General Questions
Q1
What is the null hypothesis tested by analysis of variance?
Q2
What are the assumptions of betweensubjects analysis of variance?
Q3
What is a betweensubjects variable?
Q4
Why not just compute \(t\)tests among all pairs of means instead computing an analysis of variance?
Q5
What is the difference between "\(N\)" and "\(n\)"?
Q6
How is it that estimates of variance can be used to test a hypothesis about means?
Q7
Explain why the variance of the sample means has to be multiplied by "\(n\)" in the computation of \(MSB\).
Q8
What kind of skew does the \(F\) distribution have?
Q9
When do \(MSB\) and \(MSE\) estimate the same quantity?
Q10
If an experiment is conducted with \(6\) conditions and \(5\) subjects in each condition, what are \(dfn\) and \(dfe\)?
Q11
How is the shape of the \(F\) distribution affected by the degrees of freedom?
Q12
What are the two components of the total sum of squares in a onefactor betweensubjects design?
Q13
How is the mean square computed from the sum of squares?
Q14
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?
Q15
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 treatment was 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 control condition.
 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.
Q16
An \(A(3) \times B(4)\) 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.
Q17
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.

12year olds 
16year olds 
30 minutes 
66
68
59
72
46 
74
71
67
82
76 
60 minutes 
69
61
69
73
61 
95
92
95
98
94 
Q18
Define "Threeway interaction"
Q19
Define interaction in terms of simple effects.
Q20
Plot an interaction for an \(A(2) \times B(2)\) 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 axes.
Q21
Following are two graphs of population means for \(2 \times 3\) designs. For each graph, indicate which effect(s) (\(A\), \(B\), or \(A \times B\)) are nonzero.
Q22
The following data are from an \(A(2) \times B(4)\) factorial design.

B1 
B2 
B3 
B4 
A1 
1
3
4
5 
2
2
4
5 
3
4
2
6 
4
5
6
8

A2 
1
1
2
2 
2
3
2
4 
4
6
7
8 
8
9
9
8 
 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.
Q23
Why are withinsubjects designs usually more powerful than betweensubjects design?
Q24
What source of variation is found in an ANOVA summary table for a withinsubjects design that is not in in an ANOVA summary table for a betweensubjects design. What happens to this source of variation in a betweensubjects design?
Q25
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.
\[\begin{matrix} 4 & 6 & 7\\ 3 & 7 & 7\\ 2 & 8 & 5\\ 1 & 4 & 7\\ 4 & 6 & 9 \end{matrix}\]
 Compute an ANOVA
 Test all pairwise differences between means using the Bonferroni test at the \(0.01\) level.
 Test the linear and quadratic components of trend for these data.
Q26
Give the source and df columns of the ANOVA summary table for the following experiments:
 \(22\) subjects are each tested on a simple reaction time task and on a choice reaction time task.
 \(12\) male and \(12\) female subjects are each tested under three levels of drug dosage: \(0 mg, 10 mg, 20 mg\).
 \(20\) subjects are tested on a motor learning task for \(3\) trials a day for \(2\) 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. \(10\) subjects are assigned to each group. The level of measured once a month for \(4\) months.
Questions from Case Studies
The following question is from the Stroop Interference case study.
Q27
The dataset has the scores (times) for males and females on each of three tasks.
 Do a \(Gender (2) \times Task (3)\) analysis of variance.
 Plot the interaction.
The following question is from the ADHD Treatment case study.
Q28
The data has four scores per subject.
 Is the design betweensubjects or withinsubjects?
 Create an ANOVA summary table.
The following question is from the Angry Moods case study.
Q29
Using the Anger Expression Index as the dependent variable, perform a \(2 \times 2\) ANOVA with gender and sports participation as the two factors. Do athletes and nonathletes 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 study.
Q30
Compute a \(2 \times 2\) 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 nonaggressive?). Consider carefully whether the variables are betweensubject or withinsubects variables.
The following question is from the Smiles and Leniency case study.
Q31
Compute the ANOVA summary table.