Tables for the Friedman’s Test with ties [archivos] : Interim Report

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López-Vázquez, Carlos
Hochsztain, Esther
Estos archivos acompañan al artículo Tables for the Friedman’s Test with ties: Interim Report. Contenido del artículo: Part of the steps necessary to assess if a new treatment or vaccine is better than other is to test if there exist a statistical difference between the treatments. Since its inception in 1937 this is performed using the Friedman’s Test (Friedman, 1937). The typical problem case is that of a wine contest, with k wines and N judges, not allowing ties for the rankings. Since his seminal paper, it is known that the statistic involved has asymptotic approximations with either the or the normal distribution. Such approximations are very inaccurate for low values of k and N, so Friedman offered a small set of exact tables which has been expanded over the year by other authors. Recently, López-Vázquez and Hochsztain (2017) expanded drastically the existing set of tables covering from low values of k and N not previously tabulated up to those values where the asymptotic expansion is accurate up to 1%. The assumption of no ties by the standard Friedman’s problem is somewhat unrealistic, and there are many application examples where ties are possible. Despite such evidence, only after more than forty years Conover (1980) generalized the expression of the Friedman’s statistic making it valid for both the case with and without ties. The asymptotic distributions are the same as before, and they still suffer for gross inaccuracies for low and mid values of k and N. The problem has been addressed in part only recently, where exact tables for the case with very low k and N have been published, leaving the users’s blinded for intermediate values. In this interim report we presented for the first time tables suitable to use the Friedman’s test in the case of ties covering from low to large values of k and N, considering all pairs where the asymptotic approximation has an error of more than 1%. The computation procedure was very similar to the one applied by López-Vázquez and Hochsztain (2017) and will be described elsewhere; they required more than two years wall time using a cluster of 1200 nodes. Considering the present scientific effort related with the COVID-19 pandemia, we decided to early disclose the numerical results as our two cents contribution to the task. To illustrate, we included in this document tables for those pairs (k,N) that have an error in excess of 10% w.r.t. the asymptotic expansion, and offer a link to the files where the other ~9.000 (k, N) pairs that exceed 1% are presented in tabular form.
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