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I have several discrete datasets with a small range (-2 to +2) which I want to test against the null hypothesis "the distribution is centred around zero".

The Wilcoxon signed-rank test was suggested to me as an appropriate choice, and some answers on this site back this up. The issue is that, for some datasets, a large portion of the pair deltas are 0, meaning most of the samples are discarded. The result is that some datasets pass the test at 95% confidence while others with nearly identical distributions fail it.

What would be a good alternative test for such a scenario?

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This article:

On Neutral Responses (Zeros) in the Sign Test and Ties in the Wilcoxon–Mann–Whitney Test Ronald H Randles The American Statistician Vol. 55, Iss. 2, 2001

Would seem to apply directly to your question.

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  • $\begingroup$ Thanks. For the record, the majority preference hypothesis seems the appropriate choice as suggested by the paper. $\endgroup$
    – Edward Peek
    Sep 23, 2013 at 22:47

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