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In statistics, Cramér's V (sometimes referred to as Cramér's phi and denoted as φ''c'') is a measure of association between two nominal variables, giving a value between 0 and +1 (inclusive). It is based on Pearson's chi-squared statistic and was published by Harald Cramér in 1946.〔Cramér, Harald. 1946. ''Mathematical Methods of Statistics''. Princeton: Princeton University Press, p282. ISBN 0-691-08004-6〕 ==Usage and interpretation== φ''c'' is the intercorrelation of two discrete variables〔Sheskin, David J. (1997). Handbook of Parametric and Nonparametric Statistical Procedures. Boca Raton, Fl: CRC Press.〕 and may be used with variables having two or more levels. φ''c'' is a symmetrical measure, it does not matter which variable we place in the columns and which in the rows. Also, the order of rows/columns doesn't matter, so φ''c'' may be used with nominal data types or higher (ordered, numerical, etc.) Cramér's V may also be applied to goodness of fit chi-squared models when there is a 1×k table (e.g.: ''r''=1). In this case ''k'' is taken as the number of optional outcomes and it functions as a measure of tendency towards a single outcome. Cramér's V varies from 0 (corresponding to no association between the variables) to 1 (complete association) and can reach 1 only when the two variables are equal to each other. φ''c''2 is the mean square canonical correlation between the variables. In the case of a 2×2 contingency table Cramér's V is equal to the Phi coefficient. Note that as chi-squared values tend to increase with the number of cells, the greater the difference between ''r'' (rows) and ''c'' (columns), the more likely φc will tend to 1 without strong evidence of a meaningful correlation. V may be viewed as the association between two variables as a percentage of their maximum possible variation. V2 is the mean square canonical correlation between the variables. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Cramér's V」の詳細全文を読む スポンサード リンク
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