124391

Table 2, group B: p values CPR(LM:M)>FPR

m17=binom.test(6,15,p=0.35,alternative='greater')
m15=binom.test(0,17,p=0.14,alternative='greater')
m18=binom.test(5,14,p=0.36,alternative='greater')
m19=binom.test(4,15,p=0.2,alternative='greater')
m16=binom.test(4,16,p=0.06,alternative='greater')

cbind(lapply(list(m17,m15,m18,m19,m16),function(x) return(x$p.value) ))

     [,1]      
[1,] 0.4357179 
[2,] 1         
[3,] 0.6079885 
[4,] 0.3518379 
[5,] 0.01316628

#for comparison, CP(LM:L) response rates are *** significantly higher than FPR

#e.g. ZF15
binom.test(14,18,p=0.14,alternative='greater')

    Exact binomial test

data:  14 and 18
number of successes = 14, number of trials = 18,
p-value = 1.943e-09
alternative hypothesis: true probability of success is greater than 0.14
95 percent confidence interval:
 0.5611172 1.0000000
sample estimates:
probability of success 
             0.7777778 

Table 3: Sessions to Learning Criterion (Between groups)

sessions_to_LC=c(8,7,7,
     7,15,7,9,15,
     9,6,7,8.5,4)
grp=c("LM_A","LM_A","LM_A",
      "LM_B","LM_B","LM_B","LM_B","LM_B",
      "L_0","L_0","L_0","L_0","L_0")
  
dfr=data.frame(LC=sessions_to_LC,group=grp)
glmP.out=glm(LC~group,data=dfr,family='poisson')

Warning: non-integer x = 8.500000

summary(glmP.out)

Call:
glm(formula = LC ~ group, family = "poisson", data = dfr)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-1.1992  -0.5047  -0.1240   0.5876   1.2712  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)  1.93152    0.17025  11.345   <2e-16 ***
groupLM_A    0.06091    0.27284   0.223   0.8233    
groupLM_B    0.42933    0.21875   1.963   0.0497 *  
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 13.357  on 12  degrees of freedom
Residual deviance:  8.848  on 10  degrees of freedom
AIC: Inf

Number of Fisher Scoring iterations: 4

#Percentage change in LC for LM_B vs L_0
(exp(glmP.out$coefficients['groupLM_B'])-1)*100

groupLM_B 
 53.62319 

Table 4

LM:LM recall vs LM:L response rates for group B

Within group B, between test conditions

IDs=c('z15','z16','z17','z18','z19')
CSgo=c(151,156,147,114,114) 
CSnogo=c(41,34,15,31,28) 
Lgo=c(14,20,28,21,24)
Lnogo=c(4,1,0,2,2)


dfr=data.frame(cond='LM:LM',CP=CSgo,FN=CSnogo,id=IDs )
dfr=rbind(dfr,
  data.frame(cond='LM:L',CP=Lgo,FN=Lnogo,id=c('z15','z16','z17','z18','z19') )
)

dfr$rate=dfr$CP/(dfr$FN+dfr$CP)
dfr$odds=dfr$rate/(1-dfr$rate)
dfr$logodd=log(dfr$odds)

#aggregate(cbind(rate,odds,logodd) ~ cond,data=dfr,FUN=mean)

library(lme4)

Loading required package: Matrix

mixB.out<-lme4::glmer(cbind(CP, FN) ~ cond + (1 | id) ,family = binomial, data = dfr)

summary(mixB.out)->s 

print(s)

Generalized linear mixed model fit by maximum likelihood
  (Laplace Approximation) [glmerMod]
 Family: binomial  ( logit )
Formula: cbind(CP, FN) ~ cond + (1 | id)
   Data: dfr

     AIC      BIC   logLik deviance df.resid 
    57.3     58.3    -25.7     51.3        7 

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-1.82586 -0.22402 -0.00092  0.41184  1.19998 

Random effects:
 Groups Name        Variance Std.Dev.
 id     (Intercept) 0.09391  0.3064  
Number of obs: 10, groups:  id, 5

Fixed effects:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)   2.4871     0.3738   6.655 2.84e-11 ***
condLM:LM    -0.9340     0.3594  -2.599  0.00935 ** 
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
          (Intr)
condLM:LM -0.898

logit <- function(ratio) { 
 log(ratio/(1-ratio))}

expit <- function(li) { 
  1/(1+exp(-li))
} # yields ratio

Mean response rates

# MEAN LM:L 
rL=expit(s$coefficients[1,1]) 
# MEAN LM:LM 
rLM=expit(s$coefficients[1,1]+s$coefficients[2,1]) 

OR=(rL/(1-rL))/(rLM/(1-rLM))

# directly: OR=1/exp(s$coefficients[2,1])

print(paste("CPR (LM:L) :",rL))

[1] "CPR (LM:L) : 0.923234905230892"

print(paste("CPR (LM:LM):",rLM))

[1] "CPR (LM:LM): 0.825366479312474"

print(paste("Odds Ratio:",OR))

[1] "Odds Ratio: 2.54465674818237"