The Page non parametric test is similar to Friedman's test but is used to check if ranking of a treatment levels make sense. Available in Excel with XLSTAT.
What is the Page non parametric test
The goal of the test proposed by Page (1963) is to allow analyzing rigorously the results of a study carried out within the framework of a complete design, to verify if a series of several treatments should be considered as not different, or if alternatively a ranking of the treatment makes sense. The Page test is a nonparametric method, thus not making any assumption on the distribution of the measurements. This test differs from the Friedman test by the fact that the alternative hypothesis is a ranking of the treatments and not only a difference. This test has been extended to the case of incomplete blocks by Alvo and Cabilio (2005).
If t1, t2, …, tk correspond to the k treatments, the null and alternative hypotheses used in the test are:
• H0 : The k treatments are not significantly different.
• Ha : t1 ≤. t2 ≤ … . ≤ tk
• Ha : t1 ≥. t2 ≥ … . ≥ tk
Where, for the alternative hypotheses, at least one inequality is strict.
Computation of the p-values
To compute the p-values corresponding to the various statistics, XLSTAT offers two alternative methods:
- Asymptotic method: The p-value is obtained using the asymptotic approximation of the distribution of the z statistics. The reliability of the approximation depends on the number of treatments and on the number of blocks.
- Monte Carlo method: The computation of the p-value is based on random resamplings. The user must set the number of resamplings. A confidence interval on the p-value is provided. The more resamplings are performed, the better the estimation of the p-value.
In order to avoid freezing Excel because of too long computations, it is possible with the two latter methods to set the maximum time that should be spent computing the p-value.
Multiple pairwise comparisons
If the p-value is such that the H0 hypothesis has to be rejected, then at least one treatment is different from another. To identify which treatment(s) is/are responsible for rejecting H0, a multiple comparison procedure can be used, XLSTAT allows using the procedure suggested by Cabilio and Peng (2008), with two alternative ways to compute the p-value of the paired comparisons. It can either use the normal approximation of a Monte Carlo based -pvalue.