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While the Wilcoxon signed-rank test in general doesn't assume any distribution, most exact implementations are restricted to <50 samples (i.e. scipy). Above that a normal distribution is assumed to calculate approximate values. This raises two questions:

Why do exact calculation have such a hard and low limit?

How can you handle larger datasets that don't have a normal distribution and thus the approximation can't be used?

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In R, you can include exact=T to force wilcox.test to calculate the exact p-value. It may take a long time. It has to find all the different ways that a value of the test statistic could be as large or larger than what was observed. What using the normal approximation means here is that the Wilcoxon signed rank test statistic is itself approximately normal regardless of the distribution of the data.

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