Homework 3
Here are data from a 2-condition between subjects design (whether or not each participant had previous experience with the class
material). Participants were permitted to take as many review exams as they wanted (which were observed and measured) and
then, completed the exam. The DV is a performance score. In addition to the linear, group and their interaction effect, this analysis
will examine the quadratic relationship between number of review exams and performance, as well as the possibility of a non-inear
interaction term (that the shape of the relationship between number of review exams and performance may be different for the two
groups).
data  numrev.sav
1.
Get the univariate statistics for the number of review exams variable mean = ______________ std = _______________
2.
Preparing variables for the analysis
 Construct a dummy code for the previous experience variable with “no previous experience” as the target group
 Construct a centered version of the quantitative number of review exams variable
 Construct a quadratic term for the number of review exams variable (specifically a quadratic term, not linear+quadratic)
 Construct a linear interaction term between number of review exams and previous experience
 Construct a quadratic interaction term between number of review exams and the quadratic term for previous experience
3.
Getting “hierarchical” analyses (it is easier to use regression, but you may use GLM if you prefer – use FTZ to compute R²Δ
tests). Be sure to tell me what you learned from each model and/or model test.
a.
What were the results of the main effects model?
R² _______________ F _____________ p____________
What did you learn from this?
b.
What were the results of the model with the quad term?
R² _______________ F _____________ p____________
What did you learn from this?
c.
Compare the models w/ and w/o the quad term ?
R²-change ____________ F-change __________ p ______
What did you learn from this?
d.
What were the results of adding the linear 2-way?
R² _______________ F _____________ p____________
What did you learn from this?
e.
Compare the models w/ and w/o the linear 2--way ?
R²-change ____________ F-change __________ p ______
What did you learn from this?
f.
What were the results of adding the non-linear 2-way?
R² _______________ F _____________ p____________
What did you learn from this?
g.
Compare the models w/ and w/o the non-linear 2--way ?
R²-change ____________ F-change __________ p ______
What did you learn from this?
h.
Why might someone prefer this set of analyses to a single full-model analysis?
i.
Can you reduce this model (i.e., leave out any noncontributing terms)??? Explain your answer carefully.
4.
Getting an “alternative” analyses: Imagine that you have previously explored the main effects and interactions of experience
group and number or review exams taken, as well as their interaction, but have never previously explored the possibility of
nonlinear terms or interactions. So, you decide on the following modeling and model comparison sequence. (Note: It is easier
to use regression, but you may use GLM if you prefer – use FTZ to compute R²Δ tests). Be sure to tell me what you learned
from each model and/or model test.
a.
What were the results of the main effects model?
R² _______________ F _____________ p____________
What did you learn from this?
b.
What were the results of the model with the interactioin?
R² _______________ F _____________ p____________
What did you learn from this?
j.
Compare the models w/ and w/o the interaction ?
R²-change ____________ F-change __________ p ______
What did you learn from this?
k.
What were the results of adding quadratic term?
R² _______________ F _____________ p____________
What did you learn from this?
l.
Compare the models w/ and w/o the quadratic term ?
R²-change ____________ F-change __________ p ______
What did you learn from this?
m. What were the results of adding the quad interaction?
R² _______________ F _____________ p____________
What did you learn from this?
n.
Compare the models w/ and w/o the quad interaction?
R²-change ____________ F-change __________ p ______
What did you learn from this?
o.
Why might someone prefer this set of analyses to the previous analysis?
p.
Can you reduce this model (i.e., leave out any noncontributing terms)??? Explain your answer carefully.
5.
Complete the following for the full model.
Predictor
b
t(p)
Previous Experience
Number of Practice Exams
Quadratic term for Number of Practice Exams
Linear Interaction term
Quadratic Interaction term
constant
5.
Report the regression model for each Previous Experience group
No Previous Exp
perf’ =
Previous Exp
perf’ =
6.
Plot the regression equation on other paper be sure to plot to +/- 2 std on the x axis
7.
Answer the following based on the plot and the regression model
a.
b.
c.
To what specific effect does the Task Experience regression weight refer? Describe that specific effect.
Describe the main effect for Task Experience.
Is the main effect for Task Experience descriptive or potentially misleading? Carefully explain your answer.
β
d.
e.
f.
To what specific effect does the Number of Practice Exams regression weight refer? Describe that specific effect.
Describe the main effect for Number of Practice Exams.
Is the main effect for Number of Practice Exams descriptive or potentially misleading? Carefully explain your answer.
g.
To what specific effect does the Quadratic Number of Practice Exams regression weight refer? Describe that specific
effect.
Describe the Quadratic component of the main effect for Number of Practice Exams.
Is the quadratic component of the main effect for Number of Practice Exams descriptive or potentially misleading?
Carefully explain your answer.
h.
i.
j.
k.
What specific information is given by the Task Familiarity * Number of Practice Exams interaction regression weight?
Describe the interaction of Task Familiarity * Number of Practice Exams interaction
l.
What specific information is given by the quadratic term of the Task Familiarity * Number of Practice Exams interaction
regression weight?
m. Describe the interaction of quadratic term of the Task Familiarity * Number of Practice Exams interaction
n.
What specific information is given by the constant?
The data were collected to examine the relationships practice, age, initial performance, and their interactions) as they
relate to performance on a complex motor task.
data  pract3.sav
1. Get the univariate statistics for the predictor variables
practice
mean = ______________ std = _______________
age
mean = ______________ std = _______________
initial perf
mean = ______________ std = _______________
2. Preparing variables for the analysis
 Constructed a centered version of each predictor variable
 Construct the three 2-way interaction terms
 Construct the 3-way interaction term
3. Getting “the usual” analyses (it is easier to use regression, but you may use GLM if you prefer – use FTZ to compute R²Δ tests).
Be sure to tell me what you learned from each model and/or model test.
a.
What were the results of the main effects model?
R² _______________ F _____________ p____________
What did you learn from this?
b.
What were the results of the model with 2-ways?
R² _______________ F _____________ p____________
What did you learn from this?
c.
Compare the models w/ and w/o the 2-ways ?
R²-change ____________ F-change __________ p ______
What did you learn from this?
d.
What were the results of adding the 3-way?
R² _______________ F _____________ p____________
What did you learn from this?
e.
Compare the models w/ and w/o the 3-way ?
R²-change ____________ F-change __________ p ______
What did you learn from this?
f.
Why might someone prefer this set of analyses to a single full-model analysis?
g.
Can you reduce this model (i.e., leave out any noncontributing terms)??? Explain your answer carefully.
4. Getting “a tailored analysis sequence” . Imagine that previous work has shown that while both practice and initial performance
relate to final (after practice) performance, there is no interaction between these two predictors. Based on an extensive
literature review, your research team hypothesizes there is an interaction between these two variables, but that their interaction
may be different for learners of different ages. So, you decide on the following modeling and model comparison sequence.
(Note: It is easier to use regression, but you may use GLM if you prefer – use FTZ to compute R²Δ tests). Be sure to tell me
what you learned from each model and/or model test.
a.
What were the results model including practice,
initial performance and their interaction?
R² _______________ F _____________ p____________
What did you learn from this?
b.
What were the results of the model adding age?
R² _______________ F _____________ p____________
What did you learn from this?
c.
Compare the models w/ and w/o age ?
R²-change ____________ F-change __________ p ______
What did you learn from this?
d.
What were the results of the model adding the
2-ways including age ?
R² _______________ F _____________ p____________
What did you learn from this?
e.
Compare the models w/ and w/o the age 2-ways ?
R²-change ____________ F-change __________ p ______
What did you learn from this?
f.
Compare the models w/ and w/o the 3-way?
g.
Why might someone prefer this set of analyses to a single full-model analysis?
h.
Can you reduce this model (i.e., leave out any noncontributing terms)??? Explain your answer carefully.
i.
R²-change ____________ F-change __________ p ______
Complete the following for the full model.
Predictor
b
t(p)
β
Practice
Initial Performance
Age
Practice * Initial Performance
Practice * Age
Practice * Initial Performance
Practice * Initial Performance * Age
Constant
5.
Report the regression telling the relationship between practice and performance for each of the following value combinations of
the other two predictors
+1 std Initial Performance & +1 std Age
perf’ =
+1 std Initial Performance & -1 std Age
perf’ =
-1 std Initial Performance & +1 std Age
perf’ =
-1 std Initial Performance & -1 std Age
perf’ =
6.
Plot the regression equation on other paper be sure to plot to +/- 2 std on the x axis
7.
Describe each of the following effects (be sure to tell if each is descriptive or misleading)
a.
what specific information is given by the constant?
b.
Main effect of practice
c.
Main effect of initial performance
d.
Main effect of age
e.
2-way interaction of practice and initial performance
f.
3-way interaction of practice, initial performance and age