Complete subsequent Tukey Tests and LSD tests on all significant effects and state your conclusions. When...
Complete subsequent Tukey Tests and LSD tests on all significant effects and state your conclusions. When conducting post hoc tests for the type of infection x Time interaction, I want you to examine the effects of type of brain damage at each level of time.
1-2 Years 3-5 Years 7-10 Years
Postencephalitic. 71.7 62.25 50.00
Postmeningitic. 82.0 79.25 60.0
Postoperative Control 71.75 81.75 89.75
Main Effect of Infection
Postencephalitic Postmeningitic Postoperative Control
61.32 73.75 81.08
Critical difference Tukey =
Critical difference LSD =
Conclusions Tukey:
Conclusions LSD:
Subsequent Tests for Infection x Time Interaction
Critical Difference Tukey =
Critical Difference LSD =
1-2 years
Conclusions: Tukey:
Conclusions: LSD:
3-5 years
Conclusions: Tukey:
Conclusions: LSD:
7-10 years
Conclusions: Tukey:
Conclusions: LSD:
- (10 points) Describe a main effect, simple effect and an interaction is and what the relationship between simple effects and interactions is?
Homework Answers
Solution :
| Given, | |||||
| 1-2 Years 3-5 Years 7-10 Years | |||||
| Postencephalitic 71.7 62.25 50.00 | |||||
| Postmeningitic 82.0 79.25 60.0 | |||||
| Postoperative Control 71.75 81.75 89.75 | |||||
| Main Effect of Infection | |||||
| Postencephalitic Postmeningitic Postoperative Control | |||||
| 61.32 73.75 81.08 | |||||
|
The formula for Tukey HSD: |
|||||
 |
|||||
| Where: | |||||
| Mi – Mj is the difference between the pair of means. to calculate this, Mi should be larger than Mj | |||||
| MSw is the Mean Square Within, and n is the number in the group or treatment. | |||||
| Groups count sum average variance | |||||
| Postencephalitic 3 183.95 61.32 10.88 | |||||
| Postmeningitic 3 220.05 73.75 11.98 | |||||
| Postoperative Control 3 243.24 81.08 9.01 | |||||
| X1 ? X2 = 61.32 ? 73.75 = -12.43 | |||||
| X1 ? X3 = 61.32 ?81.08= -19.76 | |||||
| X 2 ? X3 = 73.75 ?81.08 = ?7.33 | |||||
| F value: 2.616886? | |||||
| P value: 0.152362? | |||||
| The formula for the least significant difference is: | |||||
 |
|||||
| Where: | |||||
| t = critical value from the t-distribution table | |||||
| MSw = mean square within, obtained from the results of your ANOVA test | |||||
| n = number of scores used to calculate the means | |||||
| Critical Values for the Tukey Q Test | |||||
| d.f. = N – K (ANOVA Error or Within d.f.) for ANOVA: Single Factor | |||||
| d.f. = N – R*C (ANOVA Within d.f.) for ANOVA: Two-Factor With Replication | |||||
| d.f. = (R – 1)*(C – 1) (ANOVA Error d.f.) for ANOVA: Two-Factor Without Replication | |||||
| Number of Groups (Treatments) = K | |||||
| Lsd result | |||||
| SS df MS F | |||||
| Between | 135.2882 2 67.6441 0.3527 | ||||
| Within | 1150.5933 6 191.7656 | ||||
| Total | 1285.8815 8 | ||||
| LSD 0 | |||||
| SS = Sum of Squares, | df = Degrees of Freedom | ||||
| MS = Mean Squares, | F = F - Ratio Test | ||||
| LSD = Fisherman's Least Significant Difference | |||||
| Main Effect of Infection | |||||
| Lsd result | |||||
| SS df MS F | |||||
| Between | 199.5638 2 99.7819 - | ||||
| Within | 70.385 2 35.1925 - | ||||
| Total | 199.5638 2 | ||||
| LSD 0 | |||||
| 1-2 years | |||||
| Lsd result | |||||
| SS df MS F | |||||
| Between 0 0 - - |
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