A Note on Pooling Variances

Genotype×environment interactions in selected loblolly and slash pine plantations in the Southeastern United States

“…Blocks were nested within locations, while the factors of silviculture (C), planting density (D), and genotype (F) were crossed. All terms containing b(s) ij were considered to be random effects in the model and were pooled as appropriate for each variable tested using the procedure described by Bancroft and Han (1983). The only exception was b(s)CD ijkl , which was never pooled as it is used as the error term to test the main effects of S i , C k and D l .…”

Estimation of variance in bivariate normal distribution after the preliminary test of homogeneity

“…The behavior of RE of pooling two variances is similar when the samples are correlated or not, as mentioned by Bancroft and Han (1983), if the significance level of the preliminary test is carefully selected, the preliminary test estimator can be used when the experimenter is uncertain whether the variances are equal and the sample size is not big. …”

“…As mentioned by Bancroft and Han (1983), we need to find an appropriate level such that the relative efficiency of to should be high.…”

“…The relative efficiency and significance level of the preliminary test estimator was studied by Bancroft andHan (1983) andToyota andWallace (1975).…”

“…When the test is not significant the samples are pooled to obtain a pooled estimator, otherwise the individual sample variance is used. When the variables are independent Bancroft (1944) studied the estimation for the variance after a preliminary test, additional discussion are given by Bancroft and Han (1983) and Toyoda and Wallace (1975). We will consider the correlated case.…”