Y,. over the I

Hence the sample mean for the jth strength is the average of Y,. over the I batches:

+ = 2, Yy • (5.5.5)

Since batches are independent of one another, 171;., • • • , Pi, are i.i.d. normal with mean + S.; and variance Qf; as given in (5.5.4). Hence the variance of

is given by

var(Y; ) = _1 _1 cr,s + 0-;,) I K

An unbiased estimator of the variance of Y. can be obtained by substituting o-2,s, and o-2, with their ANOVA estimates given in (5.5.3), which is

cr var (Y;.) = 1 MSE + — [MS(BS)

+ JK

[MSB — MS(BS)]}

[,/ — 1 MS(BS) + MSB].