Pearson's chi-squared test is used to determine whether there is a statistically significant difference between the expected frequencies and the observed frequencies in one or more categories of a …

Nov 27, 2025 · Chi-squared test, a hypothesis-testing method in which observed frequencies are compared with expected frequencies for experimental outcomes. In hypothesis testing, data from a …

Dec 15, 2025 · Learn about the Chi-Square test, its formula, and types. Understand when to use the tests, chi-square distributions, and how to solve Chi-Square problems.

May 23, 2022 · The chi-square test of independence is used to test whether two categorical variables are related to each other. Chi-square is often written as Χ 2 and is pronounced “kai-square” (rhymes …

Oct 2, 2025 · Chi-square is a statistical test used to examine the differences between categorical variables from a random sample in order to judge the goodness of fit between expected and …

So how do we calculate this p-value? We use the Chi-Square Test! Note: Chi Sounds like "Hi" but with a K, so it sounds like " Ki square" And Chi is the greek letter Χ, so we can also write it Χ2. Important …

Aug 29, 2023 · There are three main types of Chi-square tests, tests of goodness of fit, the test of independence, and the test for homogeneity. All three tests rely on the same formula to compute a …

Aug 2, 2025 · In categorical analysis, chi-square tests are used to determine whether observed frequencies differ significantly from expected frequencies under a given hypothesis. Chi-squared …

The chi-squared test provides a way to test if an observed result (the number of heads) could feasibly have arisen randomly, or whether the original assumption (in this case of fairness) must be wrong.

Comprehensive lecture notes on Chi-Square tests (χ²), including goodness-of-fit and test of independence. Features interactive visualization, manual calculation examples, R code, formulas, …