Friedman test
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The Friedman test is a non-parametric statistical test developed by the U.S. economist Milton Friedman. It is a multiple testing technique similar to parametric ANOVA. The procedure involves ranking each row (or block) together, then considering the values of ranks by columns.
Method
- Given data [\\}_], that is, a tableau with [m] rows (the blocks), [n] columns (the treatments) and a single observation at the intersection of each block and treatment, calculate the ranks within each block. Replace the data with a new tableau [\\}_] where the entry [r_] is the rank of [x_] within block [i].
- Find the values:
- *[SS_t = m\sum_^n (\bar_ - \bar)^2],
- *[SS_e = \frac \sum_^m \sum_^n (r_ - \bar)^2]
- *[\bar_ = \frac \sum_^m }]
- *[\bar = \frac\sum_^m \sum_^n r_]
- The test statistic is given by [Q = \frac].
- Finally, the p-value is given by [\mathbf(\chi^2_ \ge Q)].
References
[link]
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