# The most important parameter to vary
sdInEffectSize = 1


# Other parameters
nbSamples  = 5e3
sampleSize = 100
effectSize = 0.2
baseSD = 3
alpha = 0.05


nbTP = 0
for (i in 1:nbSamples)
{
    x1 = rnorm(sampleSize, mean = 0, sd = baseSD)
    x2 = x1 + rnorm(sampleSize, mean = effectSize, sd = sdInEffectSize)
    if (t.test(x2-x1)$p.value < alpha)
    {
        nbTP = nbTP + 1
    }
}

print(nbTP / nbSamples)