%0 Journal Article
%T The fuzzy interpretation of the statistical test for irregular data
%A Pietraszek, Jacek
%A Sobczyk, Andrzej
%A Skrzypczak-Pietraszek, Ewa
%A Kołomycki, Maciej
%J Czasopismo Techniczne
%V 2016
%R 10.4467/2353737XCT.16.242.5991
%N Mechanika Zeszyt 4-M 2016
%P 119-125
%K statistical test, normality of distribution, fuzzy statistics, bootstrap
%@ 0011-4561
%D 2016
%U https://ejournals.eu/czasopismo/czasopismo-techniczne/artykul/the-fuzzy-interpretation-of-the-statistical-test-for-irregular-data
%X 
	The well-known statistical tests have been developed on the basis of many additional assumptions, among which the normality of a data source distribution is one of the most important. The outcome of a test is a p-value which may is interpreted as an estimation of a risk for a false negative decision i.e. it is an answer to the question “how much do I risk if I deny?”. This risk estimation is a base for a decision (after comparing with a significance level α): reject or not. This sharp trigger – p-level greater than α or not – ignores the fact that a context is rather smooth and evolves from “may be” through “rather not” to “certainly not”. An alternative option for such assessments is proposed by a fuzzy statistics, particularly by Buckley’s approach. The fuzzy approach introduces a better scale for expressing decision uncertainty. This paper compares three approaches: a classic one based on a normality assumption, Buckley’s theoretical one and a bootstrap-based one