Using a normal approximation method for the Wilcoxon Signed-Rank Test, I've seen that the expected value is [itex] \mu = \frac {n(n+1)}2 [/itex] and the variance is [itex] \sigma^2 = \frac {n(n+1)(2n+1)}{24} [/itex].(adsbygoogle = window.adsbygoogle || []).push({});

I'm wondering why these are the expected value and variance.

I do recognize the formula for the sum of N natural numbers and the sum of N squared natural numbers.

I have an idea as to why the expected value is half the sum of N natural numbers. Under the null hypothesis, roughly half of the differences should be positive, so it would make sense to half the sum of N natural numbers.

I have no intuition for the variance of the distribution.

An explanation would be appreciated.

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# Expected Value and Variance for Wilcoxon Signed-Rank Test

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