Chi-Square Test

One-Sample Goodness-of-Fit Test

Determines if a single categorical variable matches a known or hypothesized distribution.

One-Sample Goodness-of-Fit Test

Example: Comparing local car color proportions to global proportions.

Chi-Square Test of Association (Independence)

Determines if there is a relationship (association) between two categorical variables

Chi-Square Test of Association (Independence)

Example: Checking if gender correlates with political party preference

• Data must be categorical (nominal or ordinal level).

• Expected frequency in each category must be at least 5.

• Groups must be mutually exclusive.

• Observations must be independent.

ASSUMPTIONS OF THE CHI-SQUARE TEST (4)

The sample data follows the hypothesized distribution.

One-Sample Goodness-of-Fit Test

• Null Hypothesis (H₀):

The sample data does not follow the hypothesized distribution.

One-Sample Goodness-of-Fit Test:

Alternative Hypothesis (H₁):

• There is no significant association between the two variables

Chi-Square Test of Association

• Null Hypothesis (H₀):

There is a significant association between the two variables.

Chi-Square Test of Association

• Alternative Hypothesis (H₀):

p-value < 0.05.

One-Sample Goodness-of-Fit Test Decision Rule: Reject H₀ if

p-value < 0.05.

Chi-Square Test of Association Reject H₀ if