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Statistics vocabulary · Hypothesis Testing

Chi-square test

Meaning in statistics, with examples

/ˌkaɪ ˈskwer test/nounCore term

In statistics, chi-square test means: A test used with counts in categories, most often to check whether two categorical variables are related or whether observed frequencies match the expected ones.

In Turkish: ki-kare testi

How it is used

Written χ² and reported as 'χ²(2, N = 300) = 8.41, p = .015'. The two common versions are the test of independence (on a cross-tabulation) and the goodness-of-fit test. Expected counts should not be too small; otherwise Fisher's exact test is often used.

Example sentences

  1. A chi-square test showed that smoking status was associated with gender, χ²(1, N = 420) = 6.12, p = .013.

  2. Several cells have expected counts below 5, so the chi-square test may not be reliable.

Common collocations

  • chi-square test of independence
  • chi-square goodness-of-fit test
  • Pearson's chi-square
  • chi-square statistic
  • categorical variableA variable whose values are groups or labels rather than measured quantities, such as blood type, city of residence or 'yes/no' answers.
  • cross-tabulationA table that shows how the categories of two or more categorical variables combine, with the number of cases in each combination.
  • goodness of fitHow well a model or a theoretical distribution matches the observed data, measured with statistics such as R-squared, chi-square or information criteria.
  • degrees of freedomThe number of values in a calculation that are free to vary once certain constraints are fixed; it sets the exact shape of distributions such as t, chi-square and F.
  • frequencyThe number of times a value or category occurs in a data set; a relative frequency gives the same information as a proportion or percentage.

More terms: Hypothesis Testing

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