In CrumpLab/SemesterProject7709:

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

1. Use pwr package to compute power for anova:

library(pwr)

#calculate power given k, n, f
pwr.anova.test(k = 3,
               n = 10,
               f = .5,
               sig.level = .05,
               power = )

# calcuale n, given, k, f, power
pwr.anova.test(k = 3,
               n = ,
               f = .2,
               sig.level = .05,
               power = .8)

BUT what is f?

https://cran.r-project.org/web/packages/pwr/vignettes/pwr-vignette.html

1. Eta squared, a measure of effect size for anova

https://cran.r-project.org/web/packages/effectsize/vignettes/anovaES.html

library(effectsize)
library(tibble)

# generate data for anova
levels <- 3
n_per_level <- 81
alternative_data <- tibble(subjects = 1:(levels*n_per_level),
                           IV = as.factor(rep(1:levels, each = n_per_level)),
                           DV = c(rnorm(n_per_level, .5, 1),
                                  rnorm(n_per_level, 0, 1),
                                  rnorm(n_per_level, 0, 1)
                           )
)
aov.out <- aov(DV ~ IV, data = alternative_data)
summary_aov <- summary(aov.out)
summary_aov[[1]]$`Pr(>F)`[1]

# calculate eta_squared from anova object
effectsize::eta_squared(aov.out)

1. Get a sense of eta-squared

run_aov <- function(){
  # generate data for anova
levels <- 4
n_per_level <- 81
alternative_data <- tibble(subjects = 1:(levels*n_per_level),
                           IV = as.factor(rep(1:levels, each = n_per_level)),
                           DV = c(rnorm(n_per_level, .4, 1),
                                  rnorm(n_per_level, 0, 1),
                                  rnorm(n_per_level, 0, 1),
                                  rnorm(n_per_level, 0, 1)
                           )
)
aov.out <- aov(DV ~ IV, data = alternative_data)
summary_aov <- summary(aov.out)
return(c(summary_aov[[1]]$`Pr(>F)`[1],
         effectsize::eta_squared(aov.out, partial=FALSE)$Eta2))
}
# run anova simulation
save_results <- replicate(1000,run_aov())

# proportion significant simulations
length(which(save_results[1,] < .05))/1000

# effect_size
hist(save_results[2,])
mean(save_results[2,])

1. Power to detect a 5% increase in a multiple choice test?

run_aov <- function(){
  groups <- 4
  n_per_group <- 25
  num_questions <- 10
  alternative_data <- tibble(subjects = 1:(groups*n_per_group),
                             IV = as.factor(rep(1:groups, each = n_per_group)),
                             DV = c(rbinom(n_per_group,num_questions,.75),
                                    rbinom(n_per_group,num_questions,.75),
                                    rbinom(n_per_group,num_questions,.75),
                                    rbinom(n_per_group,num_questions,.80)
                             )
  )
  aov.out <- aov(DV ~ IV, data = alternative_data)
  summary_aov <- summary(aov.out)
  return(c(summary_aov[[1]]$`Pr(>F)`[1],
           effectsize::eta_squared(aov.out, partial=FALSE)$Eta2))
}

# run anova simulation
save_results <- replicate(100,run_aov())

# proportion significant simulations
length(which(save_results[1,] < .05))/100

# mean_effect size
mean(save_results[2,])

CrumpLab/SemesterProject7709 documentation built on May 18, 2022, 9:34 p.m.