Exercise 8.
The CD-ROM provided in the back of the Munro text contains an SPSS data file
called book5.sav. It contains a variable named "confid" which is a measure of
confidence and one of two subscales of the Inventory of Personal Attitudes
(IPA). It also contains a variable named "work" which indicates the current
work status as being either unemployed, full-time, or part-time and a
variable called "gender" indicating whether subjects are male or female.
Using these three variables, assess whether mean confidence varies with
current work status and/or gender.
1. Describe the population using a multivariate formulation. What are the
conditional random variables for this multivariate population? What are their
expected values and variances? How many associated cells are there? What are
the cell means and variances? Which of these are the primary parameters? What
is the primary hypothesis test in terms of these primary parameters that
needs to be conducted? What is commonly assumed for this test about the other
parameters? How can one assess whether these other parameters are reasonably
considered to satisfy this assumption or not? If they are not reasonably
considered to satisfy this assumption, how could one conduct the primary
hypothesis test? If one rejects the null hypothesis of the primary hypothesis
test, how can one further investigate the alternate hypothesis? How would
this further investigation be affected by conclusions about the other
parameters? If the overall sample size is not large, what other assumption is
necessary for all these hypothesis tests to be reliable? How can one assess
whether this assumption is reasonable or not? If this assumption is not
reasonable, how could one assess the basic question addressed by the primary
hypothesis test? Even if sample sizes are large for all levels of all
factors, what other properties are desirable for the population groups
corresponding to the levels of each factor to have in order for the results
from the primary hypothesis test to be reliable? If it is not reasonable to
consider the population groups for all factors to have these properties, what
could one consider doing to resolve this problem?
2. Formulate the full factorial model in terms of population main and
interaction effects. Express the hypotheses of the primary hypothesis test in
terms of these effects. What supplementary hypothesis tests can be conducted
for these effects?
3. Describe the sample using a multivariate formulation. What statistic is
used to conduct the primary hypothesis test? How is this statistic computed
for a full factorial model in the general case under the common assumption
about the other parameters? What are the associated values for the degrees of
freedom for this statistic in the general case? What statistics are used to
conduct the supplementary tests? How are these statistics computed in the
general case under the common assumption about the other parameters? What are
the associated values for the degrees of freedom for these statistics in the
general case?
4. Generate output required to conduct the associated analysis of the
"confid", "work", and "gender" variables using the full factorial model. Copy
the output into a Word file, and describe the generated results. How many
cases have missing values for any of these three variables? Analyze the nonmissing data cases using the process described on p. 27 of the Topic 6
lecture notes. Conduct only those parts of the analysis needed to assess the
underlying assumptions and those parts for which associated assumptions are
reasonably considered to hold. If the outcome variable requires
transformation, consider for simplicity only the square root and square
transforms and analyze the better of those 2 transformed outcome variables
whether or not it is appropriate to do so. Present hypotheses, results of
testing those hypotheses, and a final summary of the conclusions in terms of
the underlying problem.
5. Formulate the associated additive model. Express the hypotheses of the
primary hypothesis test in terms of the effects of this model. What
supplementary hypothesis tests can be conducted for these effects? What
statistic is used to conduct the primary hypothesis test? How is this
statistic computed for the additive model in the general case under the
common assumption about the other parameters? What are the associated values
for the degrees of freedom for this statistic in the general case? What
statistics are used to conduct the supplementary tests? How are these
statistics computed in the general case under the common assumption about the
other parameters? What are the associated values for the degrees of freedom
for these statistics in the general case?
6. Generate output required to conduct the associated analysis of the
"confid", "work", and "gender" variables using the additive model. Copy the
output into a Word file, and describe the generated results. Analyze the nonmissing data cases using the process described on p. 27 of the Topic 6
lecture notes. It is not necessary to duplicate parts of this analysis
conducted as part of Question 4, but indicate what those results were.
Conduct only those parts of the analysis needed to assess the underlying
assumptions and those parts for which associated assumptions are reasonably
considered to hold. Present hypotheses, results of testing those hypotheses,
and a final summary of the conclusions in terms of the underlying problem.
7. Complete the exercises on pages 17 and 26 of the Topic 6 lecture notes.
Submit completed copies of these pages in class on the due date.