An omnibus test for departures from normality is an idea developed by E. S. Pearson (letter to Bowman); he thought a test including skewness b 1 and kurtosis b 2, both of which scale and location free, would give more information than the test using lower moments only. For the normal distribution, the population skewness is \(\sqrt {\beta _1}= 0\) and the population kurtosis is β 2 = 3.