Statistical Tests

Statistical tests

Error in statistical tests of error in statistical tests

BACKGROUND A recent paper found that terminal digits of statistical values in Nature deviated significantly from an equiprobable distribution, indicating errors or inconsistencies in rounding. This finding, as well as the discovery that a large percentage of p values were inconsistent with reported test statistics, led to a great deal of concern in the popular press and scientific community. Th...

Notes on statistical tests ∗

Let an unbiased coin be used to form an ω-sequence S of independent tosses. Let N be the positive integers. The finite initial segment of length n ∈ N is denoted by Sn (thus, S1 holds exactly the first toss). For n ∈ N , let Hn be the proportion of heads that show up in Sn. Pick a positive real number D, to be thought of as a number of standard deviations from the mean of the standard normal di...

OPTIMAL STATISTICAL TESTS BASED ON FUZZY RANDOM VARIABLES

A novel approach is proposed for the problem of testing statistical hypotheses about the fuzzy mean of a fuzzy random variable.The concept of the (uniformly) most powerful test is extended to the (uniformly) most powerful fuzzy-valued test in which the test function is a fuzzy set representing the degrees of rejection and acceptance of the hypothesis of interest.For this purpose, the concepts o...

Statistical significance tests.

Statistical methods for the analysis of data can be classed as descriptive or as probabilistic. The former methods include tabulation and graphical display, of great importance both in detailed analysis and also in presentation of conclusions. Probability enters statistical analysis in various ways. The most obvious is that one recognizes explicitly that conclusions drawn from limited data are ...