I made this short presentationi however, there are examples that I took from the internet as well.

1. Justin and friends

5. Wilcoxon Test
Things to remember:
1 dependent variable (ordinal, interval, or
ratio)
1 independent variable with one group
OR two “matched-pairs” groups
2 sets of scores from different occasions or
conditions
 Ex. Condition 1: Pre-test
Condition 2: Post-test

6. In SPSS:
Click Analyze Nonparametric Tests 2-
Related Samples...
Similarities of Wilcoxon and Friedman Tests
Both are non-parametric
Both test the median between groups
Both used in skewed distributions
Both try to determine if subjects changed
significantly across occasions/conditions.

7. Friedman Test
• Overview
• The Friedman Test is the non-parametric
alternative to the one-way ANOVA with
repeated measures. It is used to test for
differences between groups when the
dependent variable being measured is
ordinal. It can also be used for continuous
data that has violated the assumptions
necessary to run the one-way ANOVA with
repeated measures; for example, marked
deviations from normality.

8. Assumptions
• One group that is measured on three or
more different occasions.
• Group is a random sample from the
population.
• One dependent variable that is either
ordinal, interval or ratio
• Samples do NOT need to be normally
distributed.

9. Differences of Wilcoxon and Friedman
Wilcoxon assess participants on two
occasions, Friedman allows for the
analysis or assessment of two OR MORE
occasions/conditions.
Wilcoxon’s parametric alternative is the
dependent t-test (paired samples t-
test), Friedman’s alternative is the one-
way repeated-measures ANOVA.

10. The Research Question
Do the employees’ medians on concern for job
pay, job climate, and job security ratings
differ in the population?
What is the independent variable?
What is the dependent variable?
Are the participants measured repeatedly?

12. Post-hoc Analysis
• If the result of the Friedman Test is significant (there is a
significant difference between the occasions/conditions where
the group was tested), you need to run post-hoc analysis
which determines where the specific differences lie.
• This will be accomplished by using the Wilcoxon Signed-
Rank Test (because it compares differences between two
groups of the same subjects). Since we want to conduct
multiple comparisons:
1. None to Classical
2. None to Dance
3. Classical to Dance
We need to use the Bonferroni adjustment to avoid a Type 1
error. It is very easy to calculate.

13. The Bonferroni Adjustment
Steps:
1. Take the significance level that you were
using (ex. Alpha level .05) and divide it by the
number of tests you are running, in our case,
there are 3.
0.05/3 = 0.017
Then, if the P value is larger than 0.017, then it
is not significant, therefore, there is no
significant difference between the three
comparisons.

15. How would you describe a
parametric test?
• It compares means,
• It makes use of real values,
• It has a large number of observations – thirty or
more observations. (observations are the values in
the rows of your SPSS in “Data view”),
• Its samples are normally distributed. A normal
distribution has the highest frequency at the
middle of the curve in a graph.

16. What are non parametric tests?
• Non parametric tests are a comparison of
medians.
• PLEASE OBSERVE THE NEXT SLIDE
FOR AN ILLUSTRATION

17. Tests for non-parametric statistics are similar to the tests covered in
AP stats, but each is slightly different. There are non-parametric
tests which are similar to the parametric tests. The following table
shows how some of the tests match up.
Parametric Test Goal for Non-Parametric Goal for Non-
Parametric Test Test Parametric Test
Two Sample T-Test To see if two samples Wilcoxon Rank-Sum Test To see if two samples
have identical population have identical
means population medians
One Sample T-Test To test a hypothesis about Wilcoxon Signed Ranks To test a hypothesis
the mean of the Test about the median of the
population a sample was population a sample was
taken from taken from
Chi-Squared Test for To see if a sample fits a Kolmogorov-Smirnov To see if a sample could
Goodness of Fit theoretical distribution, Test have come from a
such as the normal curve certain distribution
ANOVA To see if two or more Kruskal-Wallis Test To test if two or more
sample means are sample medians are
significantly different significantly different

18. Kendall’s W

19. Kendall's W (also known as Kendall's
coefficient of concordance) is a non-
parametric statistic. It is a normalization
of the statistic of the Friedman test, and
can be used for assessing agreement
among raters. Kendall's W ranges from 0
(no agreement) to 1 (complete
agreement).

20. Suppose, for instance, that a number of people
have been asked to rank a list of political
concerns, from most important to least important.
Kendall's W can be calculated from these data.
If the test statistic W is 1, then all the survey
respondents have been unanimous, and each
respondent has assigned the same order to the list of
concerns. If W is 0, then there is no overall trend of
agreement among the respondents, and their
responses may be regarded as essentially random.
Intermediate values of W indicate a greater or lesser
degree of unanimity among the various responses.

21. While tests using the standard
Pearson correlation coefficient
assume normally distributed values
and compare two sequences of
outcomes at a time, Kendall's W
makes no assumptions regarding the
nature of the probability distribution
and can handle any number of distinct
outcomes.

22. THE END

23. PSYCH 224 QUIZ
1. The following data on amount of food consumed (g) by eight rats after
0, 24, and 72 hours of food deprivation appeared in the paper “The
Relation Between Differences in Level of Food Deprivation and
Dominance in Food Getting in the Rat”. Does the data indicate a
difference in the true mean rank of food consumption for the three
experimental conditions?
Rat = 1 to 8; Food consumption (g) per hour = data in bold
Hours
1 2 3 4 5 6 7 8
0 3.5 3.7 1.6 2.5 2.8 2.0 5.9 2.5
24 5.9 8.1 8.1 8.6 8.1 5.9 9.5 7.9
72 13.9 12.6 8.1 6.8 14.3 4.2 14.5 7.9
2. Which test should you use and why?
3. How strong is the relationship between the three experimental
conditions?