statistics
1. In a study to investigate the relative effectiveness of six different instructional formats with respect to student achievement at the end of the semester, data were collected on a total of 90 students taught using one of the 6 formats described below:
Method 1: 3 hour lecture weekly
Method 2: 3 hour lecture weekly + weekly tutorial
Method 3: 3 hour lecture weekly + weekly pop quizzes
Method 4: Two 90-minute lectures weekly
Method 5: Two 90-minute lectures weekly + weekly tutorials
Method 6: Two 90-minute lectures weekly + weekly pop quizzes
Descriptive statistics for each group are given below.
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Dependent Variable:Acht |
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Group |
Mean |
Std. Deviation |
N |
|
1 |
8.4667 |
1.45733 |
15 |
|
2 |
10.2667 |
1.79151 |
15 |
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3 |
9.2267 |
1.82462 |
15 |
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4 |
10.7333 |
2.11919 |
15 |
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5 |
10.7800 |
1.68955 |
15 |
|
6 |
12.1267 |
1.99516 |
15 |
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Total |
10.2667 |
2.12999 |
90 |
An ANOVA table for testing the hypothesis of equal means was constructed and is shown below.
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Tests of Between-Subjects Effects |
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Dependent Variable:Acht |
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Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
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Corrected Model |
123.937a |
5 |
24.787 |
7.440 |
.000 |
|
Intercept |
9486.400 |
1 |
9486.400 |
2847.520 |
.000 |
|
Group |
123.937 |
5 |
24.787 |
7.440 |
.000 |
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Error |
279.843 |
84 |
3.331 |
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Total |
9890.180 |
90 |
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Corrected Total |
403.780 |
89 |
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a. R Squared = .307 (Adjusted R Squared = .266) |
(a) Based on the ANOVA table, what would you conclude about the equality of means? Show what you used to reach your conclusion.
(b) Determine Bonferroni, Tukey, and Scheffe critical values for testing all pairwise differences among the means.
(c) Construct 95% confidence intervals for Group 1 vs. Group 2 and Group 4 vs. Group 5 using each of the three procedures above, and assuming that you intend to test all pairwise comparisons (you need to use this in the Bonferroni contrasts). Explain what each contrast represents. Which procedure is the best for identifying differences?
(d) Define a contrast to determine if students in the twice weekly lecture format have different mean achievement from those in the once weekly lecture format (averaging the means for each condition). Construct 95% confidence intervals using Scheffe and Bonferroni procedures. In using the Bonferroni procedure, assume that you also planned to test all pairwise comparisons. State your conclusion.
(e) Define a contrast to determine if the difference in mean achievement for students who got pop quizzes and students who attended tutorials is the same under the once weekly lecture format as under the twice weekly format. Think of this as (popquiz-tutorial) once weekly – (popquiz-tutorial) twice weekly. This is a difference between differences. Construct 95% confidence intervals using Scheffe and Bonferroni procedures. In using the Bonferroni procedure, assume that you also planned to test all pairwise comparisons. State your conclusion.