# Wald-Wolfowitz Runs Test for Normality Assumptions Testing

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?

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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.