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Contingency table
Two-dimensional matrix presenting the joint distribution of two categorical variables, with observed counts in each cell crossing the categories.
Chi-square test
Non-parametric statistical test evaluating the association between categorical variables by comparing observed frequencies to expected frequencies under the null hypothesis.
Degrees of freedom
Statistical parameter calculated as (number of rows - 1) × (number of columns - 1) in a contingency table, determining the reference distribution of the test.
p-value
Probability of obtaining a test statistic at least as extreme as the one observed, under the null hypothesis of no association between the variables.
Independence test
Specific application of the chi-square test checking whether two categorical variables are statistically independent in the studied population.
Goodness-of-fit test
Chi-square variant comparing an observed distribution to a specified theoretical distribution, to evaluate how well the data fit an expected model.
Cross-tabulation
Tabular representation summarizing relationships between categorical variables, including absolute frequencies, relative frequencies, and margins for each category.
Observed frequency
Actual number of individuals in each cell of the contingency table, corresponding to raw data collected in the sample.
Expected frequency
Theoretical frequency in each cell under the null hypothesis, calculated as (row total × column total) / grand total of the sample.
Contingency coefficient
Measure of association between categorical variables derived from chi-square, ranging from 0 to a maximum value depending on the table size.
Cramér's V
Standardized association coefficient ranging from 0 to 1, measuring the strength of the relationship between categorical variables by adjusting chi-square for sample size.
Fisher's exact test
Alternative test to chi-square for small samples, calculating the exact probability of the observed distribution under the null hypothesis of independence.
Standardized residuals
Differences between observed and expected frequencies, normalized by their standard deviation, identifying the cells contributing most to the overall dependence.
Marginal table
Summary of a contingency table presenting row and column totals, essential for calculating expected frequencies and conditional proportions.
Theoretical frequency
Expected value in each cell if the variables were independent, serving as a reference to evaluate significant deviations in the analysis.
Pearson's chi-square
Fundamental test statistic calculated as the sum of squared normalized deviations between observed and theoretical frequencies, following a chi-square distribution.
Mc Nemar Test
Specialized statistical test for paired dichotomous data, assessing changes in proportions between two time measurements on the same sample.
Yates Correction
Continuity adjustment applied to chi-square for 2×2 tables with small sample sizes, reducing observed frequencies by 0.5 to improve approximation.
Probability Table
Joint distribution of probabilities for each combination of categories, normalized by the total sample size to facilitate interpretation.