Effect of deviations from a normal distribution on Wilcoxon signed-rank test

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Which type of deviations from a normal distribution, skewness or heavy-tailedness, appears to have a greater effect on the Wilcoxon signed-rank test? Why?

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The Wilcoxon test is non-parametric and does not require the samples to be normally distributed, unlike the t-test. The t-test is usually preferable since it is more efficient in a statistical sense, but because it is parametric its assumptions are not always fulfilled. Hence, the Wilcoxon test is very popular when the t-test cannot be used.