Specific statistical tests are used when the null hypothesis (H0) is to be tested using nonparametric nominal or ordinal data. With nominal data, experimental results are expressed by proportions or frequencies. Chi-square or related tests (the Fisher's exact test or the rows by columns test) are appropriate for testing H0 with nominal data. Ordinal data permit arrangement of statistical result...

We introduce a parameter z for the well-known Wallis’ inequality, and improve results on Wallis’ inequality are proposed. Recent results by other authors are also improved.

We present an analog of the well-known Kruskal-Katona theorem for the poset of subspaces of PG (n; 2) ordered by inclusion. For given k; ` (k < `) and m the problem is to nd a family of size m in the set of`-subspaces of PG (n; 2), containing the minimal number of k-subspaces. We introduce two lexicographic type orders O 1 and O 2 on the set of`-subspaces, and prove that the rst m of them, take...