STATISTICS 402 - Assignment 6
Due April 2, 2010
1. For each of the following problem statements, identify the response, conditions and
experimental material. Indicate the design (completely randomized, randomized
complete block, Latin square) that is used to collect the data and indicate if factorial
crossing is used. Construct a partial ANOVA table by identifying all sources of
variability and associated degrees of freedom.
a. Industrial psychologists wish to investigate the effect of music in the factory on
the productivity of workers. Four distinct music programs (Country, Soft Rock,
Hard Rock, and Classical) and no music (a control) make up the five treatments.
In order to account for variability from day to day and week to week, a different
program is used on each day (M, T, W, Th, and F). The programs are rotated
from week to week, so that over 5 randomly chosen weeks, each program appears
once on any specific working day of the week.
b. An experiment is conducted to see the effect of fishing rod length and sinker
weight on the length of the cast. There are three fishing rod lengths: 6 feet, 6.5
feet and 7 feet. There are four sinker weights: 2 ounces, 3 ounces, 4 ounces, and
5 ounces. Three casts with each of the twelve combinations of fishing rod length
and sinker weight will be made and the order of the casts will be randomized.
c. A sports physiologist is conducting an experiment on eye focus time. She is
interested in the distance of the object from the eye on the focus time. Four
different distances are of interest. She chooses 10 players at random from a
college softball team. Each player will have her focus time measured at each of
the four distances. The order of the distances will be randomized for each player.
d. An experiment is performed to see whether different operators obtain different
results in the routine analysis to determine the amount of nitrogen in soil. 50 soil
samples are chosen at random and divided at random into 5 groups of 10. Each
operator is assigned a group of 10 soil samples at random and asked to determine
the amount of nitrogen in each sample.
2. Standing from a seated position generates stress on the knee joint. The purpose of the
experiment is to discover which method of standing generates the least amount of
torque (in Newton meters, Nm) on the knees. This is especially important in older
individuals who have had knees replaced (Total Knee Arthroplasty, TKA). The
experiment is done with older males. All participants have had TKA. The height of
the chair will be the same for all trials. All participants will be wearing comfortable
clothes and tennis shoes. Each participant will experience all of the conditions. The
order will be randomly assigned for each participant. There are 15 participants. The
data appear on the next page.
a. What are the Response, Conditions and the Experimental material?
b. Give three outside variables that are controlled in the experiment?
c. Why is this block design? How are blocks made?
1
Subject
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Neutral
26.3
22.7
21.1
25.9
25.6
22.5
26.1
21.4
17.4
22.8
23.0
18.4
29.6
27.4
31.3
Position of Feet
Back
23.0
19.7
20.0
23.3
21.1
19.9
23.4
18.8
17.7
21.9
22.2
17.3
25.5
23.2
28.5
Staggered
21.3
19.8
19.5
22.4
18.5
19.6
22.5
19.0
16.6
20.0
22.1
18.6
21.8
22.3
26.5
d. Compute the sample means for the three positions for the feet and an overall
grand sample mean.
e. Compute the estimated effect for each position for the feet. Which position(s) for
the feet appear to produce the least amount of torque? Explain briefly.
f. Construct a complete ANOVA table including all appropriate sources of
variation.
g. Are there statistically significant differences among the positions for the feet in
terms of average torque? Report the appropriate F- and P-values and explain why
these support your answer.
h. If there are statistically significant differences among the positions for the feet,
indicate where those differences lie. Give the value of HSD. Clearly state which
of the positions for the feet have statistically significant differences in sample
means and which do not.
i. If one wishes to reduce torque on the knee, what statistically valid
recommendations can you make for the choice of the position for the feet?
Explain your reasoning.
j. Construct appropriate plots of the residuals and comment on whether the equal
standard deviation condition and the normally distributed errors condition are
satisfied.
3. An experiment is designed to determine which of four movies has the greatest appeal.
The four movies are A: Action, B: Science Fiction, C: Comedy and D: Drama. Only
one theater is available for one week for the experiment. The time of day and day of
the week a movie is shown may have an effect on a movie’s appeal. Therefore, we
want to account for time of day and day of week variation in our analysis. Each
movie is shown once on each day of the week (M, Tu, W, and Th) and once at each
time (early matinee, late matinee, early evening, and late evening). Each movie is
shown to 50 volunteers and the number of volunteers who would recommend the
movie to a friend is recorded. A higher number of recommendations would indicate a
greater appeal. The data appear on the next page.
2
early matinee
late matinee
early evening
late evening
Monday
C
32
B
26
D
17
A
37
Tuesday
D
23
A
36
C
38
B
28
Wednesday
B
33
C
31
A
41
D
18
Thursday
A
36
D
22
B
27
C
31
a. What are the Response, Conditions and the Experimental material?
b. Why is this experiment a Latin square design?
c. Compute the sample means for the four movies and an overall grand sample
mean.
d. Compute the estimated effect for the four movies. Which movie appears to
produce highest average appeal? Explain briefly.
e. Construct a complete ANOVA table including all appropriate sources of
variation.
f. Are there statistically significant differences among the movies in terms of
average appeal? Report the appropriate F- and P-values and explain why these
support your answer.
g. If there are statistically significant differences among the movies, indicate where
those differences lie. Give the value of HSD. Clearly state which of the movies
have statistically significant differences in sample means and which do not.
h. What statistically valid recommendations can you make for the appeal of the
movies? Is there a most appealing movie or a least appealing movie? Explain
your reasoning.
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