• Journal of the Korean Data and Information Science Society
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• v.22 no.2
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• pp.245-253
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• 2011

Powers of rank transformed statistic for testing main effects and interaction effects for $2{\times}2$ factorial design in randomized complete block design are very superior to powers of parametric statistic without regard to the block size, composition method of effects and the type of population distributions such as exponential, double exponential, normal and uniform. $2{\times}2$ factorial design in RCBD increases error effects and decreases powers of parametric statistic which results in conservativeness. However powers of rank transformed statistic maintain relative preference. In general powers of rank transformed statistic show relative preference over those of parametric statistic with small block size and big effect size.

• Journal of the Korean Data and Information Science Society
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• v.25 no.6
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• pp.1195-1205
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• 2014

Compared with single design, powers of rank transformed statistic for testing main and interaction effects for $2{\times}2$ factorial in $4{\times}4$ latin square design are rapidly increased as effect size and replication size are increased. In general powers of rank transformed statistic are superior without regard to the diversified effect composition and the type of error distributions as nontesting factors are few and effect size are small. Powers of rank transformed statistic show much higher level than those of parametric statistic in exponential and double exponential distributions. Further powers of rank transformed statistic are very similar with those of parametric statistic in normal and uniform distributions.