Initialize R with the following commands:
options(contrasts=c("contr.sum","contr.poly"))
load(url("http://pnb.mcmaster.ca/bennett/psy710/datasets/p2-2023.rda") )spot contains data from an experiment
that used a 2(age) x 2 (luminance) x 3 (duration) factorial design to
investigate how visual sensitivity (for a spot presented on a uniform,
grey background) varies with age (young
vs. old), background luminance
(low vs high), and stimulus
duration (d1 (short), d2
(medium), d3 (long)). The dependent variable was contrast
sensitivity. Twelve participants were assigned to each
condition.Confirm the data are balanced. Then use a factorial ANOVA to
evaluate the main effects of age, luminance,
duration, and all of the interactions. List the ANOVA
table.
Evaluate all pairwise differences among the marginal means of
duration.
Evaluate the simple luminance x
duration interaction at each level of age.
(N.B. You do not have to recalculate the \(F\) and \(p\) values).
Evaluate the simple-simple main effects of age in
the low-luminance, long-duration condition, and in the high-luminance,
long-duration (d3) condition.
comprehension of the material was tested one day
later. The lecture was presented in three modes:
audio only (i.e., a podcast), visual only
(i.e., a written document), and audiovisual (i.e., a
combination of podcast and written document). In addition, the
statistics material was either organized or
disorganized. The data are stored in the data frame
learning, which contains the factors sID
(subject ID), mode, and material, and the
dependent variable comprehension.Use a 2 x 3 factorial ANOVA to analyze the effects of
material and mode (and their interaction) on
memory.
Analyze the simple main effect of material for each
mode.
When evaluating simple main effects, we sometimes choose to recalculate the \(F\) and \(p\) values using values of MS-residuals and df-residuals from the main ANOVA. Why would we want to do that?
Evaluate the assumptions of normality and homogeneity of variance.
For a factorial design, it is possible to calculate an association strength for each main effect and interaction using eta-squared and partial eta-squared. For any given effect, will eta-squared or partial eta-squared be larger? Why?
Calculate partial omega-squared and partial Cohen’s \(f\) for each main effect and interaction.
anorexia contains the results from an
experiment that examined the effectiveness of three types of
therapy (behavioural, cognitive,
and psychodynamic) for inducing weight loss
(wt) in adolescent girls who were high or
low in neuroticism. The factors
therapy and neuroticism were crossed
factorially, but the design was unbalanced.Verify that the design is unbalanced.
Use factorial ANOVA to evaluate the effects of
neuroticism and therapy on weight loss
(wt). Set up your ANOVA so that the main effects are
evaluated with null hypothesis that the unweighted
marginal means are equal.
Within the framework of nested linear models, describe the
difference between Type I and Type II sums-of-squares for the main
effect of therapy.
Are Type II or Type III sums-of-squares more appropriate for
evaluating the main effects of therapy and
neuroticism? Why?