A non-parametric test for differences between t (>2) treatments using b blocks of size t, so that each treatment is used once in each block. Within each block the observed values are replaced by the equivalent ranks. Denoting the total of the ranks for treatment i by Ri, the test statistic T is given by
If there are no differences between treatments, then T has an approximate chi-squared distribution with (t−1) degrees of freedom. The test was proposed by Milton Friedman in a 1937 paper.As an example, with b = 7 blocks and t = 3 treatments, the original data
A
52
63
45
53
47
62
49
B
45
79
57
51
50
72
52
C
38
50
39
43
56
49
40
are replaced by
A
1
2
2
1
3
2
2
RA = 13
B
2
1
1
2
2
1
1
RB = 10
C
3
3
3
3
1
3
3
RC = 19
giving
Since 6 just exceeds the upper 5% point of a χ22 distribution it suggests that there are significant differences between the treatments.The Quade test is a variant in which the ranks are multiplied by block scores that reflect the variability of the values within a block. The resulting test pays more attention to those blocks that provide the clearest evidence of differences between the treatments.
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