Calculate post-hoc power of study of the effect of indoor plants on mental health

post-hoc-power-plants-mental.r

set.seed(123)

##############################################
# Study parameters
##############################################

# Sample size
n <- 63

# Mean of outcome
y_pre <- 47.9
y_post <- 46.2

# SD of outcome
sd_pre <- 10.6
sd_post <- 11.1

##############################################
# Assuming these are the TRUE values,
# how often should we see significant
# differences?
##############################################

# Number of simulations
sims <- 100000

# Simulate data, test for differences with Welch
# two-sample t-test (unequal variances), return
# p-values.
results <- vector(length = sims, mode = "numeric")

for (i in 1:sims) {
  results[i] <- t.test(
    rnorm(n = n, mean = y_pre, sd = sd_pre),
    rnorm(n = n, mean = y_post, sd = sd_post),
    var.equal = FALSE,
    conf.level = 0
  )$p.value
}

# Define function to take alpha, calculate power,
# and report it back
power_calc <- function(alpha) {
  paste0("For alpha = ",
         alpha,
         " study has ",
         prop.table(table(results < alpha))[2],
         "% power.")
  
}

# Calculate power for different alphas
power_calc(0.01)
power_calc(0.022)
power_calc(0.05)
power_calc(0.10)