Abstract
When zeroes (or ties within pairs) occur in data being analyzed with a sign test or a signed rank test, nonparametric methods textbooks and software consistently recommend that the zeroes be deleted and the data analyzed as though zeroes did not exist. This advice is not consistent with the objectives of the majority of applications. In most settings a better approach would be to view the tests as testing hypotheses about a population median. There are relatively simple p-values available that are consistent with this viewpoint of the tests. These methods produce tests with good properties for testing a different (often more appropriate) set of hypotheses than those addressed by tests that delete the zeroes.
Highlights
The sign test The sign test has a lengthy history in statistics, including its early application by Arbuthnot (1710) in eighteenth century and its formal description by Dixon and Mood (1946)
When conducting the sign test on this data, what roles should be paid by the 2 zero observations?
The purpose of this article is to recommend that the sign and signed rank tests be viewed as tests about population medians when handling observed zeroes
Summary
The sign test The sign test has a lengthy history in statistics, including its early application by Arbuthnot (1710) in eighteenth century and its formal description by Dixon and Mood (1946). We get the p-value calculated as p − value = 2P(B ≥ 15|B~bin(18,0.5)) = 0.0075 This conditional sign test’s p-value is commonly used in practices (deleting zeroes). When testing the two-sided hypothesis in (1), they recommended use of the p Note that, this p-value only depends on n+ and n−, ignoring the number of zeroes. Statisticians with practical experience often claim that zeroes, which represent “no change in condition”, are meaningful and important responses that should not be discarded They argue that in most, but not all, settings, the zeroes should lend credence to the null hypothesis. The purpose of this article is to recommend that the sign and signed rank tests be viewed as tests about population medians when handling observed zeroes. Article presents, there are simple, practical ways to find p-values for the tests corresponding to this viewpoint
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