(See Solution) Below are two data sets that are intentionally exaggerated to help clarify the procedures underlying analysis of variance. In each case, the
Question: Below are two data sets that are intentionally exaggerated to help clarify the procedures underlying analysis of variance. In each case, the experimenter is interested in the number of spelling errors made as a function of the kind of reward the teacher provides. Group 1 receives stickers; group 2 receives verbal praise; and group 3 receives candy.
| Experiment 1 | Experiment 2 |
| Group 1 | Group 2 | Group 3 | Group 1 | Group 2 | Group 3 | ||
| 5 | 0 | 1 | 1 | 5 | 4 | ||
| 0 | 0 | 10 | 2 | 3 | 4 | ||
| 3 | 10 | 8 | 2 | 4 | 5 | ||
| 0 | 1 | 3 | 3 | 5 | 7 | ||
| 2 | 9 | 3 | 2 | 3 | 5 | ||
| Mean (Xbar) | 2 | 4 | 5 | 2 | 4 | 5 |
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By inspection, in which case would you guess that the difference among groups is more likely to be
statistically significant. Why? - Carry out the analysis of variance for Experiment 1. Are the results significant at the .05 level?
- Why did you retain (or reject) Ho in part (b) above?
- Carry out the analysis of variance for Experiment 2. Are the results significant at the .05 level?
- Why did you retain (or reject) Ho in part (d) above?
- Calculate the effect sizes, or eta squared, for both Experiment 1 and 2.
- Why do the F ratio and eta squared statistics differ dramatically for the two experiments even
though the sample means (i.e., 2,5,4) are the same for both?
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