Power analysis when true effect larger than planned effect

gistfile1.R

library(pwr)
library(effsize)
library(ggplot2)

# set "true" effect size and the effect size entered into power analysis
true_effect <- 0.2
power_effect <- 1.0

# How many participants required?
power_analysis <- pwr.t.test(d = power_effect, 
                             sig.level = 0.05, 
                             power = 0.8, 
                             type = "two.sample")

sample_size <- round(power_analysis$n, 0)

# how many simulations?
n_sims <- 50

# prepare data frame
eff_sizes <- data.frame(
  simulation = 1:n_sims,
  mean = numeric(n_sims), 
  lower = numeric(n_sims), 
  upper = numeric(n_sims)
)


# conduct the simulations
for(i in 1:n_sims){
  
  # simulate the data fpr 2 groups
  sample_a <- rnorm(sample_size, 0 + true_effect, 1)
  sample_b <- rnorm(sample_size, 0, 1)

  # run the t-test
  t_test <- t.test(sample_a, sample_b)

  # get the effect size & confidence intervals
  d <- cohen.d(sample_a, sample_b)
  eff_sizes$mean[i] <- d$estimate
  eff_sizes$lower[i] <- d$conf.int[1]
  eff_sizes$upper[i] <- d$conf.int[2]
  
}

# produce the plot
ggplot(eff_sizes, aes(x = mean, y = simulation)) + 
  geom_vline(xintercept = true_effect, colour = "red") +
  geom_segment(aes(x = lower, xend = upper, y = simulation, yend = simulation)) + 
  geom_point() + 
  theme_bw() + 
  labs(x = "Mean Estimate", 
       y = "Simulation Number")  + 
  scale_x_continuous(limits = c(-1.5, 1.5)) + 
  coord_flip()