مقایسهٔ روش‌ها

	آزمون استقلال کای-دو پیرسون	ضریب V کرامر
حوزه	آمار	آمار
خانواده	Hypothesis test	Hypothesis test
سال پیدایش	1900	1946
پدیدآور	Karl Pearson	Harald Cramér
نوع	Nonparametric association / goodness-of-fit	Nonparametric association measure
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. Philosophical Magazine, Series 5, 50(302), 157–175.	Cramér, H. (1946). Mathematical Methods of Statistics. Princeton University Press. ISBN: 978-0691080420
نام‌های دیگر	chi-squared test, χ² test, Ki-Kare Testi, chi-square test	cramers v, cramer v, phi coefficient (r×c), Cramer's V (İlişki Kuvveti)
مرتبط	3	3
خلاصه	The chi-square test of independence is a nonparametric hypothesis test that determines whether two categorical variables are statistically associated or independent of one another. Introduced by Karl Pearson in 1900, it remains the standard procedure for analysing contingency tables and requires no assumption of normality — only that observations are independent and that expected cell frequencies are sufficiently large.	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.