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:

Related Topics:
Hypothesis test - Chi-square distribution - Null hypothesis

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

• Pearson's chi-square 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

The most common form of the test statistic is:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:chi^2=sumrac{(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:

Related Topics:
Chi-square test - Statistical tool

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

• randomly drawn from the population
• reported in raw counts of frequency (not percentages or rates)
• measured variables must be independent
• values on independent and dependent variables must be mutually exclusive
• 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.

Related Topics:
Independence - Goodness of fit

~ ~ ~ ~ ~ ~ ~ ~ ~ ~