6.2 A researcher has done a preliminary study in the form of a CRD with subsam- pling to help him decide on the final design. He wants to compare five (5) treat- ments. In the preliminary study he has used two (2) experimental units for each treatment and two (2) observations per experimental unit. The partial ANOVA for the data from the preliminary study is given below:

and the 5 treatment means are 10.00, 12.30, 11.80, 14.25, 13.56. In the final experiment the researcher wants to compare the same 5 treatments. He wants to use a CRD with or without subsampling. (i) Suppose he wants to detect, with probability .9, approximately the same difference between the best and worst treatment as observed in the study, using a test of size .05. Based on the information available from the pre- liminary study, how many replications does he need for a CRD without subsampling?

(ii) Suppose the testing of hypotheses is not so important. He would like to consider possible CRDS with subsampling that achieve a variance of treat- ment comparisons no larger than the variance for the CRD obtained in (i). Give possible options of designs.

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Source SS Treatments 43.58 Expt. Error 55.00 Sampling Error 30.00