مقایسهٔ روش‌ها

	ضریب V کرامر	آزمون استقلال کی-دو	آزمون دقیق فیشر
حوزه	آمار	آمار	آمار
خانواده	Hypothesis test	Hypothesis test	Hypothesis test
سال پیدایش	1946	1900	1922
پدیدآور	Harald Cramér	Karl Pearson	R. A. Fisher
نوع	Nonparametric association measure	Nonparametric test of association	Exact test of independence for categorical data
منبع بنیادین	Cramér, H. (1946). Mathematical Methods of Statistics. Princeton University Press. ISBN: 978-0691080420	Pearson, K. (1900). On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philosophical Magazine, 50(302), 157–175.	Fisher, R. A. (1922). On the interpretation of chi-squared from contingency tables, and the calculation of P. Journal of the Royal Statistical Society, 85(1), 87–94.
نام‌های دیگر	cramers v, cramer v, phi coefficient (r×c), Cramer's V (İlişki Kuvveti)	chi-squared test, Pearson's chi-square test, test of independence, ki-kare bağımsızlık testi	Fisher-Irwin test, exact test of independence, Fisher'ın Kesin Testi
مرتبط	3	2	2
خلاصه	Cramer's V is a nonparametric effect-size statistic that measures the strength of association between two categorical variables on a scale from 0 to 1. Introduced by the Swedish mathematician Harald Cramér in his 1946 work Mathematical Methods of Statistics, it generalises the phi coefficient to tables of any size, making it the standard companion statistic to the chi-square test.	The chi-square test of independence is a nonparametric hypothesis test that examines whether two categorical variables are associated by comparing observed and expected frequencies in a cross-tabulation. It rests on the chi-square criterion introduced by Karl Pearson in 1900.	Fisher's exact test is a nonparametric exact-probability test of independence for small-sample contingency tables, introduced by R. A. Fisher in 1922. Rather than relying on a large-sample approximation, it computes the exact probability of the observed table directly from the hypergeometric distribution.