Purpose

This script is used to calulate the power, Type 1 and Type 2 error in the sex differences in visual perception project.

Type 1 error in one-tailed two sample t test with unequal sample size

Because there are 4 variables, if we choose an initial \(\alpha=0.05\), the Bonferonni correction for multiple comparisons would be \(0.05/4=0.0125\). So, we choose \(p=0.01\) as our criterion.

Power analysis

We use the pwr package for this analysis.

# Power Calculations For Two Samples (Same Sizes) T-Tests Of Means
library(pwr)
# assume 50 males and 250 females are collected. Males are predicted to have lower threshold than females. So we use one-tailed t test
pwr.t.test(n = 150, d = NULL, sig.level = 0.05/4, power=0.8 ,type="two.sample",alternative="greater")
## 
##      Two-sample t test power calculation 
## 
##               n = 150
##               d = 0.3575352
##       sig.level = 0.0125
##           power = 0.8
##     alternative = greater
## 
## NOTE: n is number in *each* group
# Power Calculations For Two Samples (Different Sizes) T-Tests Of Means
library(pwr)
# assume 50 males and 250 females are collected. Males are predicted to have lower threshold than females. So we use one-tailed t test
pwr.t2n.test(n1 =150, n2= 150, d = NULL, sig.level = 0.05/4
          , power = 0.8, alternative = c( "less"))
## 
##      t test power calculation 
## 
##              n1 = 150
##              n2 = 150
##               d = -0.3575352
##       sig.level = 0.0125
##           power = 0.8
##     alternative = less

Plot of power and effect sizes given a range of possible male/female ratios

Assuming two-sample t-test, one tailed, and \(p=0.0125\).

pwr.t.test(n = NULL, d = 0.25, sig.level = 0.05/4 , power = 0.8, type = "two.sample", alternative = "greater")
## 
##      Two-sample t test power calculation 
## 
##               n = 305.4207
##               d = 0.25
##       sig.level = 0.0125
##           power = 0.8
##     alternative = greater
## 
## NOTE: n is number in *each* group

Power for correlation analysis for participants in one gender

# Power Calculations For Correlation Test
#  power of test or determine parameters to obtain target power (same as power.anova.test).
pwr.r.test(n = 147, r = NULL, sig.level = 0.05/5, power = 0.8,
    alternative = c("less"))
## 
##      approximate correlation power calculation (arctangh transformation) 
## 
##               n = 147
##               r = -0.2574376
##       sig.level = 0.01
##           power = 0.8
##     alternative = less

Plot of power and effect sizes given a range of sample size (male/female)

Assuming corelation test, one tailed, and \(p=0.0125\).