• Journal of the Korean Data and Information Science Society
• /
• v.19 no.4
• /
• pp.1059-1071
• /
• 2008

In a balanced factorial design with a nested factor where crossed factors as well as a nested factor exist simultaneously, powers of the rank transformed FR statistic for testing the main, nested and interaction effects are superior to those of the parametric F statistic. In heavy tailed distributions such as exponential and double exponential distributions, powers of the FR statistic show much higher level than those of the F statistic. Further powers of the F and FR statistic for testing the main effect show the highest level in an absolute size as compared with powers of the F and FR statistic for testing the nested and interaction effects. However powers of the FR statistic for testing the nested and interaction effects rather than the main effect are greater in a relative size than powers of F statistic for the all population distributions.

• Journal of the Korean Data and Information Science Society
• /
• v.20 no.2
• /
• pp.401-410
• /
• 2009

Due to the characteristics of 3 ${\times}$ 3 Latin square design which is composed of two block effects and one main effect, powers of rank transformed statistic for testing the main effect are very superior to powers of parametric statistic without regard to the type of population distributions. By order of when all three effects are fixed, when on one block effect is random, when two block effects are random, the rank transform statistic for testing the main effect shows relatively high powers as compared with the parametric statistic. Further when the size of main effect is big with one equivalent size of block effect and the other small size of block effect, powers of rank transformed statistic for testing the main effect demonstrate excellent advantage to powers of parametric statistic.