Some guys told me that it's appropriate to use Wald-Wolfowitz Runs Test as a normality test (like Shapiro-Wilk's or Kolmogorov-Smirnov...). Do you think this is good way to test normality assumptions?
$\begingroup$
$\endgroup$
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
1
This is not a great idea. The Wald-Wolfowitz test can detect certain departures from being independently distributed (it detects whether a series of observations is 'too bunchy' or 'too jittery' with respect to the distribution of positive and negative values), which have nothing to do with normality. It is not sensitive to the shape of the empirical distribution: it will 'pass' Cauchy, shifted uniform, $t$, polluted normal, etc. random variates.
Moreover, the WW test is sensitive to the ordering of the observations. A true test for normality should be invariant to permutations.
answered Aug 25, 2010 at 22:54
-
$\begingroup$ I suspect the idea would be to apply a runs test to a binned set of deviations (specifically those for a chi-squared goodness of fit test). The signs of the deviations are used for the runs test. I think this sort of idea (supplementing a chi-squared test by a runs test on the deviation signs) was investigated by F.N.David. ... Edit: yep, here -- F. N. David, (1947), "A $\chi^2$ 'smooth' test for goodness of fit," Biometrika, Vol. 34, pp. 299-310. $\endgroup$– Glen_bCommented Jun 26, 2018 at 12:38