1. One-Way Repeated Measures ANOVA on Ranks
The data used here are those from David Howell’s Table 18.10. The within subjects
independent variable is the number of visual aids employed by the lecturer. The dependent variable
is the mean rating given by members of the audience (higher is better).
Notice that the data are in wide format. For each lecturer all three scores are on the same line.
Analyze, Nonparametric Tests, Legacy Dialogs, K Related samples. Scoot the score variables
into the Test Variables pane. Click Statistics and select Descriptives.
2. Descriptive Statistics
N Mean
Std.
Deviation Minimum Maximum
None 17 45.35 12.845 25 72
Few 17 50.94 14.420 25 73
Many 17 44.94 17.293 18 75
Ranks
Mean
Rank
None 1.76
Few 2.65
Many 1.59
Test Statisticsa
N 17
Chi-Square 10.941
df 2
Asymp. Sig. .004
a. Friedman Test
For pairwise comparisons, select, under Legacy Dialogs, 2 Related Samples. Create the three
pairwise comparisons in the Test Pairs pane and then click Exact. Select Exact, Continue, OK.
3. Ranks
N Mean Rank Sum of Ranks
Few - None Negative
Ranks
3a
5.67 17.00
Positive Ranks 14b
9.71 136.00
Ties 0c
Total 17
Many -
None
Negative
Ranks
10d
9.75 97.50
Positive Ranks 7e
7.93 55.50
Ties 0f
Total 17
Many - Few Negative
Ranks
14g
9.86 138.00
Positive Ranks 3h
5.00 15.00
Ties 0i
Total 17
a. Few < None
b. Few > None
c. Few = None
d. Many < None
e. Many > None
f. Many = None
g. Many < Few
h. Many > Few
i. Many = Few
4. Test Statisticsa
Few -
None
Many -
None
Many -
Few
Z -2.819b
-.996c
-2.916c
Asymp. Sig. (2-
tailed)
.005 .319 .004
Exact Sig. (2-tailed) .003 .335 .002
Exact Sig. (1-tailed) .001 .167 .001
Point Probability .000 .007 .000
a. Wilcoxon Signed Ranks Test
b. Based on negative ranks.
c. Based on positive ranks.
Ratings were significant higher for the lectures with few visual aids than for those with none or
many visual aids, with the difference between none a many falling well short of significance.
While means rank is a good statistic for comparing the conditions here, psychologists usually
report medians. Measures of skewness and kurtosis would be helpful too. Here is output from the
Frequencies procedure.
Statistics
None Few Many
N Valid 17 17 17
Missing 0 0 0
Median 49.00 54.00 47.00
Skewness .206 -.301 -.045
Kurtosis -.409 -.952 -1.077
Frankly, the variables appear close enough to normal to do a parametric ANOVA.
An Alternative Approach
We shall read in the data in long format (one row for each cell in the Lecture x Visual Aids
matrix, that is, three rows for each lecturer), then rank the data, then do a one-way repeated
measures ANOVA on the ranked data.
Read in the Data
Block IV DV
1 1 50
1 2 58
1 3 54
2 1 32
5. 2 2 37
2 3 25
3 1 60
3 2 70
3 3 63
And so on
Create a new syntax window. Enter and run this syntax: rank DV by Block. The ranked data
will have variable name RDV.
Analyze, General Linear Model, Univariate
You need to exclude the interaction term, so click Model. Identify Block and IV as factors, but
do not build the interaction
6. You want LS means and pairwise comparisons among them
7. Tests of Between-Subjects Effects
Dependent Variable: RDV
Source
Type III Sum
of Squares df
Mean
Square F Sig.
Corrected
Model
10.941a
18 .608 .844 .641
Intercept 204.000 1 204.000 283.102 .000
Block .000 16 .000 .000 1.000
IV 10.941 2 5.471 7.592 .002
Error 23.059 32 .721
Total 238.000 51
Corrected Total 34.000 50
a. R Squared = .322 (Adjusted R Squared = -.060)
Significant effect of number of visual aids.
Estimates
Dependent Variable: RDV
IV Mean
Std.
Error
95% Confidence Interval
Lower
Bound
Upper
Bound
1 1.765 .206 1.345 2.184
2 2.647 .206 2.228 3.066
3 1.588 .206 1.169 2.008
Pairwise Comparisons
Dependent Variable: RDV
(I) IV (J) IV
Mean
Difference (I-
J)
Std.
Error Sig.b
95% Confidence Interval for
Differenceb
Lower Bound Upper Bound
1 2 -.882*
.291 .005 -1.475 -.289
3 .176 .291 .549 -.417 .770
2 1 .882*
.291 .005 .289 1.475
3 1.059*
.291 .001 .466 1.652
3 1 -.176 .291 .549 -.770 .417
2 -1.059*
.291 .001 -1.652 -.466
Based on estimated marginal means
*. The mean difference is significant at the 0.05 level.
b. Adjustment for multiple comparisons: Least Significant Difference (equivalent
to no adjustments).
UNIANOVA RDV BY Block IV
