1. A 25-1 fractional factorial design with defining relation I =
-ABCDE was conducted for factors A, B, C, D, and E, with 2 replicates for each
combination, yielding a sample of 32 observations. For each subpart of the
problem write one or more sentences summarizing your conclusions. The data are linked
here.
a) Select an embedded 24 design and compute the ANOVA table for those
factors.
b) Use the alias structure to draw conclusions about the effects of the five
factors.
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.
2. A researcher wants to create a quarter fraction of a 25
factorial design, with factors A, B, C, D, and E. She wants to use the defining
relation I = -ABD = -BCE.
a) Write down the eight treatment combinations to be used in the design.
b) What is the resolution of the design?
c) Write out the alias structure for all main effects and two-way interactions.
3. To investigate house prices in three areas of the country, researchers
sampled house prices in Atlanta, Indianpolis, and Albuquerque. The data are in
this file, and included the city, house
price (in thousands), and also the square footage of each house. For each
subpart of the problem write one or more sentences summarizing your conclusions.
i) Do an analysis of variance to compare the house prices in the three cities,
ignoring square footage.
ii) Produce a plot of house price with square footage, using symbols or colors
to label the city.
iii) Conduct an analysis of covariance to test for differences in house price by
cities after adjusting for house size.
iv) Calculate the adjusted means of house prices per city. How do these three
adjusted means compare to the unadjusted
means?
v) Test the assumption of parallelism for the ANCOVA. Also discuss whether the
'treatment' may have affected the covariate.
vi) Assess the normality and constant variance assumptions for the ANCOVA model.
vii) How did using the square footage of houses help in testing for differences
between cities?
4. A publishing company has developed a new font that they think readers will like. They
recruit a sample of 40 readers, half male and half female. Each reader is given a selection
of text to read for the new font and two existing fonts. The three fonts are presented in a
random order for each reader, and the reader gives each font a score for readability.
The company is interested in possible differences between fonts, gender differences, or
their interaction.
a) Name this model and write down the model equation.
b) Fill out the 'Source' and 'Degrees of Freedom' columns for the ANOVA table for these data.