Example:
Comparing four teaching techniques.
Scores on exam for students learning material
with each of the four teaching techniques:
 
 
1
2
3
4
65
75
59
94
87
69
78
89
73
83
67
80
79
81
62
88
81
72
83
 
69
79
76
 
 
90
   

 

Kruskal-Wallis Test: exam versus technique

technique   N  Median  Ave Rank      Z
1           6   76.00      10.6  -0.60
2           7   79.00      12.7   0.33
3           6   71.50       7.6  -1.86
4           4   88.50      19.5   2.43
Overall    23              12.0

H = 7.78  DF = 3  P = 0.051
H = 7.79  DF = 3  P = 0.051  (adjusted for ties)

* NOTE * One or more small samples
 
 


 
 

One-way ANOVA: exam versus technique

Source     DF      SS     MS     F      P
technique   3   712.6  237.5  3.77  0.028
Error      19  1196.6   63.0
Total      22  1909.2

S = 7.936   R-Sq = 37.32%   R-Sq(adj) = 27.43%

                         Individual 95% CIs For Mean Based on
                         Pooled StDev
Level  N    Mean  StDev  ------+---------+---------+---------+---
1      6  75.667  8.165       (------*-----)
2      7  78.429  7.115          (-----*------)
3      6  70.833  9.579  (------*------)
4      4  87.750  5.795                 (--------*-------)
                         ------+---------+---------+---------+---
                              70        80        90       100

Pooled StDev = 7.936
 
 
 
 

Example:
How is the yield of corn fields affected by the density of weeds?
Four identical plots of corn were weeded to allow either
0, 1, 3 or 9 lambs' quarter plants per meter of corn row.
 
 

Kruskal-Wallis Test: yield versus weeds
weeds     N  Median  Ave Rank      Z
0         4   169.5      13.1   2.24
1         4   163.7       8.4  -0.06
3         4   157.3       6.3  -1.09
9         4   162.6       6.3  -1.09
Overall  16               8.5

H = 5.56  DF = 3  P = 0.135
H = 5.57  DF = 3  P = 0.134  (adjusted for ties)

* NOTE * One or more small samples
 
 


 
 

One-way ANOVA: yield versus weeds

Source  DF      SS     MS     F      P
weeds    3   340.7  113.6  1.73  0.213
Error   12   785.5   65.5
Total   15  1126.2

S = 8.091   R-Sq = 30.25%   R-Sq(adj) = 12.81%
 

                         Individual 95% CIs For Mean Based on
                         Pooled StDev
Level  N    Mean  StDev  ----+---------+---------+---------+-----
0      4  170.20   5.42                  (----------*----------)
1      4  162.83   4.47         (----------*----------)
3      4  161.03  10.49      (----------*----------)
9      4  157.58  10.12  (----------*----------)
                         ----+---------+---------+---------+-----
                         152.0     160.0     168.0     176.0