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Złotoś Małgorzata (University of Economics in Katowice, Poland)
On the Use of Permutation Tests in the Significance Testing of Response Surface Function Parameters
Argumenta Oeconomica Cracoviensia, 2020, no 1(22), s. 21-29, tab., rys., bibliogr. 12 poz.
Statystyka matematyczna, Statystyka w naukach społecznych, Metody statystyczne
Mathematical statistics, Statistics in the social sciences, Statistical methods
JEL Classification: C99, C12, C15.
summ., streszcz.
Objective: The methods of experimental design were first used in agricultural experiments performed by R. A. Fisher. The development of experimental design methods took place along with their effective use in production companies. The most frequently used designs of experiments are the factorial designs. One of the stages in the factorial design of experiments is the estimation of the response surface function formula which describes the influence of factors on the response variable values. The aim of this article is to propose a method to indicate the factors which have a significant influence on the response variable.

Research Design & Methods: In this case, in the classical approach, the t-test of the significance of particular parameters of the response surface function is used. The t-test requires fulfilment of the assumptions about the distribution and independence of the model errors. If the assumptions are not fulfilled, or the sample size is not sufficient, the use of the t-test is unjustified. An alternative approach to verify the significance of response surface parameters is a permutation test. Permutation tests use simulation methods and do not entail the fulfilment of strict assumptions relating to the distribution of errors and the sample size of experimental data.

Findings: The paper deals with the use of a permutation test that allows us to assess the significance of response surface function parameters when the quantity of experimental data is small. These results were obtained using parametric tests and permutation tests.

Implications/Recommendations: Based on the performed calculations, it was found that it is possible to use permutation tests to analyse the response surface function, especially when the assumptions about the residuals of the model are not fulfilled or the number of considered experimental trials is small.

Contribution: A proper analysis of the response surface function is an important stage in the design of experiments. In the case of a small quantity of experimental data, assessment of the significance of the model and the parameters of the response surface function using parametric tests may lead to incorrect conclusions. Therefore, the use of permutation tests was indicated as an alternative approach in the analysis of the response surface function. (original abstract)
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