قارن الطرق

	اختبار مربع كاي بيرسون للاستقلال	مقياس كرَامِر V
المجال	الإحصاء	الإحصاء
العائلة	Hypothesis test	Hypothesis test
سنة النشأة	1900	1946
صاحب الطريقة	Karl Pearson	Harald Cramér
النوع	Nonparametric association / goodness-of-fit	Nonparametric association measure
المصدر التأسيسي	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
الأسماء البديلة	chi-squared test, χ² test, Ki-Kare Testi, chi-square test	cramers v, cramer v, phi coefficient (r×c), Cramer's V (İlişki Kuvveti)
ذات صلة	3	3
الملخص	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.