1. Scientists at a large food manufacturing company are excited about the new
candy bar they are creating. It has a shortbread cookie dipped in a chocolate
coating. They are considering three alterations to the candy bar. They are
considering using either milk chocolate (a=0) or dark chocolate (a=1), whether
they should use caramel (b=1) or not (b=0), and whether to use peanuts (c=1), or
not (c=0). They recruited 18 volunteer subjects, and the first six where
randomly assigned to one of the two halves of a 23-1 confounded block design. The next six
were randomly assigned to one of the two halves of a 23-1 confounded block
design using a different confounded effect, and the final six were randomly
assigned to one of the two halves of a 23-1 confounded block design
using a third different confounded effect. The subjects tasted their four
assigned combinations in a random order, and gave a taste score relative to
their favorite candy bar. 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) Name the effects used to confound each of the three sets of six subjects.
2. Any reasonable salad should have at least a choice of lettuce, spinach or a
mixture of both, tomatoes, and a choice of dressing. A restaurant owner wants to
investigate 5 other potential toppings: artichoke hearts (A), black olives (B),
capers (C), dried cranberries (D), and hard boiled eggs (E). Although getting
taste testers to try several samples is important, no one can eat all possible
32 samples.
a) Use the artichoke,caper,egg and blackolive,driedcranberry,egg interactions to
create 4 different blocks of eight samples each. List which combinations go in
each block.
b) What other interaction will also be confounded with these blocks?
c) Assuming that 16 people are recruited into the taste study, with four going
to each block, 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 effect of learning about health impacts of
sugary soft drinks on the likelihood that a person will drink these soft drinks.
Researchers randomly chose 12 subjects, 3 from each of four age groups, from a
list of people volunteering for the study. All participants had their own cell
phone. At the start of each week, subjects were asked for the probability that
they would drink at least three sugary soft drinks in the coming week. Each week
during the study, several text messages were sent to participant's phones citing
scientific evidence of the health consequences of drinking too many sugary
drinks. The data are listed below. 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 age group and week, and for both main effects, using
methods from Chapter 14.
c) Produce an interaction plot for age group and week.
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 (consumption is a probability estimate as explained above) agegroup rep week consumption adol 1 1 0.83 adol 1 2 0.79 adol 1 3 0.80 adol 1 4 0.78 adol 1 5 0.73 children 1 1 0.78 children 1 2 0.76 children 1 3 0.76 children 1 4 0.68 children 1 5 0.67 yadults 1 1 0.81 yadults 1 2 0.82 yadults 1 3 0.78 yadults 1 4 0.83 yadults 1 5 0.85 adults 1 1 0.45 adults 1 2 0.46 adults 1 3 0.45 adults 1 4 0.44 adults 1 5 0.51 adol 2 1 0.87 adol 2 2 0.80 adol 2 3 0.76 adol 2 4 0.75 adol 2 5 0.71 children 2 1 0.75 children 2 2 0.67 children 2 3 0.70 children 2 4 0.67 children 2 5 0.61 yadults 2 1 0.82 yadults 2 2 0.86 yadults 2 3 0.78 yadults 2 4 0.79 yadults 2 5 0.75 adults 2 1 0.55 adults 2 2 0.58 adults 2 3 0.65 adults 2 4 0.59 adults 2 5 0.47 adol 3 1 0.88 adol 3 2 0.86 adol 3 3 0.79 adol 3 4 0.80 adol 3 5 0.76 children 3 1 0.71 children 3 2 0.69 children 3 3 0.68 children 3 4 0.60 children 3 5 0.60 yadults 3 1 0.77 yadults 3 2 0.75 yadults 3 3 0.73 yadults 3 4 0.70 yadults 3 5 0.77 adults 3 1 0.51 adults 3 2 0.48 adults 3 3 0.42 adults 3 4 0.35 adults 3 5 0.33