For Questions 12-17: A researcher is interested in treatment of infants with plagiocephaly. He enrolled 100 infants with plagiocephaly and randomized them to one of three groups:
Group 1 – Received standard care (helmeting at 4 months)
Group 2 – Received weekly parent education sessions focused on tummy time and safe sleep
Group 3 – Received soft tissue manual therapy by an occupational therapist
The researcher evaluated the success of the interventions by measuring transcranial diameter difference (TDD) at 6 months. The researcher tested the assumptions of normality and homogeneity of variances and both assumptions were met. Here is the SPSS output:
| Descriptives |
| TDD |
| | N | Mean | Std. Deviation | Std. Error | 95% Confidence Interval for Mean | Minimum | Maximum |
| Lower Bound | Upper Bound |
| 1.00 | 33 | .6788 | .22327 | .03887 | .5996 | .7580 | .20 | 1.00 |
| 2.00 | 33 | .4667 | .29545 | .05143 | .3619 | .5714 | .00 | .90 |
| 3.00 | 34 | .6471 | .19107 | .03277 | .5804 | .7137 | .20 | .90 |
| Total | 100 | .5980 | .25544 | .02554 | .5473 | .6487 | .00 | 1.00 |
| ANOVA |
| TDD |
| | Sum of Squares | df | Mean Square | F | Sig. |
| Between Groups | .866 | 2 | .433 | 7.513 | .001 |
| Within Groups | 5.593 | 97 | .058 | | |
| Total | 6.460 | 99 | | | |
Post Hoc Tests
| Multiple Comparisons |
| Dependent Variable: TDD |
| Tukey HSD |
| (I) Treatment | (J) Treatment | Mean Difference (I-J) | Std. Error | Sig. | 95% Confidence Interval |
| Lower Bound | Upper Bound |
| 1.00 | 2.00 | .21212* | .05912 | .002 | .0714 | .3528 |
| 3.00 | .03173 | .05868 | .851 | -.1079 | .1714 |
| 2.00 | 1.00 | -.21212* | .05912 | .002 | -.3528 | -.0714 |
| 3.00 | -.18039* | .05868 | .008 | -.3201 | -.0407 |
| 3.00 | 1.00 | -.03173 | .05868 | .851 | -.1714 | .1079 |
| 2.00 | .18039* | .05868 | .008 | .0407 | .3201 |
| *. The mean difference is significant at the 0.05 level. |
1. The SPSS output above shows that the researcher ran an ANOVA. Why would the researcher chose to run an ANOVA instead of running multiple t-tests to compare the three groups? (5 points)
2. What is the null hypothesis being tested? (5 points)
3. What is the F value from this analysis? (5 points)
4. What is the p value from the ANOVA analysis? (5 points)
5. Would you reject or fail to reject the null hypothesis? (5 points)
6. Using both the ANOVA output table and the Multiple Comparisons post hoc table, what conclusion would you make? (10 points)