STATISTICS 402 - Assignment 7
Due March 27, 2009
The activities in this homework involve four treatments; A, B, C, and D and five blocks;
white, blue, green, yellow and pink. The treatments could be food additives, the blocks
litters of mice, and the response amount of weight gained. Alternatively, the treatments
could be a combination of starting technique (without starting blocks, with starting
blocks) and shoes (no spikes, spikes) with the response the time to run 400-meters, the
blocks would be different individual runners.
Activity 1: The first activity consists of two different randomizations, complete
randomization and restricted randomization (blocking) and their subsequent analyses.
a) Complete Randomization
• Shuffle all 20 squares so that they are well mixed.
• Deal out 5 squares and record the values for Treatment A in the table below.
• Deal out 5 squares from the remaining 15 and record the values for Treatment B.
• Deal out 5 squares from the remaining 10 and record the values for Treatment C.
• There should be 5 squares remaining, record the values for Treatment D.
Treatment
A B C D
b) Analysis of CRD
• Compute treatment means and construct an Analysis of Variance table.
• Report the value of the F-test and P-value for comparing treatments. What do
these tell you about the differences between the various treatments?
• Note particularly the value for the mean square error.
• If the F-test indicates that there are some statistically significant differences
follow up with an appropriate multiple comparison procedure. That is, compute a
value for the adjusted Least Significant Difference (Bonferroni), or Kramer-
Tukey HSD, and use it to determine which of the treatment means differ
significantly.
• Look at plots of residuals versus treatments and the distribution of residuals.
What do these plots tell you about the conditions necessary for the analysis
above?
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