mattnw

#Now imagine we're looking at the effect of calorie restriction, and this does actually have a true effect
#Of 5kg weight loss
#And we've managed to get a bigger sample size so our power is better!

#First we need to calculate the post-treatment sd as this is an input in the power calculation
#The post-treatment variable has sd comprised of following variance sources: pretest variance and
#Random weight loss/gain during intervention (we'll assume this random noise again has SD = 3)
post_sd = sd(population_pre + rnorm(10000, 0, 3)) #SD of about 16.6

#Now calculate power

mattnw

set.seed(123)

#Generate a population of pretest body weights for 10,000 men (1) and women (0), with some random noise
#Men, are, 13kg heavier than women on average in our population (I.e., gender is a relevant covariate)
gender = rbinom(10000, 1, 0.5)
population_pre = 65+13*gender + rnorm(10000, 0, 15)

#In each experiment, we will sample 30 people and randomly assign them to a paleo diet (1) or no treatment (0)
#Sadly, in our example, the paleo diet has zero effect on weight.
#But there is some random weight gain/loss during the intervention for each person

mattnw

#Power calculator function
power_fun = function(effect_d = 0.5, rel = 0.8){
  SEM = 1*sqrt(1-rel)
  SEdiff = sqrt(2*SEM^2)
  CR = 1.96*SEdiff
  pnorm(q = CR, mean = effect_d, sd = SEdiff, lower.tail = FALSE)
}

#Plot power by true effect size and reliability

mattnw

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  <info>
    <title>Journal of Dental Research</title>
    <id>http://www.zotero.org/styles/journal-of-dental-research</id>
    <link href="http://www.zotero.org/styles/journal-of-dental-research" rel="self"/>
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    <author>
      <name>Emmanuel Charpentier</name>
      <email>emm.charpentier@free.fr</email>