# Chi-Squared Test

Get introduced to different variations of the chi-squared test, like the goodness of fit and the test of independence.

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We use the chi-squared test to determine if there are statistically significant differences between the observed data and the expected data in a population. This test helps us investigate the relationship between two categorical variables.

Suppose we want to find the relationship between smoking and lung cancer. We would have four categories:

• Smokers with lung cancer
• Smokers without lung cancer
• Nonsmokers with lung cancer
• Nonsmokers without lung cancer

The chi-squared test calculates the difference between the expected numbers and the observed numbers of lung cancer cases as a result of smoking.

To calculate the test statistic, we sum up the squares of the differences between the observed and expected frequencies. Then, we divide the sum by the expected frequencies. The formula is as follows:

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