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# Remove most objects from the working environment
rm(list = ls())
options(stringsAsFactors = F)
# 10.2.1. t-tests
# Question 1
# install.packages("pwr")
library(pwr)
pwr.t.test(d=0.8, sig.level = 0.05, power=0.9, type = "two.sample",
alternative = "two.sided")
# Two-sample t test power calculation
#
# n = 33.82555
# d = 0.8
# sig.level = 0.05
# power = 0.9
# alternative = two.sided
#
# NOTE: n is number in *each* group
#===================================================================
# question 2
pwr.t.test(n=20, d=0.5, sig.level = 0.01, type = "two.sample",
alternative = "two.sided")
# Two-sample t test power calculation
#
# n = 20
# d = 0.5
# sig.level = 0.01
# power = 0.1439551
# alternative = two.sided
#
# NOTE: n is number in *each* group
#===================================================================
# 10.2.2. ANOVA
pwr.anova.test(k=5, f=0.25,sig.level = 0.05, power = 0.8)
# Balanced one-way analysis of variance power calculation
#
# k = 5
# n = 39.1534
# f = 0.25
# sig.level = 0.05
# power = 0.8
#
# NOTE: n is number in each group
#===================================================================
# 10.2.3. Correlations
# question 3
pwr.r.test(r=0.25, sig.level = 0.05, power = 0.90, alternative = "greater")
# approximate correlation power calculation (arctangh transformation)
#
# n = 133.2803
# r = 0.25
# sig.level = 0.05
# power = 0.9
# alternative = greater
#===================================================================
# 10.2.4. Linear models
pwr.f2.test(u=3, f2=0.0769, sig.level = 0.05, power=0.90)
# Multiple regression power calculation
#
# u = 3
# v = 184.2426
# f2 = 0.00769
# sig.level = 0.05
# power = 0.9
# v=N-K-1-->N=v+K+1=185+7+1=193
#===================================================================
# 10.2.5. Tests of proportions
# question 4
pwr.2p.test(h=ES.h(0.65, 0.6), sig.level = 0.05, power = 0.9,
alternative = "greater")
# Difference of proportion power calculation for binomial
# distribution (arcsine transformation)
#
# h = 0.1033347
# n = 1604.007
# sig.level = 0.05
# power = 0.9
# alternative = greater
#
# NOTE: same sample sizes
#===================================================================
# 10.2.6. Chi-square tests
prob <- matrix(c(.42, .28, .03, .07, .10, .10), byrow=TRUE, nrow=3)
ES.w2(prob)
# [1] 0.1853198
pwr.chisq.test(w=0.1853, df=2, sig.level = 0.05, power=0.90)
# Chi squared power calculation
#
# w = 0.1853
# N = 368.5317
# df = 2
# sig.level = 0.05
# power = 0.9
#
# NOTE: N is the number of observations
#===================================================================
# 10.2.7. Choosing an appropriate effect size in novel situations
# code listing 10.1. Sample sizes for detecting significant effects in a one-way ANOVA
library(pwr)
es <- seq(0.1, 0.5, 0.01)
nes <- length(es)
samsize <- NULL
for (i in 1:nes){
result <- pwr.anova.test(k=5, f=es[i], sig.level = 0.05, power = 0.9)
samsize[i] <- ceiling(result$n)
}
plot(samsize, es, type = "l", lwd=2, col="red",
ylab = "Effect Size",
xlab = "Sample Size (per cell)",
main = "One Way ANOVA with Power=0.90, and Alpha=0.05")
# 10.3. Creating power analysis plots
# code listing Sample size curves for detecting correlations of various sizes
library(pwr)
r <- seq(0.1, 0.5, 0.01)
nr <- length(r)
nr
p <- seq(0.4, 0.9, 0.1)
np <- length(p)
np
samsize <- array(numeric(nr*np), dim = c(nr, np))
for (i in 1:np){
for (j in 1:nr){
result <- pwr.r.test(n =NULL, r = r[j],
sig.level = 0.05, power = p[i],
alternative = "two.sided")
samsize[j, i] <- ceiling(result$n)
}
}
xrange <- range(r)
yrange <- round(range(samsize))
colors <- rainbow(length(p))
plot(xrange, yrange, type = "n",
xlab = "Correlation Coefficient (r)",
ylab = "Sample Size(n")
for (i in 1:np){
lines(r, samsize[,i], type = "l", lwd = 2, col=colors[i])
}
abline(v=0, h=seq(0, yrange[2],50), lty=2, col="grey89")
abline(h=0, v=seq(xrange[2], 0.02), lty=2, col="grey89")
title("Sample Size Estimation for Correlation Studies\n
Sig = 0.05 (Two-tailed)")
legend("topright", title = "Power", as.character(p),
fill = colors)
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