Tschuprow's T

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Tschuprow's T

In statistics, Tschuprow's T is a measure of association between two nominal variables, giving a value between 0 and 1 (inclusive). It is closely related to Cramér's V, coinciding with it for square contingency tables. It was published by Alexander Tschuprow (alternative spelling: Chuprov) in 1939.[1]


For an r × c contingency table with r rows and c columns, let be the proportion of the population in cell and let


Then the mean square contingency is given as

and Tschuprow's T as


T equals zero if and only if independence holds in the table, i.e., if and only if . T equals one if and only there is perfect dependence in the table, i.e., if and only if for each i there is only one j such that and vice versa. Hence, it can only equal 1 for square tables. In this it differs from Cramér's V, which can be equal to 1 for any rectangular table.


If we have a multinomial sample of size n, the usual way to estimate T from the data is via the formula

where is the proportion of the sample in cell . This is the empirical value of T. With the Pearson chi-square statistic, this formula can also be written as

See also

Other measures of correlation for nominal data:

Other related articles:

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  1. Tschuprow, A. A. (1939) Principles of the Mathematical Theory of Correlation; translated by M. Kantorowitsch. W. Hodge & Co.
  • Liebetrau, A. (1983). Measures of Association (Quantitative Applications in the Social Sciences). Sage Publications