Use the following commands to initialize R. The commands set R to
define effects using the sum-to-zero constraint and loads two data
frames, df0
and df1
, that we’ll analyze in the
following sections.
options(contrasts=c("contr.sum","contr.poly") ) # set definition of contrasts
load(url("http://pnb.mcmaster.ca/bennett/psy710/datasets/RLab06b.rda") )
An experiment used a factorial design to analyze the effects of three
factors A
, B
, and C
on a
dependent variable, Y
. The data are stored in the data
frame df0
. Use df0
to answer the following
questions. When analyzing simple interaction effects or simple main
effects, you do not need to recalculate \(F\) and \(p\) values using MS-error and df-error from
the original ANOVA.
Confirm that the data are balanced.
Use ANOVA to evaluate the all of the main effects and interactions. List the ANOVA table.
The 3-way interaction is significant. What null hypothesis is evaluated by this \(F\) test?
Does it make sense to analyze the sub-effects of the main effects
of A
and B
, or to decompose/analyze the
A:B
interaction? Why or why not?
Plot the 3-way interaction and come up with an idea about why it is significant.
Evaluate the simple A:C
interaction for each level
of B
. For each analysis, calculate a measure of effect size
or association strength for AxC
. For each analysis, if the
simple interaction is significant, then evaluate the simple simple main
effect of C
at each level of A
. If the simple
interaction is not significant, then evaluate the simple main effects of
A
and C
at each level of
B
.
An experiment used a factorial design to evaluate the effects of two
drugs, A
and B
, on the dependent variable
Y
. The levels of A
and B
were
drug absent (a0
& b0
) and drug present
(a1
& b1
), condition a0b0
is
a baseline (placebo) condition. The data are stored in the data frame
df1
.
Use ANOVA to evaluate the effects of A
and
B
. List the ANOVA table.
Evaluate the homogeneity of variance assumption.
Evaluate the normality assumption.
The experimenters hypothesized that both drugs
had to be present to have an effect on Y
. Perform an
analysis that follows up your ANOVA to evaluate this
hypothesis.