مقایسهٔ روش‌ها

	تحلیل فراوانی	آزمون دقیق دوجمله‌ای	تحلیل جدول ترکیبی	آمار توصیفی
حوزه	آمار	آمار	آمار	آمار
خانواده	Hypothesis test	Regression model	Hypothesis test	Hypothesis test
سال پیدایش	19th century	1988	1900	1977
پدیدآور	Classical statistics (no single inventor)	Classical exact test; textbook treatment by Siegel & Castellan	Karl Pearson	John W. Tukey
نوع	Descriptive summary	Exact one-sample test for a proportion	Descriptive and inferential categorical analysis	Summary procedure
منبع بنیادین	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.	Tukey, J.W. (1977). Exploratory Data Analysis. Addison-Wesley. ISBN: 978-0201076165
نام‌های دیگر	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	summary statistics, exploratory data summary, Betimsel İstatistik
مرتبط	3	2	5	6
خلاصه	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.	Descriptive statistics is a set of procedures that numerically and visually summarises the essential characteristics of a dataset: central tendency (mean, median, mode), spread (standard deviation, interquartile range), shape (skewness, kurtosis), and frequency distributions. Systematised for applied data analysis by John W. Tukey in his 1977 work on Exploratory Data Analysis, descriptive statistics serves as the indispensable first step before any inferential or modelling procedure.