If only fixed effects exist in a 4 $ imes$ 4 balanced incomplete block design, powers of FR statistic for testing a main effect show the highest level with a few replications. Under the exponential and double exponential distributions, FR statistic shows relatively high powers with big differences as compared with the F statistic. Further in a traditional balanced incomplete block design, powers of FR statistic having a fixed main effect and a random block effect show superior preference for all situations without regard to the effect size of a main effect, the parameter size and the type of population distributions of a block effect. Powers of FR statistic increase in a high speed as replications increase. Overall power preference of FR statistic for testing a main effect is caused by unique characteristic of a balanced incomplete block design having one main and block effect with missing observations, which sensitively responds to small increase of main effect and sample size.