Background: Anorexia is well known to bedifficult to treat. The data set provided below contains data onthe weight gain for three groups of young female anorexia patients.These groups include a control group, a group receiving cognitivebehavioral therapy and a group receiving family therapy.Source: Hand, D. J., Daly, F., McConway, K., Lunn,D. and Ostrowski, E. eds (1993) A Handbook of Small Data Sets.Chapman & Hall, Data set 285 (p. 229).
Directions: Click on the Data button below todisplay the data. Copy the data into a statistical software packageand click the Data button a second time to hide it. Then perform ananalysis of variance (ANOVA) to determine whether or not thedifferences in weight gain between the treatment groups isstatistically significant.
Data
| Control | CBT | Family |
|---|
| -0.5 | 1.7 | 11.4 |
| -9.3 | 0.7 | 11 |
| -5.4 | -0.1 | 5.5 |
| 12.3 | -0.7 | 9.4 |
| -2 | -3.5 | 13.6 |
| -10.2 | 14.9 | -2.9 |
| -12.2 | 3.5 | -0.1 |
| 11.6 | 17.1 | 7.4 |
| -7.1 | -7.6 | 21.5 |
| 6.2 | 1.6 | -5.3 |
| -0.2 | 11.7 | -3.8 |
| -9.2 | 6.1 | 13.4 |
| 8.3 | 1.1 | 13.1 |
| 3.3 | -4 | 9 |
| 11.3 | 20.9 | 3.9 |
| 0 | -9.1 | 5.7 |
| -1 | 2.1 | 10.7 |
| -10.6 | -1.4 | |
| -4.6 | 1.4 | |
| -6.7 | -0.3 | |
| 2.8 | -3.7 | |
| 0.3 | -0.8 | |
| 1.8 | 2.4 | |
| 3.7 | 12.6 | |
| 15.9 | 1.9 | |
| -10.2 | 3.9 | |
| 0.1 | |
| 15.4 | |
| -0.7 | |
- State the null and alternativehypotheses.
- Compute the test statistic. Document how SSTrand SSE were computed. Use 4 decimal places for the sample means,sample standard deviations and the grand mean and round youranswers for SSTr and SSE to 2 decimal places.
Use the values for SSTr and SSE to complete the following ANOVAtable. Round each of your answers to 2 decimal places.
| Source | S.S. | df | M.S. | F |
| Treatment | | | | |
| Error | | | | |
| Total | | | | |
- Compute the p-value. Provide the nameof the distribution and the parameters used to compute thep-value. Then enter your answer rounded to 4 decimalplaces.
- Interpret the results of the significancetest. Is this result statistically significant? Is thisresult important from a practical perspective?
