Chapter 26 Comparing Counts

Independence of Categorical Variables. Two categorical variables. Are two variables related to each other? Unrelated = independent Related = dependent

Relationship between Two Categorical Variables Two-Way Table Rows = Columns = Table entries =

Two-Way Table Eye Colors Gender Total Female 370 352 198 187 18 1125 Eye Color and Gender reported by over 2000 Stat 101 students in beginning of semester survey. Eye Colors Gender Blue Brown Green Hazel Other Total Female 370 352 198 187 18 1125 Male 359 290 110 160 24 943 729 642 308 347 42 2068

Hypothesis Test Null Hypothesis Alternative Hypothesis

Expected Counts If HO is true, we would expect to get a certain number of counts in each cell.

Expected Counts Expected cell count is close to observed cell count ______________________________________________________________ Expected cell count is far from observed cell count

Example of Calculating Expected Counts

Table with Expected Counts

Chi-Square Statistic Measures how far the observed values are from the expected values. Take sum over all cells in table.

Example of Chi-Square Statistic

Chi-square Statistic

Hypothesis Test

Hypothesis Test