Assignment 5

Question 1

library(pwr)

## Warning: package 'pwr' was built under R version 4.4.3

power.t.test(n = NULL, delta = 1.5, sd = 3, sig.level = 0.05,power = 0.75,type = c("paired"),alternative = c("one.sided"))

## 
##      Paired t test power calculation 
## 
##               n = 22.92961
##           delta = 1.5
##              sd = 3
##       sig.level = 0.05
##           power = 0.75
##     alternative = one.sided
## 
## NOTE: n is number of *pairs*, sd is std.dev. of *differences* within pairs

Analysis for question 1:-

Based on the analysis, a paired, one-sided t-test with α = 0.05, desired power = 0.75, SD of within-person differences s_d = 3%, and target mean difference Δ = −1.5% (effect size d = 0.5) requires n ≈ 23 pairs. 

Question 2

power.t.test(n = NULL, delta = 0.5, sd = 1, sig.level = 0.1,power = 0.85,type = c("two.sample"),alternative = c("one.sided"))

## 
##      Two-sample t test power calculation 
## 
##               n = 43.40568
##           delta = 0.5
##              sd = 1
##       sig.level = 0.1
##           power = 0.85
##     alternative = one.sided
## 
## NOTE: n is number in *each* group

Analysis for question 2:-

Based on the analysis, a two-sample, one-sided t-test with α = 0.10, desired power = 0.85, SD = 1, and target mean difference Δ = 0.5 (effect size d=0.5) requires n= 43.41 per group. Rounding up, you should plan for 44 participants in each group (total N = 88).

Complete Code

library(pwr)
power.t.test(n = NULL, delta = 1.5, sd = 3, sig.level = 0.05,power = 0.75,type = c("paired"),alternative = c("one.sided"))
power.t.test(n = NULL, delta = 0.5, sd = 1, sig.level = 0.1,power = 0.85,type = c("two.sample"),alternative = c("one.sided"))