Chi-square test

A chi-square test is any statistical hypothesis test in which the test statistic has a chi-square distribution if the null hypothesis is true. These include:


 * Pearson's chi-square test, the original and most widely used chi-squared test
 * General likelihood-ratio tests are approximately chi-square tests when the sample-size is large. They are widely used in logistic regression. However, in cases where the exact distribution of the likelihood-ratio statistic can be easily calculated e.g., F-tests in the analysis of variance and t-tests are likelihood-ratio tests, it is more appropriate to refer to use these exact statistics.
 * Yates' chi-square test, or Yates' correction for continuity
 * Mantel-Haenszel chi-square test
 * linear-by-linear association chi-square test
 * McNemar's test

The most common form of the test statistic is:


 * $$\chi^2=\sum\frac{(\mathrm{observed}-\mathrm{expected})^2}{\mathrm{expected}},$$

where the word "expected" often does not denote an expected value, but an observable estimate of an expected value. However, likelihood ratio tests do not have this form.

The chi-square test is a statistical tool to separate real effects from random variation. It can be used on data that is:
 * 1) randomly drawn from the population
 * 2) reported in raw counts of frequency (not percentages or rates)
 * 3) measured variables must be independent
 * 4) values on independent and dependent variables must be mutually exclusive
 * 5) observed frequencies cannot be too small

The chi-square test determines the probability of obtaining the observed results by chance, under a specific hypothesis. It tests independence as well as goodness of fit for a set of data.

Chi-Quadrat-Test Test du χ² Test chi quadrato カイ二乗検定 Hī kvadrāta kritērijs Chi-kwadraattoets Test zgodności chi-kwadrat Tes chi-kuadrat Kiểm định chi-bình phương