 1) Missing specifications and hidden assumptions in Medical Statistical hypotheses tests.

In this paper, we analyse the implicit hypotheses used in Medical Statistical  Hypotheses Tests, that are not usually  experimentally tested and we bring them to the surface. We suggest new formulations and specifications for many familiar tests.We speculate on the development of methods that could be classified as non-parametric forecasting, non-parametric regression, and non-parametric disciminant analysis. The next table gives some examples:

 Name of The test Used for Distribution used Assumptions not tested, Additional test required Vague specifications New formulae or specifications required witch is not the size of the sample for the power or significance level Z-test, variance known Comparison of means Normal Normal Population Test for the Normality of Population , Test for the equality of variance in the two samples version "Large sample" Minimum size of the sample according to the accuracy level of normality Z-test, Variance unknown Comparison of means Normal Normal Population Test   for theNormality of Population   Test for the equality of variance in the two samples version "Small Sample" Minimum size of the sample according to the accuracy level of normality T-tests Comparison of means Student Normal Population Test  for the Normality of Population   Test for the equality of variance if it is assumed in the two samples version "Small Sample" Minimum size of the sample according to the accuracy level of normality Yate's corrected X^2 independence test Comparison of proportions X^2 Normal Approximation "Sufficient large sample to apply normal approximation" Minimum size of the sample so as to have no error up to the accuracy level of normality approximation Signed rank (Wilcoxon) Test Comparison of medians Non-parametric The two samples come from the same distribution Test, that the distribution is symmetric and if it is of two samples, that they  follow the same distribution. "Sufficient Large sample to make use of the normal approximation in the central limit theorem" "Small sample", "Large sample" Minimum size of the sample according to the accuracy level for the central limit theorem to apply without error McNeamars Test Comparison of proportions X^2 Normal Approximation "Sufficient large sample to apply normal approximation" Minimum size of the sample according to the accuracy level of normality approximation Woolf's test Comparison of proportions X^2 Normal Approximation "Sufficient large sample to apply normal approximation" Minimum size of the sample according to the accuracy level of normality approximation Log-rank test Comparison of proportions X^2 Normal Approximation "Sufficient large sample to apply normal approximation" Minimum size of the sample according to the accuracy level of normality approximation Sign-test Comparison of proportions Non-parametric Test for the equality of distributions in the two samples version "Sufficient Large sample to make use of the normal approximation in the central limit theorem" "Small sample", "Large sample" Minimum size of the sample according to the accuracy level for the central limit theorem to apply without error Anova's F-test Comparison of means F Normal Population, equality of variances Test   for the Normality of the Population. Test fo the equality of variances in the two samples if it is assumed Minimum size of the sample according to the accuracy level of normality

Speculations about a preventive treatment for cancer