M3 - Chi-Squared test

Question 1

The Chi-squared test of independence

Answer 1

The Chi-Squared Test is a statistical test used to determine if there is a significant association between two categorical variables. It compares the observed counts in each category to the counts we would expect to find if there were no association between the variables.

Question 2

Hypothesis chi squared

Answer 2

Null hypothesis (H₀): The two categorical variables are independent. This means the proportion of one variable’s categories is the same across all categories of the other variable.

Alternative hypothesis (H₁): The two categorical variables are dependent (related). This means the proportion of one variable’s categories is not the same across all categories of the other variable.

Question 3

Assumptions chi squared

Answer 3

• The expected frequencies (number of expected data results) per cell is greater than 5
• Uses only categories and not rankings (e.g. it won’t work for tests where you are comparing categories that have value associated with them such as different levels of education or different levels of organisations)
• Groups must be categorical
• The observations should be independent (meaning that the result of one test doesn’t affect the result of another)