Deck 17: Factorial Analysis of Variance

Question 1

A simple effect is defined as

A) part of the interaction.
B) the effect of one variable taken by itself.
C) the effect of one variable at a single level of the other variable.
D) the difference between the row effect and the column effect.

Answer 1

the effect of one variable at a single level of the other variable.

Question 2

To look at an interaction effect we must

A) consider one variable at a time.
B) plot the data within each cell.
C) plot the data in such a way that we see how each independent variable changes at each level of the other independent variable.
D) calculate the row means.

Answer 2

plot the data in such a way that we see how each independent variable changes at each level of the other independent variable.

Question 3

Use the following ANOVA summary table to answer the following four questions:

How many cells are there in this design?

A) 1
B) 4
C) 8
D) 10

Answer 3

10

Question 4

The main effect of a variable is

A) the effect of that variable controlling for another variable.
B) the effect of that variable averaged over the levels of other independent variable(s).
C) part of the interaction effect.
D) none of the above

Question 5

Use the following research scenario to answer the next four questions:
A researcher was interested in the effects of 1) alcohol consumption and 2) content of a videotape, on how likely one is to support rape myths.  The researcher randomly assigned 60 college-aged males to one of the following three groups: no alcohol consumed, a moderated amount of alcohol consumed, and a large amount of alcohol consumed.  Additionally, half of the participants were shown the educational video on rape myths. The other half of the participants watched a documentary on owls (a control condition).  At the end of the study all the participants filled out a survey on rape myth acceptance.  Higher scores on the survey indicated higher acceptance of rape myths.
The results indicated that the participants who watched the educational video scored significantly lower on the rape myth scale compared to the group that watched the owl video. What does this suggest?

A) There is a main effect of alcohol consumption.
B) There is a main effect of video type.
C) There is an interaction between alcohol consumption and video type.
D) For some unknown reason, owls seem to promote rape myth acceptance.

Question 6

Which of the following is not an advantage of factorial designs over one-way designs?

A) They allow for greater generalizability.
B) They allow us to test an interaction.
C) They make it easier to deal with unequal sample sizes.
D) They give us greater economy.

Question 7

If the analysis of variance is significant, we are pretty sure that

A) we have an important finding.
B) at least one mean is different from one or more other means.
C) the means don't differ from each other.
D) we screwed up somewhere.

Question 8

In a factorial design a cell is

A) the combination of a row and a column.
B) the smallest number of subjects who were treated alike.
C) another name for a simple effect.
D) both a and b

Question 9

The notation ... stands for

A) the mean of any row.
B) the mean of any column.
C) the mean of any cell.
D) the grand mean.

Question 10

The difference between a one-way analysis of variance and a factorial analysis of variance is

A) the presence of an interaction.
B) the presence of more than one main effect.
C) one-way analyses of variance have an error term, whereas factorial analyses do not.
D) both a and b

Question 11

A 2 × 4 factorial has

A) 8 subjects.
B) 2 levels of one variable and 4 levels of the other.
C) 8 factors.
D) one variable with 4 levels and 2 subjects.

Question 12

Use the following research scenario to answer the next four questions:
A researcher was interested in the effects of 1) alcohol consumption and 2) content of a videotape, on how likely one is to support rape myths.  The researcher randomly assigned 60 college-aged males to one of the following three groups: no alcohol consumed, a moderated amount of alcohol consumed, and a large amount of alcohol consumed.  Additionally, half of the participants were shown the educational video on rape myths. The other half of the participants watched a documentary on owls (a control condition).  At the end of the study all the participants filled out a survey on rape myth acceptance.  Higher scores on the survey indicated higher acceptance of rape myths.
How many cells does this experiment have?

A) 2
B) 5
C) 6
D) 12

Question 13

Use the following ANOVA summary table to answer the following four questions:

What does the significant F for Group most likely mean?

A) All the groups are different from each other.
B) None of the groups are different from each other.
C) The study has problems with control.
D) There is at least one significant difference among the groups.

Question 14

Use the following research scenario to answer the next four questions:
A researcher was interested in the effects of 1) alcohol consumption and 2) content of a videotape, on how likely one is to support rape myths.  The researcher randomly assigned 60 college-aged males to one of the following three groups: no alcohol consumed, a moderated amount of alcohol consumed, and a large amount of alcohol consumed.  Additionally, half of the participants were shown the educational video on rape myths. The other half of the participants watched a documentary on owls (a control condition).  At the end of the study all the participants filled out a survey on rape myth acceptance.  Higher scores on the survey indicated higher acceptance of rape myths.
What type of statistical analysis would be most appropriate for this experiment?

A) a t -test
B) a regression
C) a one-way analysis of variance
D) a factorial analysis of variance

Question 15

A factorial analysis of variance has

A) more than one dependent variable.
B) more than one independent variable.
C) every level of every independent variable paired with every level of every other independent variable.
D) both b and c

Question 16

In the text the Eysenck study of recall as a function of Age and Instructions allowed us to see that

A) older subjects don't recall as well as earlier subjects, on average.
B) older and younger subjects differ more on tasks which involve greater depth of processing.
C) greater processing tends to lead to better recall.
D) all of the above

Question 17

Use the following ANOVA summary table to answer the following four questions:

Why does Group have 4 degrees of freedom?

A) because there are 4 groups
B) because there are 5 groups (5 - 1 = 4)
C) because gender has 1 df (1 × 4 = 4)
D) because the design has four cells

Question 18

Use the following research scenario to answer the next four questions:
A researcher was interested in the effects of 1) alcohol consumption and 2) content of a videotape, on how likely one is to support rape myths.  The researcher randomly assigned 60 college-aged males to one of the following three groups: no alcohol consumed, a moderated amount of alcohol consumed, and a large amount of alcohol consumed.  Additionally, half of the participants were shown the educational video on rape myths. The other half of the participants watched a documentary on owls (a control condition).  At the end of the study all the participants filled out a survey on rape myth acceptance.  Higher scores on the survey indicated higher acceptance of rape myths.
What would you suggest if the researcher found that alcohol consumption increased rape myth acceptance, but only when the participants had watched the owl video?

A) There is an interaction between alcohol consumption and video type.
B) There is a main effect of alcohol consumption.
C) There is a simple effect of alcohol in the educational video condition.
D) There is a main effect of the video condition.

Question 19

To calculate the sum of squares for a treatment effect in the analysis of variance, we would work with

A) the squares of the differences between the treatment means and the grand mean.
B) the variance within the treatments.
C) the number of samples.
D) both a and b

Question 20

Use the following ANOVA summary table to answer the following four questions:

The summary table suggests which of the following conclusions?

A) a main effect of gender
B) a main effect of group
C) an interaction of gender × group
D) all of the above

Question 21

In the factorial design analyses discussed in Chapter 17, the different cells

A) often have different subjects in them.
B) never have different subjects in them.
C) always have different subjects.
D) can have either the same subjects or different subjects.

Question 22

To calculate the magnitude of effect estimates for a factorial design, the methods are

A) radically different from the methods used with a one-way design.
B) simple extensions of the methods used with a one-way design.
C) not possible to calculate.
D) only useful for estimating magnitude of effects for interactions, not main efforts.

Question 23

Which of the following is NOT true in a factorial analysis of variance?

A) SS _total = SS _A + SS _B + SS _AB
B) SS _total = SS _A + SS _B + SS _AB + SS _error
C) SS _cells = SS _A + SS _B + SS _AB
D) SS _total = SS _cells + SS _error

Question 24

In the three graphs below, which one is most likely to have a main effect for quarters (the variable that increases along the X axis)?

​

A) I
B) II
C) III
D) none.

Question 25

Which of the following graphs is most likely to portray an interaction?

​

A) I
B) II
C) III
D) There is no interaction in any of these.

Question 26

To calculate the F for the interaction in an analysis of variance we

A) divide the MS _interaction by MS _error.
B) divide the MS _interaction by MS _total.
C) multiply MS ¬_interaction by its df .
D) divide MS _interaction into MS _rows.

Question 27

If ω² is calculated to yield the magnitude of effect estimates instead of η² for a particular experiment, the ω² estimates would probably be

A) higher and more biased.
B) higher and less biased.
C) lower and more biased.
D) lower and less biased.

Question 28

A pediatrician is studying weight gain in infants. He divides them into 2 groups: breast fed and bottle fed. Further, he divides them into those whose mothers feed them on a timed schedule, and those whose mothers feed them when they cry (on demand). Weight gain is the dependent measure. What type of analysis should you run?

A) a regression
B) a one-way ANOVA
C) a 2 × 2 factorial ANOVA
D) a 2 × 2 correlation

Question 29

Unequal sample sizes in a factorial analysis of variance are

A) no problem.
B) often difficult to interpret.
C) impossible to interpret.
D) easily explained by the use of simple effects.

Question 30

_______ are the effect of one variable at one level of the other variable.

A) simple effects
B) main effects
C) interactions
D) relationships

Question 31

The following is a printout from SPSS.

From this table, which of the following conclusions would be wrong?

A) There is a significant effect for Groups.
B) There is a significant effect for Education.
C) The interaction is significant.
D) Both main effects are significant.

Question 32

To calculate the F for a simple effect you

A) often use the same error term you use for main effects.
B) use the mean square for the main effect as the denominator in F .
C) first divide the mean square for the simple effect by its degrees of freedom.
D) none of the above

Question 33

Unequal sample sizes in a factorial analysis of variance

A) are difficult to deal with when doing calculations by hand.
B) are treated exactly as they were in the one-way design.
C) cannot be dealt with at all.
D) are dealt with just like equal sample sizes when doing hand calculations.

Question 34

If you have a significant interaction,

A) at least one of the main effects will be nonsignificant.
B) both of the main effects will be nonsignificant.
C) at least one simple effect is likely, though not certain, to be significant.
D) the interaction doesn't suggest anything about simple effects.

Question 35

In a study which investigated the effects of amount of coffee consumption and mood (good or bad) on driving speed, the magnitude of effects estimates were as follows: Coffee:
; Mood:
; Coffee × Mood:
. Together, how much of the variability in driving speed is accounted for by Coffee, Mood, and their interaction?

A) cannot determine
B) .49
C) .51
D) .19

Question 36

If you have a significant interaction, you should

A) think carefully about any main effects you might have.
B) ignore any main effects you might have.
C) ignore the interaction unless there is a main effect.
D) none of the above

Question 37

A simple effect is calculated by

A) looking only at the data for one level of one of the independent variables.
B) averaging across the levels of one of the independent variables.
C) ignoring one of the independent variables.
D) dividing the main effect by the degrees of freedom.

Question 38

In a factorial analysis of variance you cannot have

A) both a significant interaction and a significant main effect.
B) two significant main effects.
C) a significant main effect and a nonsignificant interaction.
D) Any combination is possible.

Question 39

The degrees of freedom for an interaction in a two-way factorial are equal to

A) the degrees of freedom for the main effects.
B) the sum of the degrees of freedom for the main effects.
C) the product of the degrees of freedom for the main effects.
D) 6.

Question 40

In graph I below, the most apparent simple effect is for the line represented by

​

A) diamonds.
B) squares.
C) triangles.
D) It is unlikely for there to be a simple effect for any level of the independent variable.

Question 41

Dr. Gates looked at the effects of frustration on the use of profanity by males and females. Males and females were asked to write a lab report on computers in a lab, but half the computers were set up to crash during the session while half of the computers were not set up to crash. Three observers recorded the use of profanity by the participants during the task. What is the design of this study?

A) 2 × 2 factorial
B) 1 × 2 factorial
C) 2 × 2 × 3 factorial
D) 2 × 2 correlational

Question 42

A factorial design has at least

A) one dependent variable and one independent variable.
B) two dependent variables and one independent variable.
C) two independent variables and one dependent variable.
D) The number of independent variables is not important.

Question 43

The mean difference in GPA based on gender and year in school is a main effect.

Question 44

To calculate the F for a simple effect you

A) use the mean square for the main effect as the denominator in F .
B) first divide the mean square for the simple effect by its degrees of freedom.
C) use the same error term you use for main effects.
D) none of the above

Question 45

When comparing differences in an experiment with two or more independent variables we should use a(n)

A) one way ANOVA.
B) paired sample t-test.
C) R squared comparison.
D) factorial design.

Question 46

What type of design is the above study?

A) 2 × 2 × 2
B) 2 × 2
C) 2 × 3
D) 3 × 3 × 3

Question 47

When you compare the effect of one variable at one level of another variable you are examining

A) a main effect
B) a simple effect
C) a correlational effect
D) both a and c

Question 48

This graph represents a/an

​

A) repeated-measures design
B) one-way ANOVA
C) 2 × 5 factorial
D) significant alpha

Question 49

The finding that women eat less in the company of men then when they are in the company of other women is a(n)

A) simple effect.
B) interaction.
C) factorial effect.
D) main effect.

Question 50

Pliner and Chaiken (1990) wanted to investigate whether the amount of food eaten depended on the gender of the participant and the gender of the confederate. It was observed that women eat less than men overall and that women eat less in the company of men than they do when in the company of other women. The finding that women eat less than men across all conditions is a(n)

A) simple effect.
B) interaction.
C) factorial effect.
D) main effect.

Question 51

The mean difference in GPA based on gender is an interaction effect.

Question 52

The overall effect of an independent variable is called a(n)

A) main effect.
B) simple effect.
C) interaction.
D) manipulation.

Question 53

A 2 × 4 factorial involves two independent variables. One has two levels and the other has four.

Question 54

Using the example in the text of a participant receiving therapy while sitting in a bath of ice water, what would be the best denominator for calculating ?

A) the square root of MS_error
B) the square root of MS_error after removing effects due to the Ice condition and its interaction with treatment
C) the standard deviation of participants in the non-ice condition
D) the standard deviation of difference scores

Question 55

In the Spilich et al. study of the effects of smoking that was discussed in the text, active smokers were found to do better than nonsmokers on a driving task but did worse than nonsmokers on a cognitive task. However, over all three tasks (the third was pattern recognition and the groups were not different on that) active smokers did not differ from nonsmokers on performance. The results suggest

A) an interaction between smoke group and task, and a main effect for smoke group.
B) an interaction between smoke group and task, but no main effect for smoke group.
C) a main effect for smoke group, but no interaction between smoke group and task.
D) a main effect for task only.

Question 56

When we compute an effect size measure such as
for a factorial ANOVA we have to decide

A) what effects should be included in estimating the denominator.
B) what are our variables of theoretical interest.
C) whether we want an r -family measure or a d -family measure.
D) all of the above

Question 57

In a factorial design involving the sex of the participant and the sex of the experimenter's confederate

A) there were multiple subjects in each cell of the design.
B) there were different subjects in each cell of the design.
C) all possible combinations of sex of subject and sex of confederate were represented.
D) all of the above

Question 58

When we say that a measure is "not of theoretical interest" we mean that

A) variability attributable to it should be removed from the denominator.
B) we can simply ignore that variable.
C) variability attributable to it should be included in the denominator.
D) there is no significant effect for that variable.

Question 59

A factorial analysis of variance involves more than one dependent variable.

Question 60

In this graph we can see that there is

​

A) a significant difference between Location 1 at time 1 and Location 2 at time 1.
B) an interaction between location and time.
C) a significant post hoc analysis.
D) a quadratic significant correlation.

Question 61

In analysis of variance, factor refers to independent variables.

Question 62

The mean difference in GPA based on Gender for Freshman only is a simple effect.

Question 63

Calculate and interpret F for each effect based on the following data.

Question 64

Three main effects and three interactions are tested in a factorial design with three independent variables.

Question 65

Calculate and explain ω ² for treatment group from the previous problem.

Question 66

What value appears in each identified cell in the following table?

a. X₁₁
b. X₂₃
c. X₄₁

Question 67

In a factorial design based on two independent variables, three F values will be calculated.

Question 68

A doctor examining the effectiveness of smoking cessation programs wanted to examine the independent and joint effect of a support group and the patch. The following data are the average number of packs smoked 2 weeks after the interventions. Each group consisted of 10 people. Answer the following questions based on this table of means.

a. What is the grand mean?
b. Calculate the mean packs smoked at each level of support group.
c. Calculate the mean packs smokes at each level of the patch.

Question 69

A human resources director for a large company wanted to compare salaries based on minority status and the type of job.   Answer the following questions based on the following SPSS output.

Calculate and explain η² for the significant effects from the previous data.

Question 70

Plot the data from the previous question three times (each main effect and the interaction effect); interpret the graphs.

Question 71

Determine whether each of the following effects is statistically significant at α = .05.

Question 72

X₁₃ refers to the value located in the first row and the third column.

Question 73

A human resources director for a large company wanted to compare salaries based on minority status and the type of job.   Answer the following questions based on the following SPSS output.

a. How many levels are there for each factor?
b. Which effects are statistically significant?

Question 74

A researcher noted that there was a significant interaction effect of amount of time studying and hours of sleep the night before an exam on exam scores. He calculated simple effects to try to interpret the data. Here are the results. Graph them and explain the nature of the interaction.