Linganisha mbinu

	Uchanganuzi wa Marudio	Kipimo kamili cha Binomial	Uchanganuzi wa Mseto wa Tabulasi
Nyanja	Takwimu	Takwimu	Takwimu
Familia	Hypothesis test	Regression model	Hypothesis test
Mwaka wa asili	19th century	1988	1900
Mwanzilishi	Classical statistics (no single inventor)	Classical exact test; textbook treatment by Siegel & Castellan	Karl Pearson
Aina	Descriptive summary	Exact one-sample test for a proportion	Descriptive and inferential categorical analysis
Chanzo asilia	Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed.). SAGE. ISBN: 978-1446249185	Siegel, S. & Castellan, N. J. (1988). Nonparametric Statistics for the Behavioral Sciences (2nd ed.). McGraw-Hill. ISBN: 978-0070573574	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	frequency distribution, frequency table, tally analysis, count analysis	exact binomial test, binomial probability test, exact test for a proportion, Tam Binom Testi	crosstab, contingency table analysis, two-way frequency table, bivariate frequency analysis
Zinazohusiana	3	2	5
Muhtasari	Frequency analysis is a fundamental descriptive technique that tallies how often each distinct value or category appears in a dataset. It produces absolute counts, relative percentages, and cumulative frequencies, giving an immediate picture of how observations are distributed across categories. It is the natural first step when exploring categorical or discrete variables before applying inferential tests.	The exact binomial test checks whether the observed number of successes in a fixed number of independent trials is consistent with a pre-specified success probability p₀. Because it computes exact binomial tail probabilities rather than relying on a normal approximation, it is the gold standard for testing a proportion in small samples; this two-sided formulation follows Siegel & Castellan's classic treatment (1988).	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.