Assumptions
The chi-squared test, when used with the standard approximation that a chi-squared distribution is applicable, has the following assumptions:
- Simple random sample – The sample data is a random sampling from a fixed distribution or population where each member of the population has an equal probability of selection. Variants of the test have been developed for complex samples, such as where the data is weighted.
- Sample size (whole table) – A sample with a sufficiently large size is assumed. If a chi squared test is conducted on a sample with a smaller size, then the chi squared test will yield an inaccurate inference. The researcher, by using chi squared test on small samples, might end up committing a Type II error.
- Expected cell count – Adequate expected cell counts. Some require 5 or more, and others require 10 or more. A common rule is 5 or more in all cells of a 2-by-2 table, and 5 or more in 80% of cells in larger tables, but no cells with zero expected count. When this assumption is not met, Yates's Correction is applied.
- Independence – The observations are always assumed to be independent of each other. This means chi-squared cannot be used to test correlated data (like matched pairs or panel data). In those cases you might want to turn to McNemar's test.
Read more about this topic: Pearson's Chi-squared Test
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