P-curve analysis simulation

Simulation 1: True Effect exists

pvals <- replicate(300, { # 300 studies
  t.test(rnorm(35, 20, 15), # random sample (n=35) from the population with mean = 20
         rnorm(35, 15, 15) # random sample (n=35) from the population with mean = 15 
         )$p.value # p-val from the t-test
})
hist(pvals[pvals < 0.05]) # histogram of significant (p < 0.05) p-values when True Effect exists

pvals <- replicate(300, { # 300 studies
  t.test(rnorm(35, 20, 15), # random sample (n=35) from the population with mean = 20
         rnorm(35, 15, 15) # random sample (n=35) from the population with mean = 15 
         )$p.value # p-val from the t-test
})
hist(pvals[pvals < 0.05]) # histogram of significant (p < 0.05) p-values when True Effect exists

pvals <- replicate(300, { # 300 studies
  t.test(rnorm(35, 20, 15), # random sample (n=35) from the population with mean = 20
         rnorm(35, 15, 15) # random sample (n=35) from the population with mean = 15 
         )$p.value # p-val from the t-test
})
hist(pvals[pvals < 0.05]) # histogram of significant (p < 0.05) p-values when True Effect exists

pvals <- replicate(300, { # 300 studies
  t.test(rnorm(35, 20, 15), # random sample (n=35) from the population with mean = 20
         rnorm(35, 15, 15) # random sample (n=35) from the population with mean = 15 
         )$p.value # p-val from the t-test
})
hist(pvals[pvals < 0.05]) # histogram of significant (p < 0.05) p-values when True Effect exists

Simulation 2: True Effect does not exists

pvals <- replicate(300, { # 300 studies
  t.test(rnorm(35, 20, 15), # random sample (n=35) from the population with mean = 20
         rnorm(35, 20, 15) # random sample (n=35) from the population with mean = 20 (no effect!) 
         )$p.value # p-val from the t-test
})
hist(pvals[pvals < 0.05]) # histogram of significant (p < 0.05) p-values when True Effect does not exist

pvals <- replicate(300, { # 300 studies
  t.test(rnorm(35, 20, 15), # random sample (n=35) from the population with mean = 20
         rnorm(35, 20, 15) # random sample (n=35) from the population with mean = 20 (no effect!) 
         )$p.value # p-val from the t-test
})
hist(pvals[pvals < 0.05]) # histogram of significant (p < 0.05) p-values when True Effect does not exist

pvals <- replicate(300, { # 300 studies
  t.test(rnorm(35, 20, 15), # random sample (n=35) from the population with mean = 20
         rnorm(35, 20, 15) # random sample (n=35) from the population with mean = 20 (no effect!) 
         )$p.value # p-val from the t-test
})
hist(pvals[pvals < 0.05]) # histogram of significant (p < 0.05) p-values when True Effect does not exist

pvals <- replicate(300, { # 300 studies
  t.test(rnorm(35, 20, 15), # random sample (n=35) from the population with mean = 20
         rnorm(35, 20, 15) # random sample (n=35) from the population with mean = 20 (no effect!) 
         )$p.value # p-val from the t-test
})
hist(pvals[pvals < 0.05]) # histogram of significant (p < 0.05) p-values when True Effect does not exist