Question: Over time, with instruction in between, each student completed a quiz
ID: 3291297 • Letter: Q
Question
Question: Over time, with instruction in between, each student completed a quiz five times. The quiz scores or the measurement of student achievement over time would serve as the dependent variable while instruction would serve as the independent variable/treatment/factor. Provide a narrative discussion of the tables, including a discussion of SPHERICITY. DATA BELOW:
Pairwise Comparisons
Measure: MEASURE_1
(I) instruction
(J) instruction
Mean Difference (I-J)
Std. Error
Sig.b
95% Confidence Interval for Differenceb
Lower Bound
Upper Bound
1
2
-.514*
.179
.049
-1.028
-.001
3
-.514*
.126
.001
-.874
-.154
4
-.333
.137
.168
-.727
.060
5
-.400
.215
.658
-1.017
.217
2
1
.514*
.179
.049
.001
1.028
3
.000
.164
1.000
-.469
.469
4
.181
.173
1.000
-.316
.678
5
.114
.129
1.000
-.255
.483
3
1
.514*
.126
.001
.154
.874
2
.000
.164
1.000
-.469
.469
4
.181
.143
1.000
-.229
.591
5
.114
.205
1.000
-.475
.703
4
1
.333
.137
.168
-.060
.727
2
-.181
.173
1.000
-.678
.316
3
-.181
.143
1.000
-.591
.229
5
-.067
.212
1.000
-.676
.542
5
1
.400
.215
.658
-.217
1.017
2
-.114
.129
1.000
-.483
.255
3
-.114
.205
1.000
-.703
.475
4
.067
.212
1.000
-.542
.676
Based on estimated marginal means
*. The mean difference is significant at the .05 level.
b. Adjustment for multiple comparisons: Bonferroni.
Descriptive Statistics
Mean
Std. Deviation
N
quiz1
7.47
2.481
105
quiz2
7.98
1.623
105
quiz3
7.98
2.308
105
quiz4
7.80
2.280
105
quiz5
7.87
1.765
105
Mauchly's Test of Sphericitya
Measure: MEASURE_1
Within Subjects Effect
Mauchly's W
Approx. Chi-Square
df
Sig.
Epsilonb
Greenhouse-Geisser
Huynh-Feldt
Lower-bound
instruction
.400
93.851
9
.000
.640
.657
.250
Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix.
a. Design: Intercept
Within Subjects Design: instruction
b. May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in the Tests of Within-Subjects Effects table.
Pairwise Comparisons
Measure: MEASURE_1
(I) instruction
(J) instruction
Mean Difference (I-J)
Std. Error
Sig.b
95% Confidence Interval for Differenceb
Lower Bound
Upper Bound
1
2
-.514*
.179
.049
-1.028
-.001
3
-.514*
.126
.001
-.874
-.154
4
-.333
.137
.168
-.727
.060
5
-.400
.215
.658
-1.017
.217
2
1
.514*
.179
.049
.001
1.028
3
.000
.164
1.000
-.469
.469
4
.181
.173
1.000
-.316
.678
5
.114
.129
1.000
-.255
.483
3
1
.514*
.126
.001
.154
.874
2
.000
.164
1.000
-.469
.469
4
.181
.143
1.000
-.229
.591
5
.114
.205
1.000
-.475
.703
4
1
.333
.137
.168
-.060
.727
2
-.181
.173
1.000
-.678
.316
3
-.181
.143
1.000
-.591
.229
5
-.067
.212
1.000
-.676
.542
5
1
.400
.215
.658
-.217
1.017
2
-.114
.129
1.000
-.483
.255
3
-.114
.205
1.000
-.703
.475
4
.067
.212
1.000
-.542
.676
Based on estimated marginal means
*. The mean difference is significant at the .05 level.
b. Adjustment for multiple comparisons: Bonferroni.
Explanation / Answer
Over time, with instruction in between, each student completed a quiz five times. The quiz scores or the measurement of student achievement over time would serve as the dependent variable while instruction would serve as the independent variable/treatment/factor.
Here we have given pairwise comparison.
We can test the hypothesis that,
H0 : mu1 = mu2 Vs H1 : mu1 not= mu2
where mu1 and mu2 are two population means.
Assume alpha = level of significance = 0.05
If P-value < alpha then reject H0 and we get significant result about that pair.
Here we see that pair (1,3), (2,1) are significant while remaining are insignificant pairs.
Also we have given the output for Mauchly's Test of Sphericitya
Here the test of hypothesis is,
H0 : The error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix.
H1 : The error covariance matrix of the orthonormalized transformed dependent variables is not proportional to an identity matrix.
Assume alpha = level of significance = 0.05
Here we see that p-value = 0.000
P-value < alpha
Reject H0 at 5% level of significance.
Conclusion : The error covariance matrix of the orthonormalized transformed dependent variables is not proportional to an identity matrix.
We get significant result about this test.
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