A replicated corn yield trial (25 entries in 3 blocks) grown at five locations gave data in which the response variable (yield) varied from 55 bu/acre in a particularly dry location to 190 bu/acre in...

A replicated corn yield trial (25 entries in 3 blocks) grown at five locations gave data in which the response variable (yield) varied from 55 bu/acre in a particularly dry location to 190 bu/acre in the most favorable environment. The mean yields and the experimental error variances (each with 48 degrees of freedom) for the five locations were as follows.

Consider these options for handling the heterogeneous variances in a combined analysis of variance: (1) an appropriate transformation on Y and (2) weighted least squares.

(a) What transformation would you suggest from inspection of the relationship between the mean and the variance?

(b) Explain what your weighting matrix would be if you used weighted least squares. This will be a very large matrix. Explain how you could do the weighting without forming this matrix.

(c) A third option would be to ignore the heterogeneous variances and proceed with the combined analysis. Discuss the merits of the three alternatives and how you would decide which to use.