Journals Information
Universal Journal of Applied Mathematics Vol. 11(1), pp. 1 - 7
DOI: 10.13189/ujam.2023.110101
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Three-way Analysis of Variance for Functional Data
Nuri Celik *
Department of Mathematics, Gebze Technical University, Turkey
ABSTRACT
As the number of observation points examined in studies increases, it is assumed that these points come from an underlying real function. Statistical methods that have been developed for this type of data are called functional data analysis. Therefore, there has been a great interest in adapting some traditional statistical methods into the functional data sets like hypothesis testing, regression or analysis of variance (ANOVA). The analysis of variance (ANOVA) is used for comparing the means of more than three groups. Therefore, if the data comes as a functional data form, the functional ANOVA methodologies must be used to compare the mean function of the groups. In literature, one-way ANOVA and two-way ANOVA methodologies have been developed for functional data set. In this paper, we expand the functional one-way and two-way analysis of variance methodologies to three-way analysis of variance methodology or so-called factorial experimental design. We obtain the parameter estimations of the cell mean function and common variance-covariance function. We also propose sum of squares and test statistics by using these estimations. The test statistics and sum of squares are obtained via pointwise test methodology which has been used for ANOVA for functional data sets. A real data set about the measure of depression levels of health employees of Turkey during the Covid-19 pandemic is conducted for the illustration. The data set is collected between January 2021 and December 2021 for monthly and we have three factors that affect the depression levels of health workers as gender, profession and age. Therefore, in order to test the effects of the treatments, we use the proposed methodology for three-way ANOVA.
KEYWORDS
Functional Data Analysis, Three-way ANOVA, Pointwise Test
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Nuri Celik , "Three-way Analysis of Variance for Functional Data," Universal Journal of Applied Mathematics, Vol. 11, No. 1, pp. 1 - 7, 2023. DOI: 10.13189/ujam.2023.110101.
(b). APA Format:
Nuri Celik (2023). Three-way Analysis of Variance for Functional Data. Universal Journal of Applied Mathematics, 11(1), 1 - 7. DOI: 10.13189/ujam.2023.110101.