The adjustments are:


 Adjustment
 Mean to 35 Adjusted
 Yield Density plants/plot Yield


 1.85 27.5 + 7.5 x 0.0425 2.17
 2.025 35 Nil 2.02
 2.375 25.5 + 9.5 x 0.0425 2.78
 2.6 36.5 1.5 x 0.0425 2.52


 It may be decided to adjust yields to some value other than 35, for example, to average achieved plot
 density. The principles and treatment differences are unchanged and the level of the covariate (density) to
 which the yields are adjusted should be chosen subjectively to obtain the most relevantly representative
 yields (to adjust to a target of 40 plants/plot would result in over-optimistic yields).

 The linearity assumption required for covariance analysis may be improved if I/density is used as the
 covariate. Whichever gives the greater Sums of Squares for the covariance term in the analysis may be
 used.

 If covariance adjustment is used at several sites, the adjustment rates = covariance coefficient may be
 different at different sites. This may be due to random variation or to real differences in yield-density
 curves. Unless there are compelling reasons for believing that the covariance coefficients should be the
 same there is no reason against using different adjustments at different sites.

 If there is no obvious covariate, it is still possible to make adjustments for any observed and quantifiable
 concomitant information. Thus, for example, if the end plot of each block give a unusually low yields a
 covariate taking the value zero for end plots and one for other plots can be used adjusting yields to a
 covariate value of one.

 The decision whether or not to use covariance adjustment of treatment mean yields is, ultimately, a
 subjective one. It should certainly involve looking at the plots of the data (as in Fig. 1). The effectiveness
 of covariance adjustment will vary, but there will usually be some benefit in accuracy or precision if the
 data plot suggests a relationship. Covariance adjustment remains valid if the covariate is apparently
 dependent on treatments. The adjusted values then represent what would have been expected if a uniform
 value of the covariate had occurred and this can sometimes provide valuable information (in parallel with
 the treatment means of the covariate and of the unadjusted mean yields).

 The basis for discarding values completely is more difficult and should normally be on the basis of the
 researcher's knowledge of unusual circumstances rendering a plot unrepresentative. In cases of real doubt
 it is legitimate to calculate analyses with and without the dubious data.

 When the discard possibility refers to a whole site the situation is rather different. It is not usually
 appropriate to consider adjusting site results to a common level because one of the purpose of using
 multiple sites is to examine behavior of treatments over varying sites. It is much more appropriate then to
 consider the set of treatment effects and relate them to possible causative variables measures at each site.
 Essentially rather than discarding "unrepresentative" sites we should seek to separate them from the rest
 and analyze them in parallel with the main data.

 Finally, various rules have been advocated for discarding sites based on CV, overall mean, check treatment
performance, or % Error SS of Total SS. Counter examples demonstrating the inappropriateness of any of