# PSY 8625 Capella University Week 8 Analysis of Variance Report Discussion

SECTION 3-GRAPHSFigure 1: Quiz 3 Histogram
Statistics
quiz3
N
Valid
Missing
Mean
Median
Std. Deviation
Variance
Skewness
Std. Error of Skewness
Kurtosis
Std. Error of Kurtosis
Minimum
Maximum
105
0
7.13
7.00
1.600
2.559
-.078
.236
.149
.467
2
10
Figure 2- Quiz 3 Descriptive statistics
Tests of Normality
Kolmogorov-Smirnova
Shapiro-Wilk
Statistic
df
Sig.
Statistic
df
Sig.
quiz3
.143
105
.000
.948
105
.000
a. Lilliefors Significance Correction
Figure 3- Quiz 3 Shapiro-Wilk SPSS Output
Test of Homogeneity of Variances
Levene
Statistic
quiz3 Based on Mean
2.898
Based on Median
2.757
Based on Median
2.757
Based on trimmed
2.945
mean
gpa
Based on Mean
.910
Based on Median
.876
Based on Median
.876
Based on trimmed
.879
mean
df1
2
2
2
df2
102
102
92.750
Sig.
.060
.068
.069
2
102
.057
2
2
2
102
102
97.314
.406
.420
.420
2
102
.418
Figure 4 Levene’s Test
Tests of Between-Subjects Effects
Dependent Variable: quiz3
Type III
Sum of
Source
Squares
Corrected Model
46.334a
Intercept
301.989
section * gpa
46.334
df
3
1
3
Mean
Square
15.445
301.989
15.445
F
7.097
138.767
7.097
Sig.
.000
.000
.000
Error
219.799
101
2.176
Total
5609.000
105
Corrected Total
266.133
104
a. R Squared = .174 (Adjusted R Squared = .150)
Figure 5, Homogeneity of Regression Slopes
SECTION 4- GRAPHS
Descriptive Statistics
Dependent Variable: quiz3
Std.
section
Mean
Deviation
1
7.27
1.153
2
6.33
1.611
3
7.94
1.560
Total
7.13
1.600
N
33
39
33
105
Figure 6 Descriptive Statistics
ANOVA
quiz3
gpa
Between Groups
Within Groups
Total
Between Groups
Within Groups
Total
Sum of
Squares
47.042
219.091
266.133
1.055
51.765
52.820
Figure 7 ANOVA Output
Tests of Between-Subjects Effects
Dependent Variable: quiz3
df
2
102
104
2
102
104
Mean
Square
23.521
2.148
.528
.508
F
10.951
Sig.
.000
1.040
.357
Type III Sum
Mean
Source
of Squares
df
Square
a
Corrected Model
46.334
3
15.445
Intercept
301.989
1
301.989
section * gpa
46.334
3
15.445
Error
219.799
101
2.176
Total
5609.000
105
Corrected Total
266.133
104
a. R Squared = .174 (Adjusted R Squared = .150)
F
7.097
138.767
7.097
Sig.
.000
.000
.000
Partial Eta
Squared
.174
.579
.174
Figure 8 One Way Ancova
Pairwise Comparisons
Dependent Variable: quiz3
Mean
Difference
(I) section (J) section
(I-J)
Std. Error
Sig.b
1
2
.941*
.336
.018
3
-.632
.350
.221
*
2
1
-.941
.336
.018
*
3
-1.573
.346
.000
3
1
.632
.350
.221
*
2
1.573
.346
.000
Based on estimated marginal means
*. The mean difference is significant at the .05 level.
b. Adjustment for multiple comparisons: Bonferroni.
Figure 9 Post Hoc Results
95% Confidence Interval
for Differenceb
Lower
Upper
Bound
Bound
.123
1.759
-1.485
.220
-1.759
-.123
-2.415
-.732
-.220
1.485
.732
2.415
Figure 10 Quiz 3 Means Plot
Figure 11- Means Plot for GPA
Overview
Our data set contains many variables related to course-specific performance and
overall GPA. In looking at the grades for the course, the teacher sees that
students in one section performed much better on the third quiz than the students
in the other two sections of the course. The teacher is concerned about why
students taking identical quizzes in each section are performing so differently.
She hypothesizes that one section might comprise students with higher overall
GPAs and therefore are stronger students than those in the other two sections.
To see if removing the variance in quiz 3 that is explained by the GPA of the
students, you will perform a one-way ANCOVA using the variables quiz 3, GPA
and section.
Preparation
Refer to Chapter 12, “The One-Way ANOVA Procedure,” in IBM SPSS Statistics 25
Step by Step for additional information on using SPSS.
• If necessary, review the copy/export output instructions to refresh your
memory on how to perform these tasks. As with previous assessments, your
submission should be in narrative format with supporting statistical output
(table and graphs) integrated into the narrative in the appropriate places (not
all at the end of the document).
You will use the following variables in the data set:

Quiz 3.

Section.

GPA.
Instructions
1. Briefly describe the goal of your analysis.

Specify the variables used in this analysis (independent, covariate, and
dependent) and the scale of measurement of each variable.

State the sample size (N) and the alpha level you will use (.05 unless
otherwise specified).

Explain why the analysis is a good choice based on the nature of your
variables.
2. Articulate a null hypothesis and alternative hypothesis. Specify a research
question for each predictor. Specify the alpha level.
3. Articulate and test the assumptions of ANOVA.

Paste the SPSS histogram output for Quiz 3 and discuss your visual
interpretations.

Paste SPSS descriptives output showing skewness and kurtosis values
for Quiz 3 and interpret them.

Paste the SPSS output for the Shapiro–Wilk test of Quiz 3 and interpret
the results.

Report the results of the Levene test and interpret it.

Present the results of the test of homogeneity of regression slopes.

Explain whether the assumptions of ANOVA are met. If assumptions
are not met, discuss how to ameliorate violations of the assumptions.
4. Paste the SPSS output of the means plot and provide an interpretation.

Paste the SPSS ANOVA output and report the results of the F test.
Include the following:

Degrees of freedom.

F values.

p values.

Calculated effect size.

Interpretation of the effect size.

Interpret statistical results against the null hypothesis and state
whether it is accepted or rejected.
Provide a brief summary of your analysis and the conclusions drawn.
o
Discuss whether the removal of the variance in Quiz 3 that was
explained by GPA influences the relationship between Quiz 3 and
section.
o
Analyze the strengths and limitations of the statistical test.
o
Provide any possible alternate explanations for the findings and
potential areas for future exploration.

Written communication: Should be free of errors that detract from the overall
message.
APA formatting: References and citations are formatted according to current
APA style guidelines. Refer to Evidence and APA for more information on how
Length: 8–10 double-spaced pages, in addition to the title page and
references page.
Hints for Week 8 Assignment
Test assumptions
In previous units you have already learned how to test the assumptions of normality (ShapiroWilk test) and equal variances (Levene’s test). In this assignment you need to test one
additional assumption: the assumption of homogeneity of regression slopes.

Open Analyze: General Linear Model: Univariate
Put quiz 3 into Dependent Variable
Put section into Fixed Factor
Put gpa into covariate.
Press the button Model
In the popup window select Build terms, move section and gpa into Model. Next, select both
variables and click on the blue arrow under interaction. This will create an interaction term of
section and gpa. Click Continue and OK to run it.
In the output check the row section * quiz 3. If the p value (Sig.) is .05 or less, it means that the
interaction term of section and gpa is significant. The effect of one variable on the dependent
variable is inconsistent across different levels of the third variable. In other words, the
regression slopes are NOT the same and thus the assumption is violated. If the p value is
above .05, it means there is no interaction and thus the assumption is met.
Run ANCOVA in SPSS
SPSS “remembers” what you did. To run ANCOVA, you need to remove the previous selections
and run ANCOVA without building the interaction term.

Open Analyze: General Linear Model: Univariate
Put quiz 3 into Dependent Variable
Put section into Fixed Factor
Put gpa into covariate.

From Options check Descriptive statistics, estimate of effect size, and homogeneity tests
The partial eta squared is the effect size contributed by the independent variable. For
example, if the partial eta squared of section is .1 (I made up this number), it means that by
controlling the pre-existing difference among students in terms of GPA, 10% of the variance of
quiz 3 score can be explained by class section.
Another way is to obtain the effect size is: Corrected model sum of squares/corrected
total sum of squared. In this case, it should be the same as partial eta squared.

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