Question

What can chi-squared tests indicate about categorical data?

Answer 1

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 = (Observed- Expected)^2/(Expected)`

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.