1. A 23-1 confounded block design was conducted at a company
recently. Due to the proprietary nature of the data, generic labels like 'blk'
for block and 'a' 'b' and 'c' are used for factor names. For each subpart
of the problem write one or more sentences summarizing your conclusions, the
data are linked here.
a) Test for all main effects and interactions, produce an ANOVA table as well.
b) Create at least one profile plot. If any interactions occur, use the plot and/or printouts of means to
help understand the interaction.
c) Assess model assumptions (normality and constant variance) by inspecting
residual plots.
d) Give an overall summary that can be understood by a non-statistician.
e) Explain, in your own words, why we cannot test for a three-way interaction between factors A, B, and C.
2. A restaurant owner wants to study combinations of toppings on pizza that are
favored by customers. She is considering using anchovies (A), bacon (B), chicken
(C), and pineapple (P). She decides that taste testers can only try four
combinations, so she wants to use a confounded block design to take a
quarter-fraction of a 24 design (a 24-2 confounded block
design). Six people will
try each combination for a total of 24 subjects.
a) If she wishes to take a quarter fraction of the 16 combinations, she will need two defining contrasts. Should one of the defining contrasts be the four-way interaction? Briefly explain.
b) Suppose she decides to obtain the quarter fraction by confounding both the bacon*chicken*pineapple and anchovies*bacon*pineapple interactions. What other effect will also be confounded?
c) List the combinations that go into the four blocks when confounding by bacon*chicken*pineapple and anchovies*bacon*pineapple.
d) Write out the ANOVA table for this design, with every row (including 'Total') and just the Source and Degrees of Freedom columns.
3. Some researchers are studying the the value of professional sports teams from
three groups. They have collected the assessed value of three (US) football
teams, three European soccer teams, and three basketball teams. They want to
study the possible effects of the type of sport, the effect of time, and the
potential interaction between the two factors. The data are listed below. A copy
of the data in univariate format is here. For each of the following questions,
use one or more sentences to explain your results:
a) Name the design and write the model equation.
b) Test for the interaction of sports type and year, and for both main effects, using
split-plot methods.
c) Produce an interaction plot for sports type and year.
d) Conduct Mauchly's test of sphericity.
e) Reanalyze the data using the GG adjustment.
f) Assess the model assumptions of normality and constant variance by inspecting
residual plots.
g) Give an overall summary that can be understood by a non-statistician.
Data (Revenue for the past five years for nine teams) Team Sport Rev2018 Rev2017 Rev2016 Rev2015 Rev2014 Cowboys USFootball 4.2 4.2 4 3.2 2.3 Patriots USFootball 3.7 3.4 3.2 2.6 1.8 Giants USFootball 3.3 3.1 2.8 2.1 1.55 ManchesterUnited EuroSoccer 4.123 3.69 3.32 3.1 2.81 RealMadrid EuroSoccer 4.088 3.58 3.65 3.26 3.44 FCBarcelona EuroSoccer 4.064 3.64 3.55 3.16 3.2 Knicks USBasketball 3.6 3.3 3 2.5 1.4 Lakers USBasketball 3.3 3 2.7 2.6 1.35 Warriors USBasketball 3.1 2.6 1.9 1.3 0.75