PROBLEM 22

PRACTICING ANALYSIS OF VARIANCE

For this problem, solve the following two problems from Mendenhall, Scheaffer, and Wackerly present on pages 635 and 636 (13.66 and 13.67):. The first problem involves a one way ANOVA with unbalanced design and the second problem is a two way ANOVA (randomized block) with balanced design.

(1) A completely randomized design was conducted to compare the effect of five stimuli on reaction time. Twenty-seven people were employed in the experiment, which was conducted using a completely randomized design. Regardless of the results of the analysis of variance, it is desired to compare stimuli A and D. The reaction times (in seconds) were as shown in the table.

STIMULUS

A B C D E

.8 .7 1.2 1.0 .6

.6 .8 1.0 .9 .4

.6 .5 .9 .9 .4

.5 .5 1.2 1.1 .7

.6 1.3 .7 .3

.9 .8

.7

total 2.5 4.7 6.4 4.6 2.4

mean .625 .671 1.067 .920 .48

(a) Conduct an analysis of variance and test for a difference in mean reaction time due to the five stimuli. Give bounds for the p-value.

(b) Compare stimuli A and D to see if there is a difference in mean reaction time. What can be said about the attained significance level?

(2) The previous experiment might have been conducted more effectively by using a randomized block design with people as blocks, because we would expect mean reaction time to vary from one person to another. Hence, four people were used in a new experiment, and each person was subjected to each of the five stimuli in a random order. The reaction times (in seconds) were as shown in the accompanying table. Conduct an analysis of variance and test for differences in treatments (stimuli)

STIMULUS

Subject A B C D E

1 .7 .8 1.0 1.0 .5

2 .6 .6 1.1 1.0 .6

3 .9 1.0 1.2 1.1 .6

4 .6 .8 .9 1.0 .4

In addition to solving this problem, is there sufficient evidence to indicate that blocking was desirable? Why or why not?