- Use the data in Problem 4.3, pp. 157. Answer all parts of questions.
- Analyze this as a randomized block design. Provide the ANOVA table. Interpret the results of the main test of interest, using alpha=0.05.
- Assess model assumptions.
- Run and interpret the results of a Tukey multiple comparison Post Hoc analysis on the main effect. Based on the results of the main test, is it necessary?
- Provide an estimate of the error standard deviation σ. Provide estimates for the treatment effects (the τ’s, must sum to zero.).
- Suppose this was actually a pilot study. Using the estimates in part d) in your calculation of the power, decide how many bolts (number of blocks) the chemist would need in a larger study, if she desired a power of at least .95 when using alpha=0.05. Show necessary work are:
- Reaction time (milliseconds) to three types of stimuli (auditory, tactile, and visual) was measured in a small study with 5 age groups and 3 subjects within each group. The age groups (blocks), stimulus types (treatments), and corresponding reaction times in () are:
20-29 Tactile (615) Auditory (490) Tactile (600) 30-39 Auditory (465) Visual (375) Auditory (520) 40-49 Tactile (685) Tactile (605) Visual (500) 50-59 Visual (520) Tactile (760) Auditory (605) 60-69 Auditory (690) Visual (510) Visual (545)
- Is this a randomized complete block (RCB) design? Why or why not?
- Find the values of the three stimulus type sample means.
- Find the values of the Least Square estimated marginal means of the three stimulus types.
- Compare the two sets of answers for part b) and c). State any difference. Which set of estimators is unbiased, part b) or part c)? Explain why the differences exist (be specific to this data set!).
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