Robustness of randomisation tests as alternative analysis methods for repeated measures design
Randomisation tests (R-tests) are regularly proposed as an alternative method of hypothesis testing when assumptions of classical statistical methods are violated in data analysis. In this paper, the robustness in terms of the type-I-error and the power of the R-test were evaluated and compared with...
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Veröffentlicht in: | Statistics in Transition New Series 2022-12, Vol.23 (4), p.77-90 |
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Zusammenfassung: | Randomisation tests (R-tests) are regularly proposed as an alternative method of hypothesis
testing when assumptions of classical statistical methods are violated in data analysis. In this
paper, the robustness in terms of the type-I-error and the power of the R-test were evaluated
and compared with that of the F-test in the analysis of a single factor repeated measures
design. The study took into account normal and non-normal data (skewed: exponential,
lognormal, Chi-squared, and Weibull distributions), the presence and lack of outliers, and
a situation in which the sphericity assumption was met or not under varied sample sizes and
number of treatments. The Monte Carlo approach was used in the simulation study.
The results showed that when the data were normal, the R-test was approximately as
sensitive and robust as the F-test, while being more sensitive than the F-test when data had
skewed distributions. The R-test was more sensitive and robust than the F-test in the
presence of an outlier. When the sphericity assumption was met, both the R-test and the
F-test were approximately equally sensitive, whereas the R-test was more sensitive and
robust than the F-test when the sphericity assumption was not met. |
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ISSN: | 1234-7655 2450-0291 2450-0291 |
DOI: | 10.2478/stattrans-2022-0043 |