# What can chi-squared tests indicate about categorical data?

Apr 15, 2016

The chi-square test can be used to estimate how closely the distribution of a categorical variable matches an expected distribution. This the so called the goodness-of-fit test. It can also be used to estimate whether two categorical variables
are independent of one another. This the independence test.
The key word is test between categorical variables.

#### Explanation:

We use the chi-square test, to examine patterns between categorical variables, such as genders, political candidates, locations, or preferences, etc.

The ${\chi}^{2}$ test, tests for "A goodness of fit". This test is concerned with the distribution of one categorical variable as compared to another. The null and alternative hypotheses are set asd follows:

${H}_{0}$ : The population distribution of the variable is the same as the proposed distribution

${H}_{A}$ : The distributions are different

${\chi}^{2} = {\left(O b s e r v e d - E x p e c t e d\right)}^{2} / \left(E x p e c t e d\right)$

Observed = actual count values in each category
Expected = the predicted (expected) counts in each category if the null hypothesis were true

How do you conduct a ${\chi}^{2}$ test?

The same way as in the more familiar tests Z-test or T-test.
Effectively, following the same steps and compare a calculated value to a value on a distribution table to evaluate the probability of getting the results we have if the null hypothesis is true, just as you would with the Z and T tests.