In many situations in which the difference in variances is not too great, the results from the AOV comparisons of the population means of the transformed data are very similar to the results that would have been obtained using the original data. In these situations, the researcher is inclined to ignore the transformations because the scale of the transformed data is not relevant to the researcher. Thus, confidence intervals constructed for the means using the transformed data may not be very relevant. One possible remedy for this problem is to construct confidence intervals using the transformed data and then perform an inverse transformation of the endpoints of the intervals. Then we would obtain a confidence interval with values having the same units of measurement as the original data. Subject A1 A2 A3 1 3.0 1.8 1.3 2 1.2 6.3 12.6 3 1.0 5.2 10.0 4 0.7 3.7 10.5 5 1.1 5.4 10.8 6 0.6 2.9 5.9 7 1.2 6.0 12.1 8 0.1 0.3 0.6 9 0.7 3.6 18.6 10 1.9 9.3 18.7 11 0.6 2.8 5.5 12 0.0 0.0 0.0 13 1.6 8.1 18.2 14 4.0 19.9 22.3 15 0.1 0.3 0.6 Mean 1.19 5.04 9.85 St. Dev. 1.097 4.97 7.41 CV .93 .99 .75 a. Test the hypothesis that the mean hours of relief for patients from the three treatments differs using a = .05. Use the original data. b. Place 95% confidence intervals on the mean hours of relief for the three treatments. c. Repeat the analysis in parts (a) and (b) using the transformed data. d. Comment on any differences in the results of the test of hypotheses. e. Perform an inverse transformation on the endpoints of the intervals constructed in part (c). Compare these intervals to the ones constructed in part (b).
In many situations in which the difference in variances is not too great, the results from the AOV comparisons of the population means of the transformed data are very similar to the results that would have been obtained using the original data. In these situations, the researcher is inclined to ignore the transformations because the scale of the transformed data is not relevant to the researcher. Thus, confidence intervals constructed for the means using the transformed data may not be very relevant. One possible remedy for this problem is to construct confidence intervals using the transformed data and then perform an inverse transformation of the endpoints of the intervals. Then we would obtain a confidence interval with values having the same units of measurement as the original data.
| Subject | A1 | A2 | A3 |
| 1 | 3.0 | 1.8 | 1.3 |
| 2 | 1.2 | 6.3 | 12.6 |
| 3 | 1.0 | 5.2 | 10.0 |
| 4 | 0.7 | 3.7 | 10.5 |
| 5 | 1.1 | 5.4 | 10.8 |
| 6 | 0.6 | 2.9 | 5.9 |
| 7 | 1.2 | 6.0 | 12.1 |
| 8 | 0.1 | 0.3 | 0.6 |
| 9 | 0.7 | 3.6 | 18.6 |
| 10 | 1.9 | 9.3 | 18.7 |
| 11 | 0.6 | 2.8 | 5.5 |
| 12 | 0.0 | 0.0 | 0.0 |
| 13 | 1.6 | 8.1 | 18.2 |
| 14 | 4.0 | 19.9 | 22.3 |
| 15 | 0.1 | 0.3 | 0.6 |
| Mean | 1.19 | 5.04 | 9.85 |
|
St. Dev. |
1.097 | 4.97 | 7.41 |
| CV | .93 | .99 | .75 |
a. Test the hypothesis that the mean hours of relief for patients from the three treatments differs using a = .05. Use the original data.
b. Place 95% confidence intervals on the mean hours of relief for the three treatments.
c. Repeat the analysis in parts (a) and (b) using the transformed data.
d. Comment on any differences in the results of the test of hypotheses.
e. Perform an inverse transformation on the endpoints of the intervals constructed in part (c). Compare these intervals to the ones constructed in part (b).
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