We will discuss the various types of tests of differences such as independent/dependent sample t-tests, ANOVAs, and MANOVAs. There will be a brief question and answer session at the end of the presentation.

1. How to Conduct and Interpret Tests
of Differences
Justin D’Souza
Quantitative Specialist

2. Table of
Contents
Statistics Solutions Services
Selecting an Appropriate Test
SPSS Demo
Summary
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3. Services Offered
by Statistics
Solutions
• Topic Development
• Prospectus or Concept Papers
• Introduction Chapter
• Literature Review Chapter (identifying articles)
• Methodology Chapter (Quantitative/Qualitative).
• IRB forms
• Data entry templates
• Survey Monkey upload
• Results Chapter (Quantitative/Qualitative)
• Discussion Chapter
• Powerpoints for Defense
• Journal Publications
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4. Parametric and
Non-Parametric
Statistics
Parametric Techniques
 Parametric statistics are based on assumptions about the distribution of
population from which the sample was taken.
 Usually this “assumption” is that the data follows a normal (bell-shaped)
distribution.
Non-Parametric Techniques
 Nonparametric statistics are not based on assumptions, that is, the data can be
collected from a sample that does not follow a specific distribution.
 A normal (bell-shaped) distribution is not required for non-parametric
techniques.
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5. Normality
Assumption
Normality Assumption
 Typically, parametric statistics assume that the data follow a normal (bell-shaped)
distribution.
 There are various ways to check for normality (Shapiro-Wilk test, Kolmogorov-
Smirnov test, skewness/kurtosis, scatterplots/histograms). And if the data do not
follow a normal distribution, non-parametric techniques can potentially be used as
an alternative.
 If you have a large sample size (>50), you can use the central limit theorem to
justify using parametric techniques even if tests normality are not showing a bell-
shaped curve. Howell (2013) states that violations of normality are not problematic
when the sample size for research exceeds 50 cases.
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6. Differences in Variable Between
Two Groups

7. Differences in
Variable Between
Two Groups
Sample Research Question:
Is there a significant difference in math scores between males and females?
Parametric Technique
 Independent sample t-test – Appropriate statistical analysis when testing for
differences in a continuous (interval/ratio) variable between two groups.
Non-Parametric Technique
 Mann-Whitney U test– Appropriate statistical analysis when testing for
differences in an ordinal variable (or non-normal continuous variable) between
two groups.
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8. Setting Up
Independent
Sample t-test and
Mann-Whitney
U Test
 Need to have an independent variable that is dichotomous (two groups).
Examples: Gender (male vs female), group in experimental study (treatment vs
control)
 Need to have a continuous or ordinal dependent variable.
 Check for assumptions of an independent sample t-test or Mann-Whitney U test.
 https://statistics.laerd.com/spss-tutorials/independent-t-test-using-spss-
statistics.php
 https://statistics.laerd.com/spss-tutorials/mann-whitney-u-test-using-spss-
statistics.php
 Run your statistical analysis in SPSS.
Need help with your dissertation? Call 727-442-4290

9. Differences in Variables Between
Two or More Groups

10. Differences In
Variables
Between Two or
More Groups
Sample Research Questions:
Is there a significant difference in math scores between classes (Class 1, Class 2, and Class 3)?
Is there a significant difference in math scores and science scores between classes (Class 1, Class 2, and Class 3)?
Parametric Technique
 Analysis of Variance (ANOVA)– Appropriate statistical analysis when testing for differences in one
continuous (interval/ratio) variable between two or more groups.
 Multivariate Analysis of Variance (MANOVA)– Appropriate statistical analysis when testing for
differences in multiple continuous (interval/ratio) variables between two or more groups.
Non-Parametric Technique
 Kruskal-Wallis Test– Appropriate statistical analysis when testing for differences in an ordinal variable
(or non-normal continuous variable) between two or more groups.
 There is not a non-parametric alternative to running multiple dependent variables at once. Instead run a
single Kruskal-Wallis Test for each dependent variable.

11. Setting Up
ANOVA,
MANOVA, and
Kruskal-Wallis
Test
 Need to have one or more independent grouping variables with two or more
groups. Examples: Ethnicity, Grade Level, College Major
 Need to have one or more continuous or ordinal dependent variables.
 Check for assumptions of an ANOVA, MANOVA, or Kruskal-Wallis test.
 https://statistics.laerd.com/spss-tutorials/one-way-anova-using-spss-
statistics.php
 https://statistics.laerd.com/spss-tutorials/one-way-manova-using-spss-
statistics.php
 https://statistics.laerd.com/spss-tutorials/kruskal-wallis-h-test-using-spss-
statistics.php
 Run your statistical analysis in SPSS.
Need help with your dissertation? Call 727-442-4290

12. Differences in Variable Between
Two Points in Time (Pretest vs
Posttest)

13. Differences in
Variable Between
Two Points in
Time (Pretest vs
Posttest)
Sample Research Question:
Is there a significant difference in reading test scores between pretest and posttest?
Parametric Technique
 Dependent (paired) sample t-test – Appropriate statistical analysis when testing
for differences in a continuous (interval/ratio) variable between two points in
time.
Non-Parametric Technique
 Wilcoxon-Signed Rank test– Appropriate statistical analysis when testing for
differences in an ordinal variable (or non-normal continuous variable) between
two points in time.
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14. Setting Up
Dependent
Sample t-test and
Wilcoxon-Signed
Rank Test
 Need to have one dependent variable that is measured two times.
 Check for assumptions of a dependent sample t-test or Wilcoxon-
Signed Rank test:
 https://statistics.laerd.com/spss-tutorials/dependent-t-test-using-
spss-statistics.php
 https://statistics.laerd.com/spss-tutorials/wilcoxon-signed-rank-
test-using-spss-statistics.php
 Run your statistical analysis in SPSS.
Need help with your dissertation? Call 727-442-4290

15. Differences in Variable Between
Three or More Points in Time
(T1 vs T2 vs T3….)

16. Differences in
Variable Between
Three or More
Points in Time
(T1 vs T2 vs
T3…)
Sample Research Question:
Is there a significant difference in reading test scores between pretest, midterm, posttest,
and follow-up?
Parametric Technique
 Repeated Measures ANOVA – Appropriate statistical analysis when testing for
differences in a continuous (interval/ratio) variable between three or more
points in time.
Non-Parametric Technique
 Friedman ANOVA– Appropriate statistical analysis when testing for differences
in an ordinal variable (or non-normal continuous variable) between three or
more points in time.
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17. Setting Up
Repeated
Measures
ANOVAand
Friedman
ANOVA
 Need to have one dependent variable that is measured three or more times.
 Check for assumptions of a repeated measures ANOVA or a Friedman ANOVA:
 https://statistics.laerd.com/statistical-guides/repeated-measures-anova-
statistical-guide.php
 https://statistics.laerd.com/spss-tutorials/friedman-test-using-spss-
statistics.php
 Run your statistical analysis in SPSS.
Need help with your dissertation? Call 727-442-4290

18. Differences in Variable Between
GroupsAND Time

19. Differences in
Variable Between
GroupsAND
Time
Sample Research Question:
Is there a significant difference in reading test scores by class and pretest/posttest?
Parametric Technique
 Mixed Model ANOVA – Appropriate statistical analysis when testing for
differences in multiple continuous (interval/ratio) variables between groups
AND time.
Non-Parametric Technique
 There is not a non-parametric technique for simultaneously examining for
differences in groups and time.
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20. Setting Up
Mixed Model
ANOVA
 Need an independent grouping variable (such as treatment vs control).
 Need to have one continuous dependent variable that is measured two or more
times.
 Check for assumptions of a mixed model ANOVA:
 https://statistics.laerd.com/spss-tutorials/mixed-anova-using-spss-
statistics.php
 Run your statistical analysis in SPSS.
Need help with your dissertation? Call 727-442-4290

21. Summary
 Determine what level of measurement of variables you are using.
 Identify all independent and dependent variables.
 Is goal to test for differences between groups, test for differences over time
(intervention), or both?
 Use SPSS to check for assumptions, analyze your data, and present interpretations.
Need help with your dissertation? Call 727-442-4290

22. Additional
Support
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company providing graduate students timely, editorial
support for their dissertations and scholarly projects
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