Chi-squared tests are important for understanding how two categories relate to each other.

1. What They Do: These tests help us see if the numbers we actually observe in a table are very different from what we would expect if the two categories didn’t affect each other.

2. Example: Imagine we have a table that shows if people like tea or coffee based on their age groups. The main idea (called the null hypothesis) says that a person’s age does not influence their drink choice.

3. Calculation: To find out if there is a difference, we use a special formula:

$$\chi^2 = \sum \frac{(O - E)^2}{E}$$

In this formula, $O$ stands for the numbers we see (observed frequency) and $E$ means the numbers we expect (expected frequency).

Once we figure out the chi-squared number, we can compare it to a set number from the chi-squared distribution. This helps us decide if the two categories are independent of each other.