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	क्रॉस-टेबुलेशन विश्लेषण	स्वतंत्रता का काई-वर्ग परीक्षण (Chi-square Test of Independence)
क्षेत्र	सांख्यिकी	सांख्यिकी
परिवार	Hypothesis test	Hypothesis test
उद्भव वर्ष	1900	1900
प्रवर्तक	Karl Pearson	Karl Pearson
प्रकार	Descriptive and inferential categorical analysis	Nonparametric test of association
मौलिक स्रोत	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.	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.
उपनाम	crosstab, contingency table analysis, two-way frequency table, bivariate frequency analysis	chi-squared test, Pearson's chi-square test, test of independence, ki-kare bağımsızlık testi
संबंधित	5	2
सारांश	Cross-tabulation analysis (contingency table analysis) is a foundational descriptive and inferential technique for examining the relationship between two or more categorical variables. It arranges observed frequencies into a table of rows and columns, enabling visual inspection of patterns and formal chi-square testing of independence between the variables.	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.