
KruskallWallis One Way Analysis of Variance
How: Place the number of rows (groups) in the contingency table in the first
text box, the number of columns (ordinal values) in the next. Place the
frequency table into the large text box. Each columns must be
separated by a white space (blank or tab). The data can
be typed in, or the cells from an excel file may be copied and pasted into
the box. Click the Do Kruskall Wallis button, and the results will show.
Reference: Siegal S, Castellan Jr. N.J. (1988) Nonparametric statistics for the Behavioral Sciences 2nd. Ed. ISBN 0070573573 0. McGraw Hill Book Company New york
P206212. Minimum mean Rank differences: ditto p. 213215
Dunn's Test:Description: Zar Z.H. (1974) Biostatistical analysis (3rd.Ed) Prentice Hall, New Jersey. ISBN 0130845426. p227,228. Table for Q values App. 106
Dunn O.J. (1964) Multiple contrasts using rank sums. Technometrics 6:241:252
Explanation: This performs the nonparametric
Kruskall Wallis One Way Analysis of variance, comparing multiple groups with
ordinal data, using a frequency table as the input. The data is a
matrix, where each row represents the data in a group, and each column an
ordinal value. The number in the cell therefore represents the
number of cases in that group with that value.
Example: Let say we compare children from 3 schools (3 rows) in
their liking for their teachers in a scale of 0 to 3 (4 cols).
From school A 10 children scored 0, 15 scored 1, 20 scored 2, and 20 scored
3. From school B 20 each scored for each value. From
school C 20 scored 0, 10 scored 1, 10 scored 2, and 10 scored 3.
The data are in the following 3 rows: 10 15 20 20, 20 20 20 20, and 20 10 10
10. From this the following results are generated.
Results
Grp1 n=65 Mean Rank=110.3077
Grp2 n=80 Mean Rank=97.3750
Grp3 n=50 Mean Rank=83.0000
KruskalWallis H=7.0782 df=2 p=0.0290
Minimum significant diff in rank (Siegal and Castellan)
grp 
grp 
Diff 
Dif(0.05) 
Dif(0.01) 
Dif(0.001) 
0 
1 
12.93 
15.55 
21.96 
29.31 
0 
2 
27.31 
17.52 
24.74 
33.02 
1 
2 
14.38 
16.79 
23.71 
31.64 
Minimum Significant diff in rank (minimum Q by Dunn)
grp 
grp 
Q 
Q(0.05) 
Q(0.01) 
Q(0.001) 
0 
1 
2.12 
2.39 
2.94 
3.59 
0 
2 
3.53 
2.39 
2.94 
3.59 
1 
2 
1.46 
2.39 
2.94 
3.59 
