Tukey–Kramer tests carried out on the results in Practice Problem 15 yielded the accompanying table of results. Groups refer to the number of genotypes in the corresponding treatment.

a. Fill in the conclusions in the table.

b. Write the sample means of the three treatment groups, from smallest to largest, and use symbols to indicate the groups to which the means belong. Summarize the result in words.

c. Are these planned or unplanned comparisons? Explain.

d. Why not use a series of two-sample t-test s instead of the Tukey–Kramer method?

e. In the preceding analysis, what is the probability of making at least one Type I error during the course of carrying out all of the pairwise tests of differences between means?

Data from problem

In a field experiment designed to investigate the role of genetic diversity in ecosystems, Reusch et al. (2005) planted eelgrass in plots in a shallow estuary in the Baltic Sea. Eighteen eelgrass shoots were planted in every plot. Some plots (randomly chosen) were planted with only one eelgrass genotype, others were planted with three genotypes, and others were planted with six different eelgrass genotypes. At the end of the experiment, the total number of shoots was counted in each plot. The results from 32 plots are given in the following table:

Transcribed Image Text:

Group ii Group jj Yi-YjY₁ - Yj 66 66 33 11 33 11 23.2623.26 12.6012.60 10.6710.67 SE 99 7.137.13 3.263.26 1.691.69 7.457.45 7.137.13 1.501.50 q0.05,K,N-k90.05,k, N-k 2.472.47 2.472.47 2.472.47 Conclusion