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Section STA 7459
Homework 4
Form B
UFID:
Name:
This form is only for students whose UFID number begins with 0, 4, 5, or 9.
Answer all problems neatly. If you turn in more than one piece of paper, they must be stapled. Work
that isnt neat or stapled may lose points. You dont need to turn in this problem listing, but you do need
to include your name, UF-ID number, and form code on your homework.
1. (a) What are the hypotheses for Two-Way ANOVA?
(b) Complete the following ANOVA table. This table is based on data with Factor A having 4 levels,
Factor B having 5 levels, and 3 replications at each combination of factor levels.
Source
Factor A
Factor B
Interaction
Error
Total
df
3
SS
239.94
291.16
MS
160.72
974.44
(c) Test for interaction eects and give an interpretation of this.
(d) When is it appropriate to test for main eects? Is it appropriate to test for main eects with
these data?
(e) Irrespective of your answer above, test for the signicance of:
i. Factor A (and interpret)
ii. Factor B (and interpret)
2. For each of the following situations, identify if it is one/two/three-way ANOVA, if there is blocking,
what any factors and levels are, and what the (quantitative) response is.
(a) Delicious cookies depend on many factors; in this case, amounts of sugar, modied starch, and
salt are being investigated. Suppose a baker wants to see if his customers have preferences among
the dierent batches, assessed by a survey where people assign scores to the cookies. He plans on
trying low, medium, and high amounts for each ingredient.
(b) A manager wants to see if the ve machines a company owns ll helium balloons with dierent
amounts of helium (in liters).
(c) An instructor wants to know if students course grades depend on whether they took the prerequisite at university or community college and if they study more or less than 10 hours per week
for the class.
(d) A company is training new employees and wants to determine if three dierent training methods
dier in eectiveness, assessed by an end-of-course exam. They have recently hired a large number
of employees, so they group the employees by the length of time since they received their last
degree for purposes of the study (each employee one receives training method, but three employees
would make up one group).
(e) A marketing rm wants to see if sales of their clients products dier in various communities.
They randomly select communities from ve geographic regions (northeast, southeast, southwest,
midwest, northwest) and three population sizes (under 200,000 people, between 200,000 and
1,000,000, and over 1,000,000 people).
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3. The following is computer output from R conducting a Two-Way ANOVA test (unrelated to the above
question).
Analysis of Variance Table
Response: Response
Df Sum Sq Mean Sq F value Pr(>F)
Base
1 6.510 6.5104 3.1881 0.09103 .
Alcohol
2 5.396 2.6979 1.3212 0.29149
Base:Alcohol 2 22.566 11.2829 5.5252 0.01346 *
Residuals
18 36.758 2.0421
--Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
(a) What is being tested?
(b) How many levels were there for:
i. Base?
ii. Alcohol?
(c) Are there interaction eects?
(d) Is it appropriate to test for main eects? If so, test to see if Factor A and Factor B are signicant.
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4. When answering this question, please refer to the following data set:
Name
Group
Ranks
Group
Ranks
Group
Ranks
Group
Ranks
A
12
13
21
B
13.5
12.5
11.5
C
22
15
14
D
2
8
3
15.5
14.5
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(a) In what situation would one wish to use the Kruskal-Wallis test?
(b) What are the hypotheses for the Kruskal-Wallis test?
(c) What is the approximate distribution of the KW test statistic and what are its degrees of freedom
for these data?
(d) Rank these data using the method we used in class (smallest is 1).
(e) Calculate the value of the KW test statistic for these data.
(f) Make a conclusion based on the value of KW you calculated and interpret it in terms of the data.
(g) The following is computer output from R conducting a One-Way ANOVA test on the same data.
Does this output support the conclusion you reached above? Should it?
Analysis of Variance Table
Response: Response
Df Sum Sq Mean Sq F value Pr(>F)
Group
3 208.95 69.649 3.8214 0.04249 *
Residuals 11 200.49 18.226
--Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
(h) If we rejected the null hypothesis, what would our next step in analyzing these data be? (You do
not need to actually perform the step.)
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