Chi-Square Test

The chi-square test is used to test if two Categorical Variable variables are independent.

It is an example of a Hypothesis Test.

Example

• Testing if people who wear luminous vests to work are more likely to be injured more often than people who wear suits
• Testing if an equal number of people come into a shop each day
• Testing if gender has an impact on political party preference

---

Usage

To perform a chi-squared test:

1. Formulate the hypotheses you wish to test
2. Calculate the value of ${\chi }^2$ with the formula
3. Calculate the degrees of freedom
4. Use the tables to read a P-value
5. Use the P-value to determine if the Null Hypothesis should be accepted or rejected.

---

Formula

${\chi }^2={\sum }_{i=1}^K\frac{(O_i-E_i{)}^2}{E_i}$

Where

• $O_i$ is the actual frequency of a value
• $E_i$ is the expected value of the frequency
• $K$ is the number of elements in the sample space you are running the chi-squared test on

---

Degrees of Freedom

The degrees of freedom for a chi-squared test can be calculated as: $df=k-1$

Where

• $k$ is the number of elements in the sample space you are running the chi-squared test on

---

Tables