ANOVA and Nonparametric Kruskal-Wallis Test Assignment
Joseph Howell
DBA: Supply Chain
BUSI 820: Quantitative Research Methods
July 5th, 2024
ANOVA and Nonparametric Kruskal-Wallis Test
Table of Contents
9.5 Identify an example of a variable measured at the scale/normally distributed level for
which there is a statistically significant overall difference (F) between the three marital
status groups. Complete the analysis and interpret the results. Do appropriate post hoc
tests..................................................................................................................................................2
Figure 1.......................................................................................................................................3
Figure 2.......................................................................................................................................3
Figure 3.......................................................................................................................................3
Figure 4.......................................................................................................................................4
Figure 5.......................................................................................................................................4
Figure 6.......................................................................................................................................4
Figure 7.......................................................................................................................................5
Figure 8.......................................................................................................................................5
9.6 Use the Kruskal–Wallis test, with Mann‒Whitney post hoc follow-up tests if needed, to
run the same problem as 9.1. Compare the results....................................................................5
Figure 9.......................................................................................................................................6
Figure 10.....................................................................................................................................6
9.7 Do students’ heights differ depending on academic track and marital status, and do
academic track and marital status interact? Run the appropriate analysis and interpret the
results..............................................................................................................................................6
Figure 11.....................................................................................................................................7
Figure 12.....................................................................................................................................8
Figure 13.....................................................................................................................................8
Figure 14.....................................................................................................................................9
9.8 Do academic track and having children interact and does either seem to affect current
GPA?...............................................................................................................................................9
Figure 15...................................................................................................................................10
Figure 16...................................................................................................................................10
Figure 17...................................................................................................................................10
Figure 18...................................................................................................................................11
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ANOVA and Nonparametric Kruskal-Wallis Test Assignment
9.5 Identify an example of a variable measured at the scale/normally distributed level for
which there is a statistically significant overall difference (F) between the three marital
status groups. Complete the analysis and interpret the results. Do appropriate post hoc
tests.
The independent variable for the ANOVA analysis was age, and the dependent variable
was marriage status. Figure 1 displays the ANOVA values with p=0.002 and F=7.475. Morgan et
al. (2020) stated, “The data is considered statistically significant if the p-value is less than or
equal to 0.05.” The variable marriage status results show the Mean p=0.097 and df=2. Figure 2
displays the Tests of Homogeneity of Variances displaying the variances between marital status.
The ANOVA analysis of the mean-based test is the main focus and is displayed in Figure
2. The marital status results show a p=0.002, F=7.48 with df=2 and df=46. The eta=0.245 in
Figure 4 provides an estimate of the overall size of the effect. The null hypothesis can be rejected
if the p-value is less than 0.05 and the age group variables p-value is less than 0.05 meaning
there is no statistical significance related to the marital status outcomes suggesting the alternative
theory is correct. The age group is statistically significant based on the evaluation using normally
distributed measures.
Figure 7 displays Post Hoc Tests which are often done as follow-up tests. Figure 7
displays identical data as Figure 6 resulting in no updates to the overall analysis.
Figure 7 displays the Multiple Comparison Table. The significant blocks indicate the
mean differences are statistically significant with a 0.05 reading. The marital status variable is
shown in the Figure displaying similar subgroups. The Homogenous Subsets table displayed in
Figure 8 has an adjusted Tukey because the variables across the analysis are statistically different
and the p=0.057 is insignificant. The means for the variables displayed in Figure 8 are distinct
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ANOVA and Nonparametric Kruskal-Wallis Test
with the 30 or more age group having an M=2.27 and the less than 22 age group having an
M=1.31.
Figure 1
Figure 2
Figure 3
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ANOVA and Nonparametric Kruskal-Wallis Test
Figure 4
Figure 5
Figure 6
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ANOVA and Nonparametric Kruskal-Wallis Test
Figure 7
Figure 8
9.6 Use the Kruskal–Wallis test, with Mann‒Whitney post hoc follow-up tests if needed, to
run the same problem as 9.1. Compare the results.
Figure 9 displays the Kruskal-Wallis Test displays the variables sex at birth and student
height. Figure 9 shows girls are typically shorter than males when measured in inches based on
the variable sex at birth. The Kruskal-Wallis Test is representative of an ensemble assessment
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ANOVA and Nonparametric Kruskal-Wallis Test
statistics. The value reading 0 displays that the relevant variables have no variation. Figure 10
displays the Test Statistics have a p-value less than 0.001.
Figure 9
Figure 10
9.7 Do students’ heights differ depending on academic track and marital status, and do
academic track and marital status interact? Run the appropriate analysis and interpret the
results.
Figure 12 displays the ANOVA test which was done using the independent variables of
sex at birth and marital status and the dependent variable students’ heights in inches. Figure 11
shows the Between-Subjects Factors and how the sex at birth differs from each other. Figure 12
displays the Descriptive Statistics.
Figure 13 displays the Tests of Between-Subjects Effects and their results. The results in
Figure 13 show there is no significant correlation between marriage status and student height and
no statistically significant correlation between marital status and birth sex. The p-values for the
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ANOVA and Nonparametric Kruskal-Wallis Test
two variables are 0.132 for sex at birth and 0.168 for marital status. Morgan et al. (2020) stated,
“If the p-value is less than 001, the difference between the two variables is statistically
significant.” The variables sex at birth and student's height in inches display statistical
significance. Marital status and students’ height in inches did not significantly correlate with
marital status represented by a p=0.132. Sex at birth and students’ heights in inches did have a
significant correlation with a p=0.001. The variables of marital status and sex at birth are
independent of each other.
Figure 14 showcases the profile plots variable projected mean height. The data displayed
showcases how the variables of sex at birth and students' heights affect each other based on the
lines intersecting. Morgan et al. (2020) stated, “These profile graphs of cell mean, which come
after the table of between-subjects effects, help us see what kind of interaction there is when
there is a significant one.” The marital status was displayed with separate lines to display the
differences between the sets of groups. Figure 14 displays the lines moving in the same direction
with little crossovers.
Figure 11
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ANOVA and Nonparametric Kruskal-Wallis Test
Figure 12
Figure 13
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ANOVA and Nonparametric Kruskal-Wallis Test
Figure 14
9.8 Do academic track and having children interact and does either seem to affect current
GPA?
Figure 15-18 examines the correlation between the independent variable Sex at Birth and
Number of Children and the dependent variable of GPA. Figure 16 displays the Descriptive
Statistics for the dependent variable GPA and the statistics provide summaries regarding the
dataset's characteristics.
Figure 15 displays the Between-Subjects Factors results. Morgan et al. (2020) stated,
“This chart demonstrates no statistically significant association between students' mean grade
point average and whether or not they have children and that there is no correlation between
students' sex at birth and whether or not they have children.” The variables sex at birth and
having children with p=0.387 and p=0.159 display statistically significant. The p-value of 0.006
between GPA and sex at birth is statistically significant.
Figure 18 displays there is a slight statistical correlation between a student’s GPA and
their parent’s birth sex. No correlations are shown between having children or not having
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ANOVA and Nonparametric Kruskal-Wallis Test
children between birth sex. The correlation between GPA and birth sex is significant statistically
with a p=0.006.
Figure 15
Figure 16
Figure 17
Figure 18
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References
Morgan, G.A. Barrett, K.C., Leech, N.L., & Gloeckner, G.W., (2020). IBM SPSS for
Introductory Statistics: Use and Interpretation (6th.). Routledge
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