The normal approximation to the Wilcoxon signed rank sum test is used whenever the number of none zero differences is 50 or more.

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The correct name of the test is Wilcoxon signed rank test or Wilcoxon signed rank sum test (depending on the context), but there is no normal approximation to this test. The Wilcoxon signed rank test is a non-parametric test that does not assume a normal distribution of the data, so it can be used regardless of the sample size or the number of none zero differences. However, for small sample sizes (i.e. less than 20), the exact distribution of the test statistic should be used instead of the normal approximation.

The Normal Approximation to the Wilcoxon Signed Rank Sum Test