مقایسهٔ روش‌ها

	آزمون استقلال کی-دو	ضریب V کرامر	آزمون مک‌نمار (McNemar's test)
حوزه	آمار	آمار	آمار
خانواده	Hypothesis test	Hypothesis test	Hypothesis test
سال پیدایش	1900	1946	1947
پدیدآور	Karl Pearson	Harald Cramér	Quinn McNemar
نوع	Nonparametric test of association	Nonparametric association measure	Nonparametric test for paired binary data
منبع بنیادین	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.	Cramér, H. (1946). Mathematical Methods of Statistics. Princeton University Press. ISBN: 978-0691080420	McNemar, Q. (1947). Note on the sampling error of the difference between correlated proportions or percentages. Psychometrika, 12(2), 153–157.
نام‌های دیگر	chi-squared test, Pearson's chi-square test, test of independence, ki-kare bağımsızlık testi	cramers v, cramer v, phi coefficient (r×c), Cramer's V (İlişki Kuvveti)	McNemar chi-square test, test for correlated proportions, paired binary test, McNemar Testi
مرتبط	2	3	5
خلاصه	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.	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.	McNemar's test is a nonparametric hypothesis test that compares two paired (correlated) binary proportions, such as a yes/no measurement taken on the same subjects before and after an intervention. It was introduced by Quinn McNemar in 1947 and works on the 2×2 table of matched outcomes.