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May Spearman's rank correlation coefficient be used for categorical data?


We cannot use Spearman's rank correlation coefficient for nominal data, but we may use it for ordinal data, i.e., categorical data that can be ranked. However, care should be taken when there are not too many categorical levels. Note the Spearman’s rank correlation coefficient works on the ranks of the data. When there are only a few ordinal levels of a variable, the ranking of the values may become ambiguous. For example, we may give ranks for the dataset "30, 23, 12, 56, 3" (the ranks are "4, 3, 2, 5, 1") but there is an ambiguity in giving ranks for the dataset "2, 3, 1, 2, 2" when a variable comprises only 3 levels, since we have three values of "2" which are called ties. Although there are correction methods for ties, an excess number of ties resulting from highly categorical data may still bias the estimation of the correlation between the variables.

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