We will discuss the application of independent and paired sample t-tests. In addition, we will review the non-parametric alternatives to these analyses.

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

2. Table of
Contents
Statistics Solutions Services
Conducting t-tests
Intellectus 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. Comparisons
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Comparison Parametric Test Non-Parametric Test
Differences between two
groups
Independent sample t-test Mann-Whitney U test
Differences between pretest
and posttest
Paired sample t-test Wilcoxon-Signed Rank test
Differences between variable
and specified value
One-sample t-test One-sample Wilcoxon test

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. Independent Sample t-Test:
Assesses for differences in a
continuous variable between two
independent groups.

7. Setting Up
Independent
Sample t-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 dependent variable.
 Check for assumptions of an independent sample t-test.
 https://statistics.laerd.com/spss-tutorials/independent-t-test-using-spss-
statistics.php
 If assumptions are not supported, run a Mann-Whitney U test.
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8. Paired (Dependent) Sample t-Test:
Assesses for differences in a matched
continuous variable between two
points in time.

9. Setting Up Paired
Sample t-test
 Need to have one matched dependent variable that is measured two
times.
 Check for assumptions of a paired sample t-test:
 https://statistics.laerd.com/spss-tutorials/dependent-t-test-using-
spss-statistics.php
 If assumptions are not supported, run a Wilcoxon-Signed Rank
test.
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10. One-Sample t-Test:
Assesses for differences between a
continuous variable and a specified
value.

11. Summary
 Identify independent grouping variables and dependent variables.
 Is goal to test for differences between groups, test for differences over time?
 Use statistical software (Intellectus Statistics, SPSS, Stata, etc.) to analyze your data
and present interpretations.
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12. Additional
Support
Statistics Solutions is a full-service dissertation consulting
company providing graduate students timely, editorial
support for their dissertations and scholarly projects
For information about our services, receive a
complementary 30-min consultation available Mon-Fri 9-5
ET
Contact us at info@statisticssolutions.com
Phone: 727-442-4290