Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

698 APPENDIX E | Hypothesis Tests for Ordinal Data: Mann-Whitney, Wilcoxon, Kruskal-Wallis, and Friedman Tests
asked to evaluate three different designs for a new smart phone. Each person practices with
each phone and then ranks them, 1st, 2nd, and 3rd in terms of ease of use.
Finally, the Friedman test can be used if the original data consist of numerical scores.
However, the scores must be converted to ranks before the Friedman test is used. The following
example demonstrates how a set of numerical scores is transformed into ranks for
the Friedman test.
EXAMPLE E.3
To demonstrate the Friedman test, we will use the results from a repeated-measures study
in which each of n 5 5 participants watched a television program from four different viewing
distances. The data consist of the participants’ rating scores for each of the four viewing
distances. To convert the data for the Friedman test, the four scores for each participant are
replaced with ranks 1, 2, 3, and 4, corresponding to the size of the original scores. As usual,
tied scores are assigned the mean of the tied ranks. The complete set of ranks is shown in
part (b) of the table.
■
■ The Hypotheses for the Friedman Test
In general terms, the null hypothesis for the Friedman test states that there are no differences
between the treatment conditions being compared so the ranks in one treatment should not
be systematically higher (or lower) than the ranks in any other treatment condition. Thus,
the hypotheses for the Friedman test can be phrased as follows:
H 0
: There is no difference between treatments. Thus, the ranks in one treatment
condition are not systematically higher or lower than the ranks in any other
treatment condition.
H 1
: There are differences between treatments. Thus, the ranks in at least one
treatment condition are systematically higher or lower than the ranks in
another treatment condition.
■ Notation and Calculation for the Friedman Test
The first step in the Friedman test is to compute the sum of the ranks for each treatment
condition. The SR values are shown in Table E.3(b). In addition to the SR values, the
TABLE E.3
Results from a repeatedmeasures
study
comparing four television-viewing
distances.
Part (a) shows the original
rating score for each
of the distances. In part
(b), the four distances are
rank-ordered according to
the preferences for each
participant.
(a) The original rating scores
Person 9 Feet 12 Feet 15 Feet 18 Feet
A 3 4 7 6
B 0 3 6 3
C 2 1 5 4
D 0 1 4 3
E 0 1 3 4
(b) The ranks of the treatment conditions for each participant
Person 9 Feet 12 Feet 15 Feet 18 Feet
A 1 2 4 3
B 1 2.5 4 2.5
C 2 1 4 3
D 1 2 4 3
E 1 2 3 4
SR 1
5 6 SR 2
5 9.5 SR 3
5 19 SR 4
5 15.5