StellarComparing Observed to Expected Counts
In Units 6-7, we compared proportions or means across two groups. Now we compare entire distributions across multiple categories.
Motivating question: A die is rolled 60 times. We'd expect 10 outcomes per face. We observe:
| Face | Observed | Expected |
|---|---|---|
| 1 | 8 | 10 |
| 2 | 13 | 10 |
| 3 | 9 | 10 |
| 4 | 11 | 10 |
| 5 | 7 | 10 |
| 6 | 12 | 10 |
Are these differences due to chance, or is the die unfair?
We need a statistic that measures the overall discrepancy between observed and expected counts across all categories.