hist(rf(n = 1000, df1 = 3, df2 = 15))

But the following produces something close to Normal:

hist(replicate(n = 1000, sum(rf(n = 20, df1 = 3, df2 = 15))))

Notice the difference between the two. The first is just a histogram of 1000 F statistics. The second is a histogram of 1000 sums of 20 random F statistics.

Hope that helps.

]]>I have some thoughts. According to CLT, random sampling of any statistic will eventually result in normal distribution of that statistic. But why this not apply to F statistics? I did bootstrapping of F statistic on 10000 samples, and I still got skewed distribution of F statistics.

]]>dmeans <- numeric(dim(p)[2])

for (i in 1:dim(p)[2]) {

dmeans[i] <- mean(alls[p[, i]]) – mean(alls[-p[, i]])

}

hist(dmeans)

abline(v = d0, lty = 2)

abline(v = -d0, lty = 2) ]]>

Now trying to work out if I can do a similar thing for paired data… ]]>