SPSS Worksheet 4 Resubmit needed tomorrow! 11-11-17 @ 12 noon
bjsith
StatsWeek4WorksheetResubmissionNeeded.docxSMITHBEDR8202-4
<Add Learner comments here>
Faculty Use Only
Hi,
I have asked that you submit all assignments in the question and answer format and have shared in your previous assignments what that looks like. I am not sure why you are not submitting your assignments in that format. I am unable to tell what responses go with what questions and am unable to grade this assignment as provided. Please resubmit this assignment by 10/31/2017 in the proper format as indicated below:
1. Present two tables:
a. Table 1 should show the results of a one-way ANOVA based on current family income, including Eta.
b. Table 2 should show the results of a two-way ANOVA based on both current family income and gender, including Eta.
Your answer goes here
2. Provide a narrative discussion of both tables. Include Eta, the Levene test, and the observed change in the F-value of current family income when moving from a one-way to a two-way analysis.
Your answer would go here.
You must write out each question and then place the answer directly under that question. Do not lump all of the answers together, just answer each question. This must be resubmitted by 10/31/2017 in the proper format with the question directly above the answer. For every day the assignment is late, there will be a 10% deduction from the final assignment grade. Please contact me with any questions.
Dr. Jane, CPM, LPC, NCC 0/15 10/30/2017
Part I:
Using General Linear Model/univariate, analyze the differences between the genders when using life satisfaction as the dependent variable.
In this study, we are interested in studying life satisfaction as the dependent variable and the effects of gender and current family income on life satisfaction.
A one-way ANOVA was performed to analyze the hypothesis research question that whether the males and females have the same mean life satisfaction.
Null Hypothesis: Males and Females have the same mean life satisfaction.
:
Alternate Hypothesis: Males and Females do not have the same mean life satisfaction.
:
The One-Way Analysis of Variance was performed in SPSS.
The Levene’s test shows that there is no homogeneity of variance; F (1, 227) = .031, p-value = .860. In other words, there is no evidence to suggest that the error variance of the dependent variable is not equal across groups. We assume that all the other assumptions required for performing a one-way ANOVA are satisfied by the data.
Table-1: The following table shows the results for the one-way ANOVA:
|
Tests of Between-Subjects Effects |
||||||
|
Dependent Variable: life satisfaction |
||||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
Partial Eta Squared |
|
Corrected Model |
.644a |
1 |
.644 |
.802 |
.372 |
.004 |
|
Intercept |
5296.512 |
1 |
5296.512 |
6596.001 |
.000 |
.967 |
|
sex |
.644 |
1 |
.644 |
.802 |
.372 |
.004 |
|
Error |
182.278 |
227 |
.803 |
|
|
|
|
Total |
5492.225 |
229 |
|
|
|
|
|
Corrected Total |
182.922 |
228 |
|
|
|
|
|
a. R Squared = .004 (Adjusted R Squared = -.001) |
There is no sufficient evidence to conclude that the males and the females do not have the same mean life satisfaction; F (1, 227) = .802, p = .372, at α = 0.05 significance.
Using the General Linear Model/univariate, conduct a two-way ANOVA analyzing both gender and family income levels as related to life satisfaction.
A one-way ANOVA was performed to analyze the hypothesis research question that whether the various current family income levels have the same mean life satisfaction.
Null Hypothesis: All the seven current family income groups have the same mean life satisfaction.
:
Alternate Hypothesis: At least one of the current family income groups has a different mean life satisfaction than the rest.
The One-Way Analysis of Variance was performed in SPSS.
The Levene’s test shows that there is no homogeneity of variance; F (6, 222) = .617, p-value = .717. In other words, there is no evidence to suggest that the error variance of the dependent variable is not equal across the current family income groups.
We assume that all the other assumptions required for performing a one-way ANOVA are satisfied by the data.
Table-1: The following table shows show the results of a one-way ANOVA based on current family income:
|
Tests of Between-Subjects Effects |
||||||
|
Dependent Variable: life satisfaction |
||||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
Partial Eta Squared |
|
Corrected Model |
18.618a |
6 |
3.103 |
4.193 |
.001 |
.102 |
|
Intercept |
1934.535 |
1 |
1934.535 |
2613.859 |
.000 |
.922 |
|
income |
18.618 |
6 |
3.103 |
4.193 |
.001 |
.102 |
|
Error |
164.304 |
222 |
.740 |
|
|
|
|
Total |
5492.225 |
229 |
|
|
|
|
|
Corrected Total |
182.922 |
228 |
|
|
|
|
|
a. R Squared = .102 (Adjusted R Squared = .078) |
There is sufficient evidence to conclude that the different current family income groups do not have the same mean life satisfaction; F (6, 222) = 4.193, p = .001, at α = 0.05 significance.
Next, a two-way ANOVA was performed to analyze the effects of gender and family income levels on life satisfaction.
Hypothesis 1
Null hypothesis: Gender has no effect on life satisfaction.
Alternative hypothesis: Gender has an effect on life satisfaction.
Hypothesis 2
Null hypothesis: Current family income has no effect on life satisfaction.
Alternative hypothesis: Current family income has an effect on life satisfaction.
Hypothesis 3
Null hypothesis: There is no interaction effect of gender and current family income on life satisfaction.
Alternative hypothesis: There is an interaction effect of and current family income on life satisfaction.
The Two-Way Analysis of Variance was performed in SPSS.
The Levene’s test shows that there is no homogeneity of variance; F (13, 215) = .853, p-value = .604. In other words, there is no evidence to suggest that the error variance of the dependent variable is not equal across the various groups based on gender and current family income. We assume that all the other assumptions required for performing a two-way ANOVA are satisfied by the data.
Table 2: The following table shows the results of the two-way ANOVA based on both current family income and gender:
|
Tests of Between-Subjects Effects |
||||||
|
Dependent Variable: life satisfaction |
||||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
Partial Eta Squared |
|
Corrected Model |
25.957a |
13 |
1.997 |
2.735 |
.001 |
.142 |
|
Intercept |
1765.270 |
1 |
1765.270 |
2417.945 |
.000 |
.918 |
|
income |
18.663 |
6 |
3.110 |
4.260 |
.000 |
.106 |
|
sex |
1.998 |
1 |
1.998 |
2.737 |
.100 |
.013 |
|
income * sex |
4.395 |
6 |
.733 |
1.003 |
.424 |
.027 |
|
Error |
156.965 |
215 |
.730 |
|
|
|
|
Total |
5492.225 |
229 |
|
|
|
|
|
Corrected Total |
182.922 |
228 |
|
|
|
|
|
a. R Squared = .142 (Adjusted R Squared = .090) |
There is a significant main effect of current family income on life satisfaction; F (6, 215) = 4.260, p-value < 0.001,, at α = 0.05 significance level. There is no significant main effect of gender on life satisfaction; F (1, 215) = 2.737, p-value =.100,, at α = 0.05 significance level. There is no significant interaction effect of current family income and gender on life satisfaction; F (6, 215) = 1.003, p-value = .424,, at α = 0.05 significance level.
Given the significance of the main effect of current family income on life satisfaction, a Tukey’s post-hoc analysis was performed to analyze which current family income groups had significantly different mean life satisfaction as compared to the rest.
The F-value of current family income changes from F (6, 222) = 4.193 to F (6, 215) = 4.260 when moving from a one-way to a two-way analysis.
Table-3: The following table shows the results of Tukey’s post-hoc analysis:
|
Multiple Comparisons |
||||||
|
Dependent Variable: life satisfaction Tukey HSD |
||||||
|
(I) current family income |
(J) current family income |
Mean Difference (I-J) |
Std. Error |
Sig. |
95% Confidence Interval |
|
|
|
|
|
|
|
Lower Bound |
Upper Bound |
|
DTS |
<10,000 |
.2426 |
.35377 |
.993 |
-.8104 |
1.2956 |
|
|
10-20,000 |
-.0783 |
.34440 |
1.000 |
-1.1034 |
.9468 |
|
|
20-30,000 |
-.4828 |
.34288 |
.797 |
-1.5034 |
.5378 |
|
|
30-40,000 |
-.4553 |
.35007 |
.851 |
-1.4973 |
.5867 |
|
|
40-50,000 |
-.5171 |
.35144 |
.761 |
-1.5632 |
.5289 |
|
|
50,000+ |
-.8038 |
.58962 |
.821 |
-2.5588 |
.9512 |
|
<10,000 |
DTS |
-.2426 |
.35377 |
.993 |
-1.2956 |
.8104 |
|
|
10-20,000 |
-.3209 |
.18755 |
.609 |
-.8791 |
.2373 |
|
|
20-30,000 |
-.7254* |
.18475 |
.002 |
-1.2753 |
-.1754 |
|
|
30-40,000 |
-.6979* |
.19776 |
.009 |
-1.2865 |
-.1092 |
|
|
40-50,000 |
-.7597* |
.20018 |
.004 |
-1.3555 |
-.1639 |
|
|
50,000+ |
-1.0464 |
.51402 |
.395 |
-2.5763 |
.4836 |
|
10-20,000 |
DTS |
.0783 |
.34440 |
1.000 |
-.9468 |
1.1034 |
|
|
<10,000 |
.3209 |
.18755 |
.609 |
-.2373 |
.8791 |
|
|
20-30,000 |
-.4045 |
.16610 |
.189 |
-.8989 |
.0899 |
|
|
30-40,000 |
-.3770 |
.18046 |
.363 |
-.9141 |
.1601 |
|
|
40-50,000 |
-.4388 |
.18311 |
.205 |
-.9838 |
.1062 |
|
|
50,000+ |
-.7255 |
.50761 |
.785 |
-2.2364 |
.7854 |
|
20-30,000 |
DTS |
.4828 |
.34288 |
.797 |
-.5378 |
1.5034 |
|
|
<10,000 |
.7254* |
.18475 |
.002 |
.1754 |
1.2753 |
|
|
10-20,000 |
.4045 |
.16610 |
.189 |
-.0899 |
.8989 |
|
|
30-40,000 |
.0275 |
.17755 |
1.000 |
-.5010 |
.5559 |
|
|
40-50,000 |
-.0344 |
.18024 |
1.000 |
-.5708 |
.5021 |
|
|
50,000+ |
-.3210 |
.50659 |
.996 |
-1.8289 |
1.1868 |
|
30-40,000 |
DTS |
.4553 |
.35007 |
.851 |
-.5867 |
1.4973 |
|
|
<10,000 |
.6979* |
.19776 |
.009 |
.1092 |
1.2865 |
|
|
10-20,000 |
.3770 |
.18046 |
.363 |
-.1601 |
.9141 |
|
|
20-30,000 |
-.0275 |
.17755 |
1.000 |
-.5559 |
.5010 |
|
|
40-50,000 |
-.0618 |
.19356 |
1.000 |
-.6379 |
.5143 |
|
|
50,000+ |
-.3485 |
.51148 |
.994 |
-1.8709 |
1.1739 |
|
40-50,000 |
DTS |
.5171 |
.35144 |
.761 |
-.5289 |
1.5632 |
|
|
<10,000 |
.7597* |
.20018 |
.004 |
.1639 |
1.3555 |
|
|
10-20,000 |
.4388 |
.18311 |
.205 |
-.1062 |
.9838 |
|
|
20-30,000 |
.0344 |
.18024 |
1.000 |
-.5021 |
.5708 |
|
|
30-40,000 |
.0618 |
.19356 |
1.000 |
-.5143 |
.6379 |
|
|
50,000+ |
-.2867 |
.51242 |
.998 |
-1.8119 |
1.2385 |
|
50,000+ |
DTS |
.8038 |
.58962 |
.821 |
-.9512 |
2.5588 |
|
|
<10,000 |
1.0464 |
.51402 |
.395 |
-.4836 |
2.5763 |
|
|
10-20,000 |
.7255 |
.50761 |
.785 |
-.7854 |
2.2364 |
|
|
20-30,000 |
.3210 |
.50659 |
.996 |
-1.1868 |
1.8289 |
|
|
30-40,000 |
.3485 |
.51148 |
.994 |
-1.1739 |
1.8709 |
|
|
40-50,000 |
.2867 |
.51242 |
.998 |
-1.2385 |
1.8119 |
|
Based on observed means. The error term is Mean Square(Error) = .730. |
||||||
|
*. The mean difference is significant at the .05 level. |
There is a significant difference in mean life satisfaction between those who have a current family income of $10000 or less and those who have a current family income of $20000-$30000; MD = -.7254, SE = .18475, p-value = .002, as α = 0.05 significance. There is a significant difference in mean life satisfaction between those who have a current family income of $10000 or less and those who have a current family income of $30000-$40000; MD = -.6979, SE = .19776, p-value = .009, as α = 0.05 significance. There is a significant difference in mean life satisfaction between those who have a current family income of $10000 or less and those who have a current family income of $40000-$50000; MD =-.7597, SE =.20018, p-value = .004, as α = 0.05 significance.
Appendix:
Table-1: Descriptive Statistics for One-way ANOVA (Independent Variable: Sex)
|
Descriptive Statistics |
|||
|
Dependent Variable: life satisfaction |
|||
|
sex |
Mean |
Std. Deviation |
N |
|
female |
4.8660 |
.91150 |
119 |
|
male |
4.7599 |
.87911 |
110 |
|
Total |
4.8151 |
.89571 |
229 |
Table-2: Levene’s Test for One-way ANOVA (Independent Variable: Sex)
|
Levene's Test of Equality of Error Variancesa |
|||
|
Dependent Variable: life satisfaction |
|||
|
F |
df1 |
df2 |
Sig. |
|
.031 |
1 |
227 |
.860 |
|
Tests the null hypothesis that the error variance of the dependent variable is equal across groups. |
|||
|
a. Design: Intercept + sex |
Table-3: One-way ANOVA (Independent Variable: Sex)
|
Tests of Between-Subjects Effects |
||||||
|
Dependent Variable: life satisfaction |
||||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
Partial Eta Squared |
|
Corrected Model |
.644a |
1 |
.644 |
.802 |
.372 |
.004 |
|
Intercept |
5296.512 |
1 |
5296.512 |
6596.001 |
.000 |
.967 |
|
sex |
.644 |
1 |
.644 |
.802 |
.372 |
.004 |
|
Error |
182.278 |
227 |
.803 |
|
|
|
|
Total |
5492.225 |
229 |
|
|
|
|
|
Corrected Total |
182.922 |
228 |
|
|
|
|
|
a. R Squared = .004 (Adjusted R Squared = -.001) |
Table-4: Descriptive Statistics for One-way ANOVA (Independent Variable: Current Family Income)
|
Descriptive Statistics |
|||
|
Dependent Variable: life satisfaction |
|||
|
current family income |
Mean |
Std. Deviation |
N |
|
DTS |
4.5429 |
1.04987 |
7 |
|
<10,000 |
4.3003 |
.90816 |
35 |
|
10-20,000 |
4.6212 |
.90083 |
51 |
|
20-30,000 |
5.0256 |
.74775 |
55 |
|
30-40,000 |
4.9982 |
.92114 |
40 |
|
40-50,000 |
5.0600 |
.82334 |
38 |
|
50,000+ |
5.3467 |
.59501 |
3 |
|
Total |
4.8151 |
.89571 |
229 |
Table-5: Levene’s Test for One-way ANOVA (Independent Variable: Current Family Income)
|
Levene's Test of Equality of Error Variancesa |
|||
|
Dependent Variable: life satisfaction |
|||
|
F |
df1 |
df2 |
Sig. |
|
.617 |
6 |
222 |
.717 |
|
Tests the null hypothesis that the error variance of the dependent variable is equal across groups. |
|||
|
a. Design: Intercept + income |
Table-6: One-way ANOVA (Independent Variable: Current Family Income)
|
Tests of Between-Subjects Effects |
||||||
|
Dependent Variable: life satisfaction |
||||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
Partial Eta Squared |
|
Corrected Model |
18.618a |
6 |
3.103 |
4.193 |
.001 |
.102 |
|
Intercept |
1934.535 |
1 |
1934.535 |
2613.859 |
.000 |
.922 |
|
income |
18.618 |
6 |
3.103 |
4.193 |
.001 |
.102 |
|
Error |
164.304 |
222 |
.740 |
|
|
|
|
Total |
5492.225 |
229 |
|
|
|
|
|
Corrected Total |
182.922 |
228 |
|
|
|
|
|
a. R Squared = .102 (Adjusted R Squared = .078) |
Table-7: Descriptive Statistics (Two-way ANOVA)
|
Descriptive Statistics |
||||
|
Dependent Variable: life satisfaction |
||||
|
current family income |
sex |
Mean |
Std. Deviation |
N |
|
DTS |
female |
4.7500 |
1.11727 |
3 |
|
|
male |
4.3875 |
1.13893 |
4 |
|
|
Total |
4.5429 |
1.04987 |
7 |
|
<10,000 |
female |
4.2961 |
.99789 |
23 |
|
|
male |
4.3083 |
.74669 |
12 |
|
|
Total |
4.3003 |
.90816 |
35 |
|
10-20,000 |
female |
4.7029 |
.84114 |
35 |
|
|
male |
4.4425 |
1.02549 |
16 |
|
|
Total |
4.6212 |
.90083 |
51 |
|
20-30,000 |
female |
5.1852 |
.72982 |
23 |
|
|
male |
4.9109 |
.75067 |
32 |
|
|
Total |
5.0256 |
.74775 |
55 |
|
30-40,000 |
female |
5.3886 |
.97630 |
17 |
|
|
male |
4.7096 |
.77850 |
23 |
|
|
Total |
4.9982 |
.92114 |
40 |
|
40-50,000 |
female |
4.9525 |
.61500 |
16 |
|
|
male |
5.1382 |
.95341 |
22 |
|
|
Total |
5.0600 |
.82334 |
38 |
|
50,000+ |
female |
5.6450 |
.41719 |
2 |
|
|
male |
4.7500 |
. |
1 |
|
|
Total |
5.3467 |
.59501 |
3 |
|
Total |
female |
4.8660 |
.91150 |
119 |
|
|
male |
4.7599 |
.87911 |
110 |
|
|
Total |
4.8151 |
.89571 |
229 |
Table-8: Levene’s Test (Two-way ANOVA)
|
Levene's Test of Equality of Error Variancesa |
|||
|
Dependent Variable: life satisfaction |
|||
|
F |
df1 |
df2 |
Sig. |
|
.853 |
13 |
215 |
.604 |
|
Tests the null hypothesis that the error variance of the dependent variable is equal across groups. |
|||
|
a. Design: Intercept + income + sex + income * sex |
Table -9: Two-way ANOVA
|
Tests of Between-Subjects Effects |
||||||
|
Dependent Variable: life satisfaction |
||||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
Partial Eta Squared |
|
Corrected Model |
25.957a |
13 |
1.997 |
2.735 |
.001 |
.142 |
|
Intercept |
1765.270 |
1 |
1765.270 |
2417.945 |
.000 |
.918 |
|
income |
18.663 |
6 |
3.110 |
4.260 |
.000 |
.106 |
|
sex |
1.998 |
1 |
1.998 |
2.737 |
.100 |
.013 |
|
income * sex |
4.395 |
6 |
.733 |
1.003 |
.424 |
.027 |
|
Error |
156.965 |
215 |
.730 |
|
|
|
|
Total |
5492.225 |
229 |
|
|
|
|
|
Corrected Total |
182.922 |
228 |
|
|
|
|
|
a. R Squared = .142 (Adjusted R Squared = .090) |
Table-10: Tukey’s post-hoc test
|
Multiple Comparisons |
||||||
|
Dependent Variable: life satisfaction Tukey HSD |
||||||
|
(I) current family income |
(J) current family income |
Mean Difference (I-J) |
Std. Error |
Sig. |
95% Confidence Interval |
|
|
|
|
|
|
|
Lower Bound |
Upper Bound |
|
DTS |
<10,000 |
.2426 |
.35377 |
.993 |
-.8104 |
1.2956 |
|
|
10-20,000 |
-.0783 |
.34440 |
1.000 |
-1.1034 |
.9468 |
|
|
20-30,000 |
-.4828 |
.34288 |
.797 |
-1.5034 |
.5378 |
|
|
30-40,000 |
-.4553 |
.35007 |
.851 |
-1.4973 |
.5867 |
|
|
40-50,000 |
-.5171 |
.35144 |
.761 |
-1.5632 |
.5289 |
|
|
50,000+ |
-.8038 |
.58962 |
.821 |
-2.5588 |
.9512 |
|
<10,000 |
DTS |
-.2426 |
.35377 |
.993 |
-1.2956 |
.8104 |
|
|
10-20,000 |
-.3209 |
.18755 |
.609 |
-.8791 |
.2373 |
|
|
20-30,000 |
-.7254* |
.18475 |
.002 |
-1.2753 |
-.1754 |
|
|
30-40,000 |
-.6979* |
.19776 |
.009 |
-1.2865 |
-.1092 |
|
|
40-50,000 |
-.7597* |
.20018 |
.004 |
-1.3555 |
-.1639 |
|
|
50,000+ |
-1.0464 |
.51402 |
.395 |
-2.5763 |
.4836 |
|
10-20,000 |
DTS |
.0783 |
.34440 |
1.000 |
-.9468 |
1.1034 |
|
|
<10,000 |
.3209 |
.18755 |
.609 |
-.2373 |
.8791 |
|
|
20-30,000 |
-.4045 |
.16610 |
.189 |
-.8989 |
.0899 |
|
|
30-40,000 |
-.3770 |
.18046 |
.363 |
-.9141 |
.1601 |
|
|
40-50,000 |
-.4388 |
.18311 |
.205 |
-.9838 |
.1062 |
|
|
50,000+ |
-.7255 |
.50761 |
.785 |
-2.2364 |
.7854 |
|
20-30,000 |
DTS |
.4828 |
.34288 |
.797 |
-.5378 |
1.5034 |
|
|
<10,000 |
.7254* |
.18475 |
.002 |
.1754 |
1.2753 |
|
|
10-20,000 |
.4045 |
.16610 |
.189 |
-.0899 |
.8989 |
|
|
30-40,000 |
.0275 |
.17755 |
1.000 |
-.5010 |
.5559 |
|
|
40-50,000 |
-.0344 |
.18024 |
1.000 |
-.5708 |
.5021 |
|
|
50,000+ |
-.3210 |
.50659 |
.996 |
-1.8289 |
1.1868 |
|
30-40,000 |
DTS |
.4553 |
.35007 |
.851 |
-.5867 |
1.4973 |
|
|
<10,000 |
.6979* |
.19776 |
.009 |
.1092 |
1.2865 |
|
|
10-20,000 |
.3770 |
.18046 |
.363 |
-.1601 |
.9141 |
|
|
20-30,000 |
-.0275 |
.17755 |
1.000 |
-.5559 |
.5010 |
|
|
40-50,000 |
-.0618 |
.19356 |
1.000 |
-.6379 |
.5143 |
|
|
50,000+ |
-.3485 |
.51148 |
.994 |
-1.8709 |
1.1739 |
|
40-50,000 |
DTS |
.5171 |
.35144 |
.761 |
-.5289 |
1.5632 |
|
|
<10,000 |
.7597* |
.20018 |
.004 |
.1639 |
1.3555 |
|
|
10-20,000 |
.4388 |
.18311 |
.205 |
-.1062 |
.9838 |
|
|
20-30,000 |
.0344 |
.18024 |
1.000 |
-.5021 |
.5708 |
|
|
30-40,000 |
.0618 |
.19356 |
1.000 |
-.5143 |
.6379 |
|
|
50,000+ |
-.2867 |
.51242 |
.998 |
-1.8119 |
1.2385 |
|
50,000+ |
DTS |
.8038 |
.58962 |
.821 |
-.9512 |
2.5588 |
|
|
<10,000 |
1.0464 |
.51402 |
.395 |
-.4836 |
2.5763 |
|
|
10-20,000 |
.7255 |
.50761 |
.785 |
-.7854 |
2.2364 |
|
|
20-30,000 |
.3210 |
.50659 |
.996 |
-1.1868 |
1.8289 |
|
|
30-40,000 |
.3485 |
.51148 |
.994 |
-1.1739 |
1.8709 |
|
|
40-50,000 |
.2867 |
.51242 |
.998 |
-1.2385 |
1.8119 |
|
Based on observed means. The error term is Mean Square (Error) = .730. |
||||||
|
*. The mean difference is significant at the .05 level. |
Part 2:
Using General Linear Model/repeated measures, conduct a Repeated Measures ANOVA to analyze the influence of repeating the quiz over time on the quiz scores. Include descriptive statistics as an option.
In this study, we are interested in analyzing the influence on the scores of a quiz by repeating the quiz over time. 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.
A Repeated Measures ANOVA was performed to analyze the hypothesis research question as whether there is a difference in the mean scores of the related quizzes.
Null Hypothesis: All the quizzes have the same mean score.
:
Alternate Hypothesis: At least one of the quizzes has a different mean score than the rest.
The Repeated Measures ANOVA was performed in SPSS.
Mauchly’s Test of Sphericity indicated that the assumption of sphericity was violated, χ^2(9) = 93.851, p<0.001, and therefore a Greenhouse-Geisser correction was used.
We assume that all the other assumptions required for performing a Repeated Measures ANOVA are satisfied by the data.
Table-1: The following table shows the Mauchly’s Test of Sphericity:
|
Mauchly's Test of Sphericitya |
|||||||
|
Measure: Quiz |
|||||||
|
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. |
Table-2: The following table shows the results for the Repeated Measures ANOVA:
|
Tests of Within-Subjects Effects |
|||||||
|
Measure: MEASURE_1 |
|||||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
Partial Eta Squared |
|
|
Instruction |
Sphericity Assumed |
18.819 |
4 |
4.705 |
3.049 |
.017 |
.028 |
|
|
Greenhouse-Geisser |
18.819 |
2.559 |
7.355 |
3.049 |
.037 |
.028 |
|
|
Huynh-Feldt |
18.819 |
2.629 |
7.159 |
3.049 |
.035 |
.028 |
|
|
Lower-bound |
18.819 |
1.000 |
18.819 |
3.049 |
.084 |
.028 |
|
Error(Instruction) |
Sphericity Assumed |
641.981 |
416 |
1.543 |
|
|
|
|
|
Greenhouse-Geisser |
641.981 |
266.100 |
2.413 |
|
|
|
|
|
Huynh-Feldt |
641.981 |
273.385 |
2.348 |
|
|
|
|
|
Lower-bound |
641.981 |
104.000 |
6.173 |
|
|
|
A Repeated Measures ANOVA, with a Greenhouse-Geisser correction, revealed that the mean scores for the quizzes were statistically significantly different (F (2.559, 266.100) = 3.049, p = 0.037, at Table-1: Descriptive Statistics α = 0.05 significance.
Appendix:
Table-1: Descriptive Statistics
|
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 |
Table-2: Multivariate Tests
|
Multivariate Testsa |
|||||||
|
Effect |
Value |
F |
Hypothesis df |
Error df |
Sig. |
Partial Eta Squared |
|
|
Instruction |
Pillai's Trace |
.152 |
4.539b |
4.000 |
101.000 |
.002 |
.152 |
|
|
Wilks' Lambda |
.848 |
4.539b |
4.000 |
101.000 |
.002 |
.152 |
|
|
Hotelling's Trace |
.180 |
4.539b |
4.000 |
101.000 |
.002 |
.152 |
|
|
Roy's Largest Root |
.180 |
4.539b |
4.000 |
101.000 |
.002 |
.152 |
|
a. Design: Intercept Within Subjects Design: Instruction |
|||||||
|
b. Exact statistic |
Table-3: Mauchly’s Test of Sphericity
|
Mauchly's Test of Sphericitya |
|||||||
|
Measure: Quiz |
|||||||
|
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. |
Table-4: Test for Within Subjects Effects
|
Tests of Within-Subjects Effects |
|||||||
|
Measure: Quiz |
|||||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
Partial Eta Squared |
|
|
Instruction |
Sphericity Assumed |
18.819 |
4 |
4.705 |
3.049 |
.017 |
.028 |
|
|
Greenhouse-Geisser |
18.819 |
2.559 |
7.355 |
3.049 |
.037 |
.028 |
|
|
Huynh-Feldt |
18.819 |
2.629 |
7.159 |
3.049 |
.035 |
.028 |
|
|
Lower-bound |
18.819 |
1.000 |
18.819 |
3.049 |
.084 |
.028 |
|
Error(Instruction) |
Sphericity Assumed |
641.981 |
416 |
1.543 |
|
|
|
|
|
Greenhouse-Geisser |
641.981 |
266.100 |
2.413 |
|
|
|
|
|
Huynh-Feldt |
641.981 |
273.385 |
2.348 |
|
|
|
|
|
Lower-bound |
641.981 |
104.000 |
6.173 |
|
|
|
Table-4: Test for Within Subjects Contrasts
|
Tests of Within-Subjects Contrasts |
|||||||
|
Measure: Quiz |
|||||||
|
Source |
Instruction |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
Partial Eta Squared |
|
Instruction |
Linear |
4.024 |
1 |
4.024 |
2.917 |
.091 |
.027 |
|
|
Quadratic |
8.686 |
1 |
8.686 |
7.858 |
.006 |
.070 |
|
|
Cubic |
6.095 |
1 |
6.095 |
2.323 |
.131 |
.022 |
|
|
Order 4 |
.014 |
1 |
.014 |
.013 |
.910 |
.000 |
|
Error(Instruction) |
Linear |
143.476 |
104 |
1.380 |
|
|
|
|
|
Quadratic |
114.956 |
104 |
1.105 |
|
|
|
|
|
Cubic |
272.905 |
104 |
2.624 |
|
|
|
|
|
Order 4 |
110.644 |
104 |
1.064 |
|
|
|
Table-5: Table for Between Subject Effects
|
Tests of Between-Subjects Effects |
||||||
|
Measure: Quiz Transformed Variable: Average |
||||||
|
Source |
Type III Sum of Squares |
df |
Mean Square |
F |
Sig. |
Partial Eta Squared |
|
Intercept |
32097.190 |
1 |
32097.190 |
1974.033 |
.000 |
.950 |
|
Error |
1691.010 |
104 |
16.260 |
|
|
|
