Chapter 13 Exercises
David M. Lane
material presented in Chapter 13
- What is the null hypothesis tested by analysis of variance?
- What are the assumptions of between-subjects analysis of
- What is a between-subjects variable?
- Why not just compute t-tests among all pairs of means instead
computing an analysis of variance?
- What is the difference between "N" and "n"?
- How is it that estimates of variance can be used to test
a hypothesis about means?
- Explain why the variance of the sample means has to be multiplied
by "n" in the computation of MSB.
- What kind of skew does the F distribution have?
- When do MSB and MSE estimate the same quantity?
- If an experiment is conducted with 6 conditions and 5 subjects
in each condition, what are dfn and dfe?
- How is the shape of the F distribution affected by the degrees
- What are the two components of the total sum of squares in
a one-factor between-subjects design?
- How is the mean square computed from the sum of squares?
- An experimenter is interested in the effects of two independent
variables on self esteem. What is better about conducting a factorial
experiment than conducting two separate experiements, one for
each independent variable?
- An experiment is conducted on the effect of age and treatment
condition (experimental versus control) on reading speed. Which
statistical term (main effect, simple effect, interaction, specific
comparison) applies to each of the descriptions of effects.
- The effect of the treatmentwas larger for 15-year olds
than it was for 5- or 10-year olds.
- Overall, subjects in the
treatment condition performed faster than subjects in the
- The difference between the 10- and 15-year
olds was significant under the treatment condition.
- The difference
between the 15- year olds and the average of the 5- and 10-year
olds was significant.
- As they grow older, children read faster.
- An A(3) x B(4) factorial design with 6 subjects in each
group is analyzed. Give the source and degrees of freedom columns
of the analysis of variance summary table.
- The following data are from a hypothetical study on the effects
of age and time on scores on a test of reading comprehension.
Compute the analysis of variance summary table.
- Define "Three-way interaction"
- Define interaction in terms of simple effects.
- Plot an interaction for an A(2) x B(2) design in which the
effect of B is greater at A1 than it is at A2. The dependent
variable is "Number correct." Make sure to label both
- Following are two graphs of population means for 2 x 3 designs.
For each graph, indicate which effect(s) (A, B, or A x B) are
- The following data are from an A(2) x B(4) factorial design.
- Compute an analysis of variance.
- Test differences among the
four levels of B using the Bonferroni correction.
- Test the
linear component of trend for the effect of B.
- Plot the interaction.
- Describe the interaction in words.
- Why are within-subjects designs usually more powerful than
- What source of variation is found in an ANOVA summary table
for a within-subjects design that is not in in an ANOVA summary
table for a between-subjects design. What happens to this source
of variation in a between-subjects design?
- The following data contain three scores from each of five subjects.
The three scores per subject are their scores on
three trials of a memory task.
4 6 7
3 7 7
2 8 5
1 4 7
4 6 9
- Compute an ANOVA
- Test all pairwise differences
between means using the Bonferroni test at the .01
- Test the linear and quadratic components of trend for
- Give the source and df columns of the ANOVA summary table
for the following experiments:
Questions from Case Studies:
Twenty two subjects are each tested on a simple reaction time
task and on a choice reaction time task.
- Twelve male and 12 female
subjects are each tested under three levels
of drug dosage: 0 mg, 10 mg, and 20 mg.
- Twenty subjects
are tested on a motor learning task for three trials
a day for two days.
- An experiment is conducted in which
depressed people are either assigned to a drug therapy
group, a behavioral therapy group, or a control group.
Ten subjects are assigned to each group. The level of measured
once a month for four months.
The following question is from the Stroop
Interference case study.
- The dataset has
the scores (times) for males and females on each of three tasks.
The following question is from the ADHD
a. Do a Gender (2) x Task (3) analysis of variance.
b. Plot the interaction.
- The data has four scores per subject.
- Is the design between-subjects or within-subjects?
- Create an ANOVA summary table.
The following question is from the Angry
- Using the Anger Expression Index as the dependent variable,
perform a 2x2 ANOVA with gender and sports participation as the
two factors. Do athletes and non-athletes differ significantly
in how much anger they express? Do the genders differ significantly
in Anger Expression Index? Is the effect of sports participation
significantly different for the two genders?
The following question is from the Weapons
and Aggression case
- Compute a 2x2 ANOVA on this data with the following
two factors: prime type (was the first word a weapon or not?)
and word type (was the second word aggressive or non-aggressive?). Consider
carefully whether the variables are between-subject or within-subects
The following question is from the Smiles
and Leniency case
- Compute the ANOVA summary table.
Please answer the questions: