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1. ED602 - Statistics with
Computer Analysis
Submitted by
SILONGAN, DATU MOHAMMAD E.

2. TWO WAY
ANALYSIS OF
VARIANCE by
RANKS
FRIEDMAN
Topic no. 24

3. Agenda
Introduction
Definition
Running the test
When to use Friedman’s
test
Test Example
Presentation title 3

4. Introduction
Friedman test was developed by an
American economist Milton Friedman.
What is Milton Friedman best known for?
Mr. Friedman was awarded the Nobel
Prize for Economic Science in 1976. He
was best known for explaining the role
of money supply in economic and
inflation fluctuations.
4
MILTON
FRIEDMAN
Source:
THE WALL STREET JOURNAL
By Greg Ip and
Mark Whitehouse
Nov. 17, 2006
https://www.wsj.com/articles/SB116369744597625238

5. DEFINITION
5
Friedman’s test is a non-parametric test for finding differences in
treatments across multiple attempts. Nonparametric means the test
doesn’t assume your data comes from a particular distribution (like the
normal distribution). Basically, it’s used in place of the ANOVA test
when you don’t know the distribution of your data.
The objective is to determine if we may conclude from sample
evidence that there is a difference in treatment effects.

6. Running the test
6
Data should be
ordinal (e.g. the
Likert scale) or
continuous
1 Data comes from a
single group,
measured on at least
three different
occasions.
2 The sample was
created with a
random sampling
method.
3
Blocks are mutually
independent (i.e. all of
the pairs are
independent — one
doesn’t affect the other),
4 The observations
within each block may
be ranked in order of
magnitude.
5

7. When to Use the Friedman Test
7
1. Measuring the mean scores of subjects during three or more time
points.
For example, you might want to measure the resting heart rate of
subjects -one month before they start a training program,
-one month after starting the program, and
-two months after using the program.
You can perform the Friedman Test to see if there is a significant
difference in the mean resting heart rate of patients across these three
time points.

8. When to Use the Friedman Test
8
2. Measuring the mean scores of subjects under three different
conditions.
For example, you might have subjects watch three different movies and
rate each one based on how much they enjoyed it. Since each subject
shows up in each sample, you can perform a Friedman Test to see if
there is a significant difference in the mean rating of the three
movies.

9. 9
The data:
In this analysis the one variable
is the type of animal (fish,
reptiles, or mammals), and the
response variable is the number
of animals on display. From our
database, we use three variables
reptnum (number of reptiles on
display), fishnum (number of fish
on display) and mamlnum
(number of mammals on
display). These scores are
shown for the 12 stores below
(reptnum, fishnum, mamlnum).
Friedman Test:
Example
The Data
12,32,34 14,41,38 15,31,45 12,38,32 7,21,12 4,13,11
10,17,22 4,22,9 14,24,20 4,11,8 5,17,19 10,20,8
These scores are shown for the 12 stores below (reptnum, fishnum, mamlnum).
Petshop reptnum fishnum mamlnum
1 12 32 34
2 14 41 38
3 15 31 45
4 12 38 32
5 7 21 12
6 4 13 11
7 10 17 22
8 4 22 9
9 14 24 20
10 4 11 8
11 5 17 19
12 10 20 8
Step 1 Rearrange the data so that scores from each
subject are in the appropriate columns, one for each condition.

10. Research Hypothesis:
The data come from the Pet shop database. The researcher hypothesized that stores would
tend to display more fish than other types of animals, fewer reptiles, and an intermediate
number of mammals.
Null Hypothesis for this analysis:
Pet shops display the same number of reptiles, fish and mammals.

11. Step 2
Rank order the scores SEPARATELY FOR EACH SUBJECT'S DATA with
the smallest score getting a value of 1. If there are ties (within the scores for a subject)
each receives the average rank they would have received.
Petshop
1
2
3
4
5
6
7
8
9
10
11
12

12. Step 3
Compute the sum of the ranks for each
condition.
Step 4
Determine the number of subjects.
Step 5
Determine the number of conditions.

13. Step 6
Compute Friedman's F, using the following formula (you should carry at
least 3 decimals in these calculations).

14. For small samples (k < 6 AND N < 14):
Step 7
Determine the critical value of F by looking at the table of critical values for
Friedman's test
F (k=3, N=12, a = .05) = 6.17
Fr Critical values for Friedman's two-way analysis of Variance by ranks

15. Step 8
Comparethe obtained F and the critical F values to determine whether to retain or reject
the null hypothesis.
-- if the obtained F value (from Step 6) is larger than the critical value of F, then reject Ho:
-- if the obtained F value is less than or equal to the critical value of F, then retain Ho:
For the example data, we would decide to reject the null hypothesis, because
the
obtained value of F (15.526) is greater than the larger critical F value (8.67).
Critical F value = 6.17 F = 15.526

16. For large samples (k > 5 or N > 13):
Step 1
Determine the critical value of F by looking at the table of critical values for the Chi-Square
test (df = k - 1).
(As an example, here is how you would apply this version of the significance test to these
data.)

17. For large samples (k > 5 or N > 13):
X² (df = 2, p=.05) = 5.99

18. Step 10
Compare the obtained F and the critical X² values to determine whether to retain or reject
the null hypothesis.
-- if the obtained F value (from Step 6) is less than or equal the critical value of
X², then retain Ho:
-- if the obtained F value is larger than the critical value of X², then reject Ho:
For the example data, we would decide to reject the null hypothesis, because the
obtained value of F (15.526) is greater than the larger critical C² value (5.99).
Null Hypothesis for this analysis:
Pet shops display the same number of reptiles, fish and
mammals.
reject

19. Thank
you
Silongan, Datu Mohammad E.
ED 602 – Statistics with Computer Analysis
Saturday 10:00 am – 1:00 pm