مقایسهٔ روش‌ها

	آزمون استقلال کای-دو پیرسون	ضریب V کرامر	رگرسیون لجستیک	آزمون مک‌نمار (McNemar's test)
حوزه	آمار	آمار	آمار پژوهش	آمار
خانواده	Hypothesis test	Hypothesis test	Process / pipeline	Hypothesis test
سال پیدایش	1900	1946	1958	1947
پدیدآور	Karl Pearson	Harald Cramér	David Roxbee Cox	Quinn McNemar
نوع	Nonparametric association / goodness-of-fit	Nonparametric association measure	Method	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. Philosophical Magazine, Series 5, 50(302), 157–175.	Cramér, H. (1946). Mathematical Methods of Statistics. Princeton University Press. ISBN: 978-0691080420	Cox, D. R. (1958). The regression analysis of binary sequences. Journal of the Royal Statistical Society, Series B, 20(2), 215–242.	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, χ² test, Ki-Kare Testi, chi-square test	cramers v, cramer v, phi coefficient (r×c), Cramer's V (İlişki Kuvveti)	logit model, binomial logistic regression, LR	McNemar chi-square test, test for correlated proportions, paired binary test, McNemar Testi
مرتبط	3	3	3	5
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.	Logistic regression is a statistical method for modeling the probability of a binary outcome (disease present/absent, success/failure) as a function of continuous and categorical predictors. Developed by David Roxbee Cox (1958), it solves the problem of predicting categorical outcomes by applying a logistic transformation to constrain predictions to the [0,1] probability interval, enabling accurate risk stratification, diagnostic prediction, and causal inference in epidemiology, medicine, and social science.	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.