Sample size based on total scores

Sample size calculations

We calculate the required sample size based on the effect sizes (Hedges g) of Intensity, Frequency and Distress. Type 1 error is set to .05, type 2 is set to .2 and we used a two sided paired sample t-test.

Intensity

#Sample size based on Intensity, Frequency, Distress
library(pwr)

## Warning: package 'pwr' was built under R version 3.5.2

Intensity.m<-c(10.2,10.2,7.9,8.5)
Intensity.sd<-c(3,2,5,4.3,3.9)
Intensity.n<-c(95,101,80,90)

            
xm1<- mean(Intensity.m[c(1,2)])
xm2<- mean(Intensity.m[c(3,4)])
sd1<- mean(Intensity.sd[c(1,2)])
sd2<- mean(Intensity.sd[c(3,4)])
n=min(Intensity.n)  

d<-(xm1-xm2)/sqrt((sd1^2+sd2^2)/2)
Hedgesg<-d*(1-(3/(4*(n-1)-1)))

sample.size.Intensity<-pwr.t.test(d=Hedgesg,power=0.8,sig.level=0.05,type="one.sample",alternative="two.sided")
sample.size.Intensity

## 
##      One-sample t test power calculation 
## 
##               n = 29.85201
##               d = 0.5306413
##       sig.level = 0.05
##           power = 0.8
##     alternative = two.sided

Frequency

#Sample size based on Intensity, Frequency, Distress
library(pwr)


Frequency.m<-c(12.3,12.7,9.2,10.5)
Frequency.sd<-c(3.6,4,4.6,4.6)
Frequency.n<-c(95,101,80,90)


xm1<- mean(Frequency.m[c(1,2)])
xm2<- mean(Frequency.m[c(3,4)])
sd1<- mean(Frequency.sd[c(1,2)])
sd2<- mean(Frequency.sd[c(3,4)])
n=min(Frequency.n)      

d<-(xm1-xm2)/sqrt((sd1^2+sd2^2)/2)
Hedgesg<-d*(1-(3/(4*(n-1)-1)))

sample.size.Frequency<-pwr.t.test(d=Hedgesg,power=0.8,sig.level=0.05,type="one.sample",alternative="two.sided")
sample.size.Frequency

## 
##      One-sample t test power calculation 
## 
##               n = 22.27598
##               d = 0.6221282
##       sig.level = 0.05
##           power = 0.8
##     alternative = two.sided

Distress

#Sample size based on Intensity, Frequency, Distress
library(pwr)


Distress.m<-c(173.1,171,105.7,135.8)
Distress.sd<-c(74.6,75.2,86.4,85.2)
Distress.n<-c(95,101,80,90)

d<-(xm1-xm2)/sqrt((sd1^2+sd2^2)/2)
Hedgesg<-d*(1-(3/(4*(n-1)-1)))
    
xm1<- mean(Distress.m[c(1,2)])
xm2<- mean(Distress.m[c(3,4)])
sd1<- mean(Distress.sd[c(1,2)])
sd2<- mean(Distress.sd[c(3,4)])
n=min(Distress.n)      

d<-(xm1-xm2)/sqrt((sd1^2+sd2^2)/2)
Hedgesg<-d*(1-(3/(4*(n-1)-1)))

sample.size.Distress<-pwr.t.test(d=Hedgesg,power=0.8,sig.level=0.05,type="one.sample",alternative="two.sided")
sample.size.Distress

## 
##      One-sample t test power calculation 
## 
##               n = 21.7163
##               d = 0.6309265
##       sig.level = 0.05
##           power = 0.8
##     alternative = two.sided

Conclusion

The required sample sizes were 30, 23, 22 for intensity, frequency and distress. So, in order to find a significant effect for the three measures al least 30 participants are required.