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Comparison of selected tests for univariate normality based on measures of moments

100%
Domański C., Szczepocki P.
Statistics in Transition new series
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2020
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vol. 21
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issue 5
151-178
EN
Univariate normality tests are typically classified into tests based on empirical distribution, moments, regression and correlation, and other. In this paper, power comparisons of nine normality tests based on measures of moments via the Monte Carlo simulations is extensively examined. The effects on power of the sample size, significance level, and on a number of alternative distributions are investigated. None of the considered tests proved uniformly most powerful for all types of alternative distributions. However, the most powerful tests for different shape departures from normality (symmetric short-tailed, symmetric long-tailed or asymmetric) are indicated.
2
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Sequential Tests with Power Equal to 1 for Chosen Location Parameters

100%
Pekasiewicz D., University of Łódź C. o. S. M.
Acta Universitatis Lodziensis. Folia Oeconomica
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2007
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vol. 206
EN
We often verify hypotheses about random variable distribution parameters, when the variable distribution is unknown. In these cases we apply nonparametric tests, in particular nonparametric sequential tests. This paper presents sequential tests for the mean and median. These tests have important property - their power is equal to 1.
PL
Nieparametryczne testy sekwencyjne mogą służyć do weryfikacji hipotez o wartościach parametrów zmiennej losowej, takich jak wartość oczekiwana i mediana, w przypadku gdy nie znamy klasy rozkładu badanej zmiennej. W pracy przedstawione zostały przykłady testów sekwencyjnych, których moc, przy dużej liczebności próby, jest równa 1. Testy tego typu mogą znaleźć zastosowanie zarówno w kontroli jakości produkcji, jak i badaniach medycznych.
3

A Comparative Study of the Power of Parametric and Permutation Tests for a Multidimensional Two-sample Location Problem

88%
Polko-Zając D.
Argumenta Oeconomica Cracoviensia
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2020
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issue 2(23)
69-79
EN
Objective: A comparison of multidimensional populations is a very interesting and common statistical problem. It most often involves verifying a hypothesis about the equality of mean vectors in two populations. The classical test for verification of this hypothesis is the Hotelling’s T2 test. Another solution is to use simulation and randomization methods to test the significance of differences between the studied populations. Permutation tests are to enable statistical inference in situations where it is not possible to use classical parametric tests. These tests are supposed to provide comparable power to parametric tests with a simultaneous reduction of assumptions, e.g. regarding the sample size taken or the distribution of the tested variable in the population. The purpose of this study is a comparative analysis of the parametric test, the (usual) permutation test, and the nonparametric permutation procedure using two-stage ASL determination. Research Design & Methods: The study considered the analysis of multivariate data. The paper presents theoretical considerations and refers to the Monte Carlo simulation. Findings: The article presents a permutational, complex procedure for assessing the overall ASL (achieved significance level) value. The applied nonparametric statistical inference procedure uses combining functions. A simulation study was carried out to determine the size and power of the test under normality. A Monte Carlo simulation made it possible to compare the empirical power of this test with that of Hotelling’s T2 test. The most powerful test was the permutation test based on a two-stage ASL determination method using the Fisher combining function. Implications/Recommendations: The advantage of the proposed method is that it can be used even when samples are taken from any type of continuous distributions in a population. Contribution: The proposed test can be used in the analysis of multidimensional economic phenomena.
4
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PROPERTIES OF SELECTED SIGNIFICANCE TESTS FOR EXTREME VALUE INDEX

88%
Pekasiewicz D.
Acta Universitatis Lodziensis. Folia Oeconomica
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2014
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vol. 3
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issue 302
EN
The paper presents two tests verifying the hypothesis about the shape parameter of the generalized distribution of maximum statistic. It is called the extreme value index. The inverse of the positive index is called  the tail index and determines the degree of fatness of the tail. The asymptotic properties of the Pickands and the Hill estimator of the shape parameter are used to construct the test statistics. Simulation studies of the properties of these significance tests allow us to formulate some conclusions regarding their applications.
5
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Pojęcie wielkości efektu na tle teorii Neymana-Pearsona testowania hipotez statystycznych

63%
Szymczak W., Uniwersytet Łódzki W. N. o. W., wieszym@uni.lodz.pl
Acta Universitatis Lodziensis. Folia Psychologica
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2015
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vol. 19
PL
Celem tej pracy jest zwrócenie uwagi badaczy wykorzystujących metody statystyczne w analizie wyników swoich badań na pomieszanie dwóch różnych teorii testowania hipotez statystycznych, teorii Fishera i teorii Neymana–Pearsona. Zawarcie, w obecnie stosowanym instrumentarium statystycznym, pomysłów z obu tych teorii, powoduje, że znakomita większość badaczy bez chwili namysłu za prawdziwą przyjmuje stwierdzenie, iż im mniejsze prawdopodobieństwo, tym silniejsza zależność. Przedstawione zostały słabe strony teorii Neymana–Pearsona i wynikające z nich problemy przy podejmowaniu decyzji w wyniku przeprowadzonych testów. Problemy te stały się usprawiedliwionym poszukiwaniem mniej zawodnych rozwiązań, jednakże zaproponowane mierniki wielkości efektu, jako wykorzystujące z jednej strony dogmat o związku między wielkością prawdopodobieństwa w teście i siłą zależności, a z drugiej – brak jakichkolwiek podstaw teoretycznych tego rozwiązania, wydają się jeszcze jednym pseudorozwiązaniem rzeczywiście występujących problemów. Dodatkowo, wykorzystywanie mierników wielkości efektów wygląda na próbę zwolnienia badaczy z głębokiego myślenia o uzyskanych wynikach z analizy statystycznej, w kategoriach merytorycznych. Powstał trywialny przepis: odpowiednia wartość miernika natychmiast implikuje siłę zależności – podejście takie wydaje się niegodne badacza.
EN
The aim of this study is to draw the attention of researchers using statistical methods in the analysis of the results of their research on the combination of two different theories testing statistical hypothesis, Fisher’s theory and Neyman-Pearson’s theory. Including in the presently used statistical instruments, ideas of both of these theories, causes that the vast majority of researchers without a moment’s thought, acknowledge that the smaller the probability the stronger relationship. The study presents the weaknesses of Neyman-Pearson’s theory and the resulting problems with decision-making as a result of the conducted tests. These problems have become a justified quest for less unreliable solutions, however, the proposed measures of the size effect as using on one hand dogma about the relationship between the degree of probability in the test and the strength of dependence, on the other, lack of any theoretical basis of this solution, seem to be another pseudo solution to actual problems. Moreover, the use of measures of size effect seems to be an attempt to free researchers from the profound thinking about the results obtained from the statistical analysis. A trivial recipe was established: the corresponding value of the measures instantly implies the strength of the relationship – this approach seems unworthy of the researcher.
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