Stat404
Fall 2009
Lab 12
1. Add the following two parts to the first question in
lab 11:
f. Calculate 'W' (the goodness of fit statistic discussed in your
notes [and in Pedhazur, 2nd ed.], that compares the full and the
restricted models).
g. Does the restricted path model fit the data well? (Use the .05
level of significance, and be sure to show your work.)
2. Add the following two parts to the second question in lab 11:
d. Use chi-square to test which path model provides the best fit to
the data. What do you conclude? (Use the .05 level of
significance.)
e. Do your data provide support for one of the two theories?
(Justify your answer by interpreting the best-fitting path model.)
3. Add the following two parts to the third question in lab 11:
e. Use chi-square and the .01 level of significance to test whether
the path model from part a fits the data better than the path model
from part b. Which model fits the data better? (Hint: Consider
KIDS to be included as a variable in model a, but that KIDS has no
paths leading to or from it.)
f. Does the above analysis bear out the industrial psychologist's
theory (mentioned in part b) about the role that "the number of an
employee's children" has on the well-established causal relations
among marital happiness, job commitment, and job performance?
Justify your answer by referring to your findings in earlier parts
of this problem.
4. Unbeknownst to the American public, the Coca-Cola Company fooled
everyone into believing that "Coca-Cola" would be replaced by "New
Coke" in the 1980s. The ploy was to sell more soft drinks, of course.
A reporter recently uncovered an internal marketing research report
that presents the interrelations among five variables in a fully
recursive path model. The data are from 100 cities (actually, 100
"marketing areas") in the United States. The five variables are as
follows:
1
CONSUMPTION1
Per capita Coca-Cola consumption prior to
the announcement that "Coca-Cola" would be
replaced by "New Coke"
ADVERTISING1
=
=
Amount of television advertising dollars
per capita spent in announcing that
"Coca-Cola" would be replaced by "New Coke"
OUTRAGE
=
Number of letters to the Coca-Cola company from the
marketing area criticizing the company's choice to
replace "Coca-Cola" with "New Coke"
ADVERTISING2
=
Amount of television advertising dollars per capita
spent after the announcement to reassure Americans
that "Coca-Cola" would NOT be replaced by "New Coke"
CONSUMPTION2
=
Per capita Coca-Cola consumption after the
announcement reassuring Americans that "Coca-Cola"
would NOT be replaced by "New Coke"
The path model:
2
A partially filled-in correlation matrix among these variables:
X1
X2
X3
X4
X5
CONSUMPTION1
ADVERTISING1
OUTRAGE
ADVERTISING2
CONSUMPTION2
X1
1.00
.050
.335
.242
.700
X2
.050
1.00
AAAA
.441
.300
X3
.335
AAAA
1.00
.538
.300
X4
.242
.441
.538
1.00
.400
X5
.700
.300
.300
.400
1.00
a. Solve for
AAAA
in the above correlation matrix.
b. Make up a table of just those total, direct, and indirect
effects on CONSUMPTION2 from this fully recursive path
model. Be sure and show how any indirect effects were
calculated.
c. From the evidence presented in the table of effects in
part b, decide whether or not the public outrage that resulted from
the company's advertising strategy was transformed into profit (via
Coca-Cola consumption) when the company reassured Americans that
"Coca-Cola" would NOT be replaced by "New Coke." That is, would you
conclude that it was profitable for Coca-Cola to outrage its
customers? (Explain your answer.)
d. In planning their advertising trick, Coca-Cola deliberately
manipulated ADVERTISING1 so that no more advertising dollars were
spent in market areas with either high or low per capita Coca-Cola
consumption. That is, the low correlation between CONSUMPTION1 and
ADVERTISING1 is due to the research design. (NOTE: Any effect [such
as this unanalyzed effect] built into one's research design must
remain estimated in any statistical model.) On the other hand,
because the Coca-Cola Company's policy is to allow advertising to be
directed solely by consumer demands [e.g., in letters of complaint],
you have theoretical reasons for dropping two paths from the model:
(i) The indirect effect of CONSUMPTION1 on ADVERTISING2 through
OUTRAGE makes sense: Marketing areas with high Coca-Cola
consumption are most likely to send letters of complaint to the
company, which would stimulate the company to advertise that
"Coca-Cola" would not be replaced by "New Coke." However, beyond
this indirect effect there is no reason to posit a direct effect
of CONSUMPTION1 on ADVERTISING2.
(ii) Likewise due to chaotic changes in the company's
post-announcement advertising policy, it is reasonable to assume
no direct effect of ADVERTISING1 on ADVERTISING2.
Redraw a path diagram among the variables that depicts a restricted
model that excludes these two paths. Onto this path diagram enter
your estimates of only those paths that have changed from the fully
recursive path model.
e. Use chi-square to test whether the fully recursive or the
restricted path model provides the best fit to the data. Which is
the best-fitting path model? (Use the .05 level of significance.)
3