Linganisha mbinu

	Kipimo cha Robust Chi-Square	Kipimo cha Chi-square cha Uhuru
Nyanja	Takwimu	Takwimu
Familia	Hypothesis test	Hypothesis test
Mwaka wa asili	1984 (power divergence); 1900 (Pearson baseline)	1900
Mwanzilishi	Cressie & Read (power divergence framework); Pearson chi-square extended by multiple authors	Karl Pearson
Aina	Robust categorical association / goodness-of-fit test	Nonparametric test of association
Chanzo asilia	Cressie, N., & Read, T. R. C. (1984). Multinomial goodness-of-fit tests. Journal of the Royal Statistical Society: Series B, 46(3), 440–464.	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.
Majina mbadala	robust chi-squared test, Cressie-Read power divergence test, adjusted chi-square test, robust contingency test	chi-squared test, Pearson's chi-square test, test of independence, ki-kare bağımsızlık testi
Zinazohusiana	3	2
Muhtasari	The robust chi-square test extends the classic Pearson chi-square framework to remain reliable when standard assumptions — especially the minimum expected-cell-count rule — are violated. Using power divergence statistics (Cressie & Read, 1984) or resampling-based corrections, it produces valid inferences for sparse contingency tables, small samples, and unbalanced categorical data where the ordinary chi-square approximation breaks down.	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.