# Examples

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```					                              Anova Examples
1. A study of depression and exercise was conducted. Three groups were used: those in a designed exercise
program; a group that is sedentary; and a group of runners. A depression rating was given to members in each
group. Small random samples from each groups provided the following data:

Exercise Group: 63 58 61 60 62                       SST = 56.00, SSE = 140.00
Sedentary Group: 71 64 68 65 67 67
Runners:         49 52 47 51 48

Fill in the ANOVA table.

SOURCE           DF          SS          MS          F
Treatment
Error
Total

2. Four different leadership styles (A, B, C, and D) used by Big-Six accountants were investigated. As
part of a designed study, 15 accountants were randomly selected from each of the four leadership style
groups. Each accountant was asked to rate the degree to which their subordinates performed substandard
field work on a 10-point scale -- called the "substandard work scale". The objective is to compare the
mean substandard work scales of the four leadership styles. The data on substandard work scales for all 60
observations were subjected to an analysis of variance.

ONE-WAY ANOVA FOR SUBSTAND BY STYLE

SOURCE           DF         SS            MS          F          P-value
Treatment        3          2220          740         5,21       0.003
Error          56         7954          142
Total          59         10,174

3. An industrial psychologist is investigating the effects of work environment on employee attitudes. A
group of 20 recently hired sales trainees were randomly assigned to one of four different "home rooms" -
five trainees per room. Each room is identical except for wall color. The four colors used were light green,
light blue, gray and red. The psychologist wants to know whether room color has an effect on attitude,
and, if so, wants to compare the mean attitudes of the trainees assigned to the four room colors. At the end
of the training program, the attitude of each trainee was measured on a 60-pt. scale (the lower the score,
the poorer the attitude). The data was subjected to a one-way analysis of variance.

ONE-WAY ANOVA FOR ATTITUDE BY COLOR

SOURCE           DF          SS          MS          F           P-value
Treatment                                560                     0.000
Error                      160
Total
4. 150 students are randomly assigned to three classes, 50 students per class. The same instructor is
used for all 3 classes, but a different text is used in each one. All students take the same test at the
end of the course. Do the scores differ significantly across classes? (The treatment is textbook.)

5. A certain strain of corn is grown at 10 different locations. Four different fertilizers are used to
determine which results in the largest yield of corn. (The treatment is fertilizer.)

6. Three different companies produce a particular type of electrical component. Random samples of
components are selected from the output of each company. Components are put into service until
they die. Does average lifetime differ from one company to another? (Populations are companies.)

7. In a study of automobile traffic and air pollution, air samples taken at four different times and at five
different locations were analyzed to obtain the amount of particulate matter present in the air. Is there any
difference in true average amount of particulate matter present in the air due either to different sampling
times or to different locations?

8. We wanted to see how studying method affected grades on a World Civilizations midterm for
underclassmen and upperclassmen. Regardless of prior study preference, equal amounts of students were
assigned randomly to one of the two categories. This is a two way ANOVA with two independent
variables: Year in school (underclass versus upperclass) and Study type (along versus group). The
dependent variable is grades (measured on a scale of 0 to 100)

Type of studying
Alone       In a group Row Means
Underclassmen        85          88         86.5
Upperclassmen        90          86         88
Column means         87.5        87
9. A local consumer reporter wants to compare the average costs of grocery items purchased at three
different supermarkets, A, B, and C. Prices (in dollars) were recorded for a sample of 60 randomly
selected grocery items at each of the three supermarkets. In order to reduce item-to-item variation, the
prices were recorded for each item on the same day at each supermarket.

Item            A     B      C
1) paper towels          1.23 1.42 1.28
2) cereal                2.85 3.02 3.09
3) floor cleaner         6.01 5.89 6.07
--------- -------- ---           --    ---
59) shaving cream        0.99 0.89 0.95
60) canned green beans 0.43 0.52 0.35
The results of the ANOVA are summarized in the following table.

SOURCE           DF           SS            MS      F             P-value
Treatment        2            2.64          1.32    39.23         0.0001
Block          59           215.64        3.65    108.24        0.0001
Error          118          3.97          0.03
Total          179          222.25

What is the value of the test statistic for determining whether the three supermarkets have the same
average prices?

Identify the treatments for this experiment.

Identify the dependent (response) variable for this experiment.

Identify the blocks for this experiment.

Based on the p-value of the test, make the proper conclusion.

The results of a Bonferroni analysis are summarized below.

Supermarket                  A               B        C
___________
Mean Price                   1.67            1.93   1.95

Interpret the Bonferroni analysis results.

Describe the experiment, including the response variable, factors, and levels.

Is there evidence to indicate a difference in the mean prices of the three supermarkets? Test using  =
.01.
10. The lateral drift of a newly constructed skyscraper can be estimated with sophisticated computer
software. The goal is to compare the mean drift estimates made by three different computer programs (A,
B, and C). Recognizing that lateral drift will depend on building level (floor), the drift (in inches) at each
of five levels (Floors 1, 30, 70, 120, and 200) was estimated by each of the three programs:

Program
Level               A       B        C
Floor   1                    1.23    1.42     1.28
Floor   30                   2.85    3.02     3.09
Floor   70                   6.01    5.89      6.07
Floor   120                  8.07    7.96      8.10
Floor   200                  9.99    9.89      9.95

Explain how to properly analyze this data.

11. Suppose a company makes 3 different frozen dinners, and tests their ability to attract customers. They
test the frozen dinners in 11 different stores in order to account for any extraneous sources of variation.
The company records the number of customers who purchase each product at each store. What
assumptions are necessary for the validity of the F statistic for comparing the response means of the 3
frozen dinners?

12. A market research firm is interested in the possible success of new flavors of ice cream. A study was
conducted with three different flavors-- peach, almond, and coconut. Three participants were given a
sample of each ice cream, in random order, and asked to rate the flavors on a 100-point scale.

13. A certain HMO is attempting to show the benefits of managed health care to an insurance company.
The HMO believes that certain types of doctors are more cost-effective than others. One theory is that
both Primary Specialty and whether the physician is a foreign or USA medical school graduate are an
important factors in measuring the cost-effectiveness of physicians. To investigate this, the president
obtained independent random samples of 40 HMO physicians, half foreign graduates and half USA
graduates, from each of four primary specialties-- General Practice (GP), Internal Medicine (IM),
Pediatrics (PED), and Family Physician (FP)-- and recorded the total per-member, per-month charges for
each. Thus, information on charges were obtained for a total of n = 160 doctors. The sample mean charges
for each of the eight categories are shown in the table.

What type of design was used for this experiment?

4 x 2 factorial design with 20 replications

completely randomized design with eight treatments

completely randomized design with two treatments

2 x 2 factorial design with 160 replications

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 views: 24 posted: 8/17/2011 language: English pages: 5