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templeton_prereg_power.R
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library(tidyverse)
# set up parameters
random_stimuli <- function(n_stimuli, effect_treatment, effect_sd, n_participants, n_sims) {
cond <- c(rep('a', n_participants/2), rep('b', n_participants/2))
subj <- c(1:n_participants)
p_value <- c()
f_value <- c()
t_value <- c()
### simulations where stimuli are drawn at random from a population ever time, and then those means used for random data draws (e.g. double random draw)
for (y in 1:n_sims) {
print(y)
y1 <- c()
y2 <- c()
y1_stimuli <- c()
y2_stimuli <- c()
mean_control <- rnorm(n = n_stimuli, mean = 0, sd = effect_sd)
mean_cond <- rnorm(n = n_stimuli, mean = effect_treatment, sd = effect_sd)
for (i in 1:n_stimuli) {
y1 <- c(y1, rnorm(n = n_participants/(2*n_stimuli), mean = mean_control[i], sd = 1))
y2 <- c(y2, rnorm(n = n_participants/(2*n_stimuli), mean = mean_cond[i], sd = 1))
y1_stimuli <- c(y1_stimuli, c(rep(i, n_participants/(2*n_stimuli))))
y2_stimuli <- c(y2_stimuli, c(rep(i, n_participants/(2*n_stimuli))))
}
data <- as_tibble(cbind(subj, c(y1_stimuli, y2_stimuli), cond, c(y1, y2))) %>%
mutate(V2 = as.factor(V2),
cond = as.factor(cond),
V4 = as.numeric(V4)) %>%
rename(stimuli = V2, response = V4)
if (n_stimuli > 1) {
model <- aov(response ~ stimuli + cond, data)
p_value <- c(p_value, summary(model)[[1]][2, 5])
f_value <- c(f_value, summary(model)[[1]][2, 4])
} else {
model <- t.test(response ~ cond, data)
p_value <- c(p_value, model$p.value)
t_value <- c(t_value, model$statistic)
}
}
power = sum(p_value <= .05)/n_sims
if (n_stimuli < 2){
cohen_d = (2*t_value)/sqrt(n_participants)
} else {
cohen_d = (2*sqrt(f_value))/sqrt(n_participants)
}
return(set_names(c(power, mean(cohen_d)), c('power', 'mean_d')))
}
rnorm2 <- function(n,mean,sd) {
mean+sd*scale(rnorm(n))
}
fixed_stimuli <- function(n_stimuli, effect_treatment, effect_sd, n_participants, n_sims) {
cond <- c(rep('a', n_participants/2), rep('b', n_participants/2))
subj <- c(1:n_participants)
p_value <- c()
f_value <- c()
t_value <- c()
### simulations where stimuli are drawn at random from a population ever time, and then those means used for random data draws (e.g. double random draw)
for (y in 1:n_sims) {
print(y)
y1 <- c()
y2 <- c()
y1_stimuli <- c()
y2_stimuli <- c()
if (n_stimuli > 1) {
mean_control <- c(rnorm2(n_stimuli, 0, effect_sd))
mean_cond <- c(rnorm2(n_stimuli, 0 + effect_treatment, effect_sd))
} else {
mean_control <- 0
mean_cond <- mean_control + effect_treatment
}
for (i in 1:n_stimuli) {
y1 <- c(y1, rnorm(n = n_participants/(2*n_stimuli), mean = mean_control[i], sd = 1))
y2 <- c(y2, rnorm(n = n_participants/(2*n_stimuli), mean = mean_cond[i], sd = 1))
y1_stimuli <- c(y1_stimuli, c(rep(i, n_participants/(2*n_stimuli))))
y2_stimuli <- c(y2_stimuli, c(rep(i, n_participants/(2*n_stimuli))))
}
data <- as_tibble(cbind(subj, c(y1_stimuli, y2_stimuli), cond, c(y1, y2))) %>%
mutate(V2 = as.factor(V2),
cond = as.factor(cond),
V4 = as.numeric(V4)) %>%
rename(stimuli = V2, response = V4)
if (n_stimuli > 1) {
model <- aov(response ~ stimuli + cond, data)
p_value <- c(p_value, summary(model)[[1]][2, 5])
f_value <- c(f_value, summary(model)[[1]][2, 4])
} else {
model <- t.test(response ~ cond, data)
p_value <- c(p_value, model$p.value)
t_value <- c(t_value, model$statistic)
}
}
power = sum(p_value <= .05)/n_sims
if (n_stimuli < 2){
cohen_d = (2*t_value)/sqrt(n_participants)
} else {
cohen_d = (2*sqrt(f_value))/sqrt(n_participants)
}
return(set_names(c(power, mean(cohen_d)), c('power', 'mean_d')))
}
stimuli_as_random <- crossing(n_stimuli = c(1, 5, 10),
effect_treatment = c(0, .25),
effect_sd = c(.05, .1, .15, .2, .25),
n_participants = 600,
n_sims = 5000) %>%
mutate(sim_results = pmap(list(n_stimuli, effect_treatment, effect_sd, n_participants, n_sims), random_stimuli)) %>%
unnest_wider(sim_results)
stimuli_as_fixed <- crossing(n_stimuli = c(1, 5, 10),
effect_treatment = c(0, .25),
effect_sd = c(.05, .1, .15, .2, .25),
n_participants = 600,
n_sims = 5000) %>%
mutate(sim_results = pmap(list(n_stimuli, effect_treatment, effect_sd, n_participants, n_sims), fixed_stimuli)) %>%
unnest_wider(sim_results)
top_level <- function(n_sims, effect_treatment, effect_sd, n_stimuli) {
mean_control <- c()
mean_cond <- c()
for (y in 1:n_sims) {
print(y)
y1 <- c()
y2 <- c()
y1_stimuli <- c()
y2_stimuli <- c()
control_means <- rnorm(n = n_stimuli, mean = 0, sd = effect_sd)
cond_means <- rnorm(n = n_stimuli, mean = effect_treatment, sd = effect_sd)
mean_control <- c(mean_control, mean(control_means))
mean_cond <- c(mean_cond, mean(cond_means))
}
return(set_names(c(mean(mean_control), mean(mean_cond)), c('mean_control', 'mean_cond')))
}
stimuli_means <- crossing(n_stimuli = c(1, 5),
effect_treatment = c(0, .25),
effect_sd = c(.05, .1, .15, .2),
n_sims = 1000) %>%
mutate(sim_results = pmap(list(n_sims, effect_treatment, effect_sd, n_stimuli), top_level)) %>%
unnest_wider(sim_results)
lower_means <- function(n_stimuli, effect_treatment, effect_sd, n_participants, n_sims) {
cond <- c(rep('a', n_participants/2), rep('b', n_participants/2))
subj <- c(1:n_participants)
control_mean <- c()
cond_mean <- c()
### simulations where stimuli are drawn at random from a population ever time, and then those means used for random data draws (e.g. double random draw)
for (y in 1:n_sims) {
print(y)
y1 <- c()
y2 <- c()
y1_stimuli <- c()
y2_stimuli <- c()
mean_control <- rnorm(n = n_stimuli, mean = 0, sd = effect_sd)
mean_cond <- rnorm(n = n_stimuli, mean = effect_treatment, sd = effect_sd)
for (i in 1:n_stimuli) {
y1 <- c(y1, rnorm(n = n_participants/(2*n_stimuli), mean = mean_control[i], sd = 1))
y2 <- c(y2, rnorm(n = n_participants/(2*n_stimuli), mean = mean_cond[i], sd = 1))
y1_stimuli <- c(y1_stimuli, c(rep(i, n_participants/(2*n_stimuli))))
y2_stimuli <- c(y2_stimuli, c(rep(i, n_participants/(2*n_stimuli))))
}
control_mean <- c(control_mean, mean(y1))
cond_mean <- c(cond_mean, mean(y2))
}
return(set_names(c(mean(control_mean), mean(cond_mean)), c('control_mean', 'cond_mean')))
}
overall_means <- crossing(n_stimuli = c(1, 5),
effect_treatment = c(0, .25),
effect_sd = c(.05, .1, .15, .2),
n_participants = 600,
n_sims = 1000) %>%
mutate(sim_results = pmap(list(n_stimuli, effect_treatment, effect_sd, n_participants, n_sims), lower_means)) %>%
unnest_wider(sim_results)
all_results <- bind_rows(stimuli_as_fixed %>% mutate(data_gen = 'fixed_sample'),
stimuli_as_random %>% mutate(data_gen = 'random_sample')) %>%
mutate(data_gen = as.factor(data_gen),
effect_treatment = as.factor(effect_treatment))
ggplot(all_results %>% filter(n_stimuli == 5 & effect_sd < .25), aes(x = effect_sd, y = power, color = effect_treatment)) +
geom_line() +
scale_y_continuous(name = 'percent p < .05', breaks = c(0, .1, .2, .3, .4, .5, .6, .7, .8, .9)) +
scale_x_continuous(name = 'vignette_sd') +
facet_grid(cols = vars(data_gen))