1. Chapter 26
Comparing Counts

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

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

4. Two-Way Table Eye Colors Gender Total Female 370 352 198 187 18 1125
Eye Color and Gender reported by over 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

5. Hypothesis Test
Null Hypothesis
Alternative Hypothesis

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

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

8. Example of Calculating Expected Counts

9. Table with Expected Counts

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

11. Example of Chi-Square Statistic

12. Chi-square Statistic

13. Hypothesis Test

14. Hypothesis Test