Comparing Groups with T Test, Analysis of Variance (ANOVA) and Similar Non-
Parametric Tests
1
[Jerton Balfour]
[BUSI 820: Quantitative Analysis: Comparing Groups with T Test, Analysis of Variance
(ANOVA) and Similar Nonparametric Tests]
[August 10, 2025]
[Discussion Forum #7: Quantitative Analysis: Comparing Groups with T Test, Analysis of
Variance (ANOVA) and Similar Nonparametric Tests]
Author Note
Jerton Balfour
I have no known conflict of interest to disclose.
Correspondence concerning this article should be addressed to Jerton Balfour.
Email: [email protected]
Table of Contents
SPSS Problems.............................................4
Comparing Groups with T Test, Analysis of Variance (ANOVA) and Similar Non-
Parametric Tests
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G 9.1 Interpretation Sex at Birth and Students' Height.........................4
G 9.1(a) Group Statistics..........................................................................5
G 9.1(b) Independent Samples Test.........................................................5
G 9.1(c) Independent Samples Effect Sizes..........................................................5
G 9.2 Difference - Hours Students Study and Hours They Work......................6
G 9.2 (a) One-Sample Statistics...............................................................................6
G 9.2 (b) One-Sample Test..............................................................................7
G 9.2 (c) One-Sample Effect Sizes...................................................................7
G 9.2 (d) Descriptive.........................................................................................8
G 9.2 (e) Tests of Homogeneity of Variance......................................................9
G 9.2 (f) ANOVA..................................................................................................9
G 9.2 (g) ANOVA Effect Sizes..............................................................................9
G 9.3 What is the difference between the average time people spend watching television and the
average time they spend working?...........................................................................10
G 9.3 (a) Paired Samples Statistics...............................................................................10
G 9.3 (b) Paired Samples Correlations..........................................................................11
G 9.3 (c) Paired Samples Test..........................................................................................11
G 9.3 (d) Paired Samples Effect Sizes................................................................................11
G 9.4 Nonparametric Statistic............................................................................................12-13
G 9.4 (a) Ranks..................................................................................................................14
G 9.4 (b) Test Statistics..................................................................................................................14
G 9.4 (c) Group Statistics...............................................................................................................15
G 9.4 (d) Independent Sample Test........................................................................15
Table of Contents cont.
G 9.4 (e) Independent Sample Effect Sizes.............................................................................16
References...................................................................................17
Comparing Groups with T Test, Analysis of Variance (ANOVA) and Similar Non-
Parametric Tests
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SPSS Problems
G 9.1 Interpretation Sex at Birth and Students' Height
Comparing Groups with T Test, Analysis of Variance (ANOVA) and Similar Non-
Parametric Tests
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A significant difference exists in the average height of students based on sex at
birth. The provided data indicates that male students have a noticeably greater average
height, at approximately 70.24 inches, when compared to female students, whose average
height is about 64.13 inches. The descriptive statistics demonstrate a substantial
difference of over six inches. Further statistical analysis confirms the height disparity
between the two groups. The Levene's test for equality of variances, a crucial preliminary
step in the study (Morgan et al., 2020), yielded a significance value of 0.000. Because the
p-value is well below the conventional threshold of 0.05, researchers must conclude that
the population variances are not equal. Following the finding of unequal variances, the
"Equal variances not assumed" line of the independent samples t-test provides the
appropriate statistics for analysis. The t-test yielded a large t-statistic of 8.802, and the
corresponding p-value was less than 0.05. These findings provide strong evidence of a
statistically significant difference in mean height, suggesting the observed disparity is not
simply due to random chance. Therefore, the data reveals differing levels of variability
within each group. Heights among female students show less spread, as their standard
deviation (2.07) is smaller than the standard deviation for male students (2.80). The
analysis provides compelling evidence that a person's sex at birth is a significant factor in
predicting average student height.
G 9.1 (a) Group Statistics
Comparing Groups with T Test, Analysis of Variance (ANOVA) and Similar Non-
Parametric Tests
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G 9.1 (b) Independent Samples Test
G 9.1 (c) Independent Samples Effect Sizes
G 9.2 Difference - Hours Students Study and Hours They Work
Comparing Groups with T Test, Analysis of Variance (ANOVA) and Similar Non-
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An investigation examined whether a disparity exists between the hours students
allocate to studying and working, as well as the relationship between these two activities.
The analysis utilized data from 49 of 50 planned participants. A one-sample t-test
revealed that students dedicated more time to studying than to working. This outcome is
supported by a large effect size, with Hedges' and Cohen's d values between 1.731 and
1.880. A one-way ANOVA yielded an F-value of 1.123. The study found no significant
difference between the two variables, as the p-value was greater than .005. The evidence
proved insufficient to disprove the assertion of no difference. The eta-squared value of
0.000 further confirmed a negligible effect. Despite the lack of a significant difference, a
weak positive correlation was found between study and work hours (r=0.219), suggesting
that an increase in one variable is associated with a slight increase in the other.
G 9.2 (a) One-Sample Statistics
G 9.2 (b) One-Sample Test
Comparing Groups with T Test, Analysis of Variance (ANOVA) and Similar Non-
Parametric Tests
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G 9.2 (c) One-Sample Effect Sizes
G 9.2 (d) Descriptive
Comparing Groups with T Test, Analysis of Variance (ANOVA) and Similar Non-
Parametric Tests
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G 9.2 (e) Tests of Homogeneity of Variances
Comparing Groups with T Test, Analysis of Variance (ANOVA) and Similar Non-
Parametric Tests
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G 9.2 (f) ANOVA
G 9.2 (g) ANOVA Effect Sizes
G 9.3 What is the difference between the average time people spend watching television
and the average time they spend working?
Comparing Groups with T Test, Analysis of Variance (ANOVA) and Similar Non-
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A comparison of the data on television viewing and work hours reveals a notable
disparity between the two activities. A paired sample t-test, as described by Amariei et al.
(2025), was used to compare the means of these two related measurements from the same
individuals. Graph G 9.3 (c) displays the results of the Paired Samples Test, showing a p-
value of .001. A p-value less than .05 indicates that the observed difference is statistically
significant. The mean of the paired differences is 14.4, with a standard deviation of 18.7,
indicating that, on average, participants spent 14.4 fewer minutes watching TV than
working. The effect size, represented by Cohen's d, is .053, suggesting a small effect.
Moreover, Graph G 9.3 (b) shows a negative correlation (r = -.541) between the two
variables, indicating that as time spent working increases, time spent watching TV tends
to decrease. The significance for both one-sided and two-sided p-values is less than .001,
confirming the strength of this correlation. Overall, the analysis reveals a clear and
significant difference in the time dedicated to these two activities.
G 9.3 (a) Paired Samples Statistics
G 9.3 (b) Paired Samples Correlations
Comparing Groups with T Test, Analysis of Variance (ANOVA) and Similar Non-
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G 9.3 (c) Paired Samples Test
G 9.3 (d) Paired Samples Effect Sizes
G 9.4 Nonparametric Statistic
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Hours of Study Per Week
Chen et al. (2024) highlighted how to enhance the Mann-Whitney-Wilcoxon
rank-sum test for causal inference in observational studies. The traditional Mann-
Whitney-Wilcoxon test, used for comparing two groups, is modified to account for
confounding factors. The use of inverse probability weighting and a doubly robust
method allows for this outcome. The goal is to produce more precise and dependable
estimates of causal effects compared to what is possible with a basic application of the
Mann-Whitney-Wilcoxon test in these kinds of studies. There's a statistically significant
difference in the average hours of study per week. The nonparametric Mann-Whitney U
test reveals a two-tailed p-value of .047, which is below the standard significance level of
.05. This indicates a significant difference between the two groups. Females, with a mean
rank of 29.73 and an average of 18.08 hours per week, tend to study more than males,
who have a mean rank of 21.60 and an average of 13.35 hours per week. The independent
samples t-test also shows a significant difference with a two-sided p-value of .043, and
the Cohen's d effect size of -.589 suggests a medium effect, indicating that the difference
is not only statistically significant but also practically meaningful.
Hours Per Week Spent Working
There's no statistically significant difference in the average hours spent working
per week. The Mann-Whitney U test shows a two-tailed p-value of .928, which is much
greater than .05. This suggests no significant difference in the hours worked between
males and females. The independent samples t-test reinforces this finding, with a two-
Comparing Groups with T Test, Analysis of Variance (ANOVA) and Similar Non-
Parametric Tests
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sided p-value of .988. The mean hours worked are very similar: 26.15 hours for males
and 26.09 hours for females, and the Cohen's d effect size of .004 indicates a negligible
effect.
Amount of TV Watched
There's no statistically significant difference in the average hours of TV watched
per week. The Mann-Whitney U test provides a two-tailed p-value of .215, which is
greater than .05, suggesting no significant difference between the groups. Similarly, the
independent samples t-test shows a two-sided p-value of .204. While males, with a mean
of 13.04 hours, watch slightly more TV than females, who watch an average of 10.83
hours, this difference isn't statistically significant. Cohen's d effect size of .364 suggests a
small to medium effect, but it's not strong enough to be considered statistically
significant.
G 9.4 (a) Ranks
Comparing Groups with T Test, Analysis of Variance (ANOVA) and Similar Non-
Parametric Tests
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G 9.4 (b) Test Statistics
G 9.4 (c) Group Statistics
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Parametric Tests
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G 9.4 (d) Independent Sample Test
G 9.4 (e) Independent Sample Effect Sizes
Comparing Groups with T Test, Analysis of Variance (ANOVA) and Similar Non-
Parametric Tests
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References
Comparing Groups with T Test, Analysis of Variance (ANOVA) and Similar Non-
Parametric Tests
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Amariei, O.-I., Amariei, D.-M., Minda, A.-A., & Lolea, M. (2025). Statistical Evaluation of
Personalized Training in School Physical Education. German International Journal of Modern
Science / Deutsche Internationale Zeitschrift Für Zeitgenössische Wissenschaft, 106, 43–50.
https://doi.org/10.5281/zenodo.15705956
Chen, R., Lin, T., Liu, L., Liu, J., Chen, R., Zou, J., Liu, C., Natarajan, L., Tang, W., Zhang, X.,
& Tu, X. (2024). A doubly robust estimator for the Mann-Whitney Wilcoxon rank sum test when
applied for causal inference in observational studies. Journal of Applied Statistics, 51(16), 3267–
3291. https://doi.org/10.1080/02664763.2024.2346357
Morgan, G., Leech, N., Gloeckner, G., Barrett, K. (2020). IBM SPSS for Introductory Statistics
(5th Ed.). New York, NY
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