# Chi squared Test

## Definition

### Health Economics

C

^{2}(chi-squared or 'chi-square') is a statistical test of how well sampled or modelled data 'fit' other data sets, for example, data on sickness and data on exposure to a hazard, or data predicted by a model and the actual data. The test is based on the chi-square distribution. The latter is a skewed distribution obtained from a variable c having a normal distribution so that the variable's square (c^{2}) has a chi-squared distribution. Formally, it is used to test the null hypothesis that two or more population distributions do not differ. It is the ratio of the sum of the squared differences between observed (*O*) and expected (*E*) values to the expected value:[

*O*_{i}-*E*_{i}]^{2}c

^{2}= S*E*_{i}There are two well-known versions, the Pearson c

^{2}test and the Mantel-Haenszel test.