For Exercises 15.1 to 15.3, see pages 15-6 to 15-7; for 15.4 to 15.6, see page 15-10; for 15.7, see pages 15-12 to 15-13; for 15.8 to 15.10, see page 15-15; for 15.11, see page 15-16; for 15.12 and 15.13, see page 15-18; and for 15.14 to 15.16, see pages 15-20 to 15-21.
15.13 Numerical summaries for Case 15.2.
CASE 15.2 Find the means and standard deviations for each of the promotion-by-discount treatment combinations for the data in Case 15.2. Display the means in a table that also includes the marginal means. Plot the means and describe the main effects and the interaction. Do the standard deviations suggest that it is reasonable to pool the group standard deviations to get MSE?
15.13
We cannot pool the standard deviations because the largest is more than twice the smallest . There doesn’t appear to be an interaction. The expected price is higher for a 10% discount than for a 30% discount; the expected price is also higher with only 1 promotion compared with 5 promotions.
| Promotions | Discount | N | Mean | Standard Deviation |
| . | . | 40 | 4.357 | 0.45211 |
| . | 10 | 20 | 4.6565 | 0.34379 |
| . | 30 | 20 | 4.0575 | 0.33546 |
| 1 | . | 20 | 4.5725 | 0.45661 |
| 5 | . | 20 | 4.1415 | 0.33661 |
| 1 | 10 | 10 | 4.92 | 0.15202 |
| 1 | 30 | 10 | 4.225 | 0.38561 |
| 5 | 10 | 10 | 4.393 | 0.26854 |
| 5 | 30 | 10 | 3.89 | 0.16289 |
freqd2