Deck 10: Factorial Analysis of Variance

Question 1

In a two-way factorial design,there can be

A)one interaction and one main effect.
B)one interaction and two main effects.
C)two interactions and one main effect.
D)two interactions and two main effects.

Answer 1

one interaction and two main effects.

Question 2

The scenarios below are possible results of a study in which participants completed a measure of how important religion was to them personally. Participants are either from a Rural or Urban area, and are either Poor or Rich.
Which of the following statements is true based on the information presented in Scenario C?

A)On the average,religion is more important to rich people than to poor people.
B)The column means show that religion is more important to poor people.
C)The row means show that there is no difference between rich and poor in their average interest in religion.
D)There is a clear interaction effect in which poor people value religion more in urban areas,while rich people value it more in rural areas.

Answer 2

On the average,religion is more important to rich people than to poor people.

Question 3

A consumer psychologist is interested in the effects of Annual Income and Motivations to Shop on shopping patterns of consumers.If Annual Income is divided into two levels (High and Moderate)and Motivation to Shop is divided into three levels (Escape,Necessity,and Socializing),and both are considered in one study,the number of cells will be

A)2
B)3
C)4
D)6

Answer 3

6

Question 4

A two-way factorial design

A)is "two-way" because there are two variables that divide the groups being studied.
B)varies only in name from a one-way analysis of variance.
C)considers two levels of a single variable.
D)considers a single level of two variables.

Question 5

The scenarios below are possible results of a study in which participants completed a measure of how important religion was to them personally. Participants are either from a Rural or Urban area, and are either Poor or Rich.
Which of the following interpretations is consistent with Scenario A?

A)Religion is more important to poor people when they live in rural areas.In the urban areas,poor people are socialized to be more like rich people,who are less religious,regardless of where they live.
B)Rich people,regardless of where they live,value religion moderately.Poor people value religion more in urban centers than in rural areas because it is more accessible.
C)People who live in the urban areas need religion more than people in rural areas,regardless of how rich or poor they are.
D)Poor people in urban areas have a harder time than people in rural areas,so they value religion more.Rich people who move to rural areas are trying to get away from their materialistic lifestyle and tend to be more religious.

Question 6

Most psychology research

A)avoids anything more than a one-way analysis of variance.
B)concurrently examines four or five main variables.
C)is limited to two-way and occasionally three-way factorial designs.
D)concurrently examines at least 20 variables.

Question 7

What is the relationship between the amount of time spent shopping, Short (under 15 minutes) or Long (over 15 minutes), and the age of the shopper, Young (under 22) or Old (over 22), and the amount of money spent by shoppers in a music store.
Which interpretation is most consistent with the interaction effect in Scenario B?

A)If there is only a short time to shop,age makes no difference,but if there is a long time to shop,younger buyers spend more money than older buyers.
B)Younger buyers spend more money in general than older buyers.
C)More money is spent when people shop for a long time as compared with a short time.
D)None,because there is no interaction effect.

Question 8

An interaction effect can be identified by

A)looking at the pattern of cell means.
B)conducting a series of t tests.
C)dividing each cell mean by its marginal mean.
D)dividing each cell mean by a weighted marginal mean.

Question 9

In a factorial design,a "cell" is

A)each combination of levels of the variables that divide the groups.
B)the combination of different levels of one variable that divides the groups,ignoring any other variables that divide the groups.
C)a study with a single two-level variable that divides the groups.
D)the same thing as a "main effect."

Question 10

The scenarios below are possible results of a study in which participants completed a measure of how important religion was to them personally. Participants are either from a Rural or Urban area, and are either Poor or Rich.
Which statement is true about Scenario B?

A)There is a moderate interaction effect.
B)Religion is consistently more important for rich people than for poor people,regardless of where they live.
C)Religion is more important to people who live in the urban areas,regardless of their wealth.
D)Religion is particularly important to people who are both poor and live in rural areas.

Question 11

Marginal means are

A)the means of one grouping variable alone.
B)used to identify interaction effects.
C)always reported in research articles.
D)the means of both grouping variables,minus the interaction.

Question 12

If an experimenter "crosses Intelligence with Attractiveness" in a factorial design in which intelligence has three levels (high,medium,and low)and attractiveness has two levels (high and low),the study will

A)be a three-way analysis of variance.
B)be a 3 × 2 analysis of variance.
C)have eight cells to the third power.
D)have five cells.

Question 13

In a three-way factorial design,there can be

A)four main effects and three interactions.
B)three main effects and three interactions.
C)two main effects and three interactions.
D)three main effects and four interactions.

Question 14

An interaction effect can be identified in all of the following ways EXCEPT

A)through inspecting cell means.
B)through inspecting marginal means.
C)by using graphs.
D)by a verbal description of results.

Question 15

A 2 × 3 factorial design has

A)two variables that divide the groups.
B)six variables that divide the groups.
C)three variables that divide the groups.
D)five variables that divide the groups.

Question 16

What is the relationship between the amount of time spent shopping, Short (under 15 minutes) or Long (over 15 minutes), and the age of the shopper, Young (under 22) or Old (over 22), and the amount of money spent by shoppers in a music store.
Which interpretation is consistent with Scenario A?

A)More money is spent when people shop for a long time as compared with a short time.
B)Younger buyers spend more money in general than older buyers.
C)Less money is spent when people shop for a long time as compared with a short time.
D)Older buyers spend more money in general than younger buyers.

Question 17

What is the relationship between the amount of time spent shopping, Short (under 15 minutes) or Long (over 15 minutes), and the age of the shopper, Young (under 22) or Old (over 22), and the amount of money spent by shoppers in a music store.
Which interpretation is most consistent with Scenario C?

A)Length of time makes no difference in the amount of money spent.
B)Age makes no difference in the amount of money spent.
C)Younger buyers spend more money when they shop for a shorter time whereas older buyers spend more money when they shop for a longer time.
D)Neither age nor length of time makes a difference in amount of money spent.

Question 18

All of the following are advantages of factorial designs EXCEPT

A)they automatically provide an indicator of effect size for the measured variable.
B)they are more efficient.
C)the combined influences of variables can be studied.
D)more than one grouping variable can be considered in the same study.

Question 19

What is the relationship between the amount of time spent shopping, Short (under 15 minutes) or Long (over 15 minutes), and the age of the shopper, Young (under 22) or Old (over 22), and the amount of money spent by shoppers in a music store.
A store manager said,"How much money people spend isn't related to age.All that matters is how long they shop." If she said that after seeing the results of one of these studies,which scenario was she probably looking at?

A)Scenario A
B)Scenario B
C)Scenario C
D)none of the above

Question 20

An interaction effect in a two-way factorial design

A)is the effect of one variable that divides the groups,ignoring the influence of the other variable that divides the groups.
B)occurs when the influence of one variable that divides the groups changes according to the level of the other variable that divides the groups.
C)almost never occurs when more than one variable that divides the groups is considered at a time.
D)is rare in a well-designed study,and usually indicates some error in computation.

Question 21

In a 2 × 2 analysis of variance,the basis for estimating the numerator of the F ratio for the interaction effect is

A)the variance among the four cell means.
B)the variance between the two column marginal means.
C)the variance between the two row marginal means.
D)the variance between the means of the two diagonals.

Question 22

In a two-way analysis of variance,what is the population variance estimate for the denominator of the F ratios for the main and interaction effects?

A)All effects are tested using the same estimate based on averaging the estimates of the variance of scores within each cell.
B)Each effect is tested using a variance estimate based on the variation within the appropriate groupings.
C)Each effect is tested using a variance estimate based on the variation among the appropriate marginal means.
D)The row and column effects are tested using an estimate based on the variation within the appropriate groupings,but the interaction effect is tested based on averaging the estimates based on variance of scores within each cell.

Question 23

In a 3 × 3 analysis of variance,the number of null hypotheses is

A)1
B)3
C)6
D)9

Question 24

Advanced topic: According to the structural model of the two-way analysis of variance,each score's overall deviation from the grand mean is divided into

A)2 components.
B)4 components.
C)7 components.
D)as many components as there are cells in the design.

Question 25

For a factorial analysis of variance,the assumptions that were necessary for a one-way analysis of variance

A)are no longer required.
B)are necessary for each cell.
C)are unchanged.
D)are unchanged,but less important,because factorial analysis of variance is more robust than one-way analysis of variance.

Question 26

When an interaction effect is present,significant main effects

A)should not be interpreted.
B)should be interpreted,but cautiously.
C)should be interpreted in the usual manner,as they are unaffected by interactions.
D)will never occur.

Question 27

A repeated measures analysis of variance is to an ordinary analysis of variance as a t test for dependent means is to

A)a t test for a single sample.
B)a t test for independent means.
C)a two-way analysis of variance.
D)any factorial analysis of variance.

Question 28

Advanced topic: When considering the power of a main effect in a factorial analysis of variance,all of the following must be taken into account EXCEPT

A)the number of scores per cell.
B)the number of levels of the other grouping variable.
C)the predicted effect size for this main effect.
D)the predicted effect size for the other grouping variable.

Question 29

In research articles,the results of a factorial analysis of variance

A)rarely include a textual description.
B)are often shown in table format only.
C)are usually presented with a combination of table and textual description.
D)typically give brief explanations of the underlying logic of the factorial analysis of variance.

Question 30

If the cell means of a factorial design study are graphed,and the pattern of bars in one section of the graph is different from the pattern in the other section,the pattern indicates that

A)marginal means should also be plotted.
B)there are more participants in one of the conditions.
C)there is an interaction effect.
D)a rounding error was made or the means were plotted improperly on the graph.

Question 31

Dichotomizing a numeric variable usually is done so that

A)one group is high on the variable,and one group is low on the variable.
B)one group is extreme on the variable,and one group has scores near the middle range on the variable.
C)overall differences between means on the measured variable are reduced.
D)overall variance on the measured variable is increased.

Question 32

The scenarios below are possible results of a study in which participants completed a measure of how important religion was to them personally. Participants are either from a Rural or Urban area, and are either Poor or Rich.
A sociologist said,"As far as how important religion is to people,it doesn't matter where they live.What matters is how much money they make." If this conclusion was based on one of these scenarios,which scenario was being considered?

A)Scenario A
B)Scenario B
C)Scenario C
D)none of the above

Question 33

Advanced topic: In a factorial analysis of variance,the effect size for each main and interaction effect

A)is the same for each effect.
B)is the same number for row and column effects,but different for the interaction effect.
C)is different for each row,column,and interaction effect.
D)cannot be calculated because only an effect size for the overall combination of main and interaction effects can be calculated.

Question 34

In a 3 × 3 analysis of variance,the number of cells is

A)1
B)3
C)6
D)9

Question 35

In a 3 × 3 analysis of variance,the number of populations is

A)2
B)3
C)6
D)9

Question 36

Advanced topic: In a two-way analysis of variance,the degrees of freedom for each main effect are

A)the number of cells minus the number of variables.
B)the number of variables minus the total scores within the column or row.
C)the number of levels of the variable minus 1.
D)the total number of scores in that row or column minus 2.

Question 37

In a 2 × 3 analysis of variance,the number of null hypotheses is

A)1
B)2
C)3
D)6

Question 38

Advanced topic: Using the structural model of the two-way analysis of variance,the first computation is the overall deviation of the score from the grand mean.Next,the deviation of the score from its cell's mean,the deviation of the score's row's mean from the grand mean,and the deviation of the score's column's mean from the grand mean are computed.The remaining deviation is the basis of

A)within-groups variance estimate.
B)row between-groups variance estimate.
C)column between-groups variance estimate.
D)interaction between-groups variance estimate.

Question 39

How many F ratios are figured in a two-way analysis of variance?

A)1
B)2
C)3
D)as many as there are cells in the design

Question 40

In a 2 × 2 analysis of variance,the basis for estimating the numerator of the F ratio for the column effects is

A)the variance among the four cell means.
B)the variance between the two column marginal means.
C)the variance between the two row marginal means.
D)the variance between the means of the two diagonals.

Question 41

In a 2 × 3 × 3 analysis of variance,the number of null hypotheses is __________.

Question 42

In a 4 × 2 design,"4" means that __________.

Question 43

A study that contains one between-subjects grouping variable and one within-subjects grouping variable is referred to as a(n)__________.

Question 44

In a 2 × 3 × 3 analysis of variance,the number of cells is __________.

Question 45

In a 4 × 2 design,"2" means that __________.

Question 46

In a graph of a two-way analysis of variance,the absence of an interaction effect is indicated when the pattern of bars in one section is __________ the pattern of bars in the other section.

Question 47

Researchers simultaneously assessed the effects of self-esteem (high or low),mindset (abstract or concrete),and goal orientation (performance or learning)on academic achievement by using a __________ design.

Question 48

The design used in a study of the success of a certain training program in which participants were measured before,immediately after,and three months after completing the program is an example of a(n)__________ design.

Question 49

Interaction effects can be described verbally,numerically,and __________.

Question 50

In a 2 × 2 analysis of variance,the variation between (a)the mean of all the scores in one diagonal,and (b)the mean of all the scores in the other diagonal are used to figure the numerator for a(n)__________ effect.

Question 51

A study exploring the relationship between financial security (shaky,stable,or very secure)and annual income (low,moderate,or high)on satisfaction with life is an example of a two-way factorial design,specifically,a __________ × __________ factorial design.(Give numbers.)

Question 52

In factorial analysis of variance,the assumptions of population normality and equal variances apply to each __________.

Question 53

When the influence of one variable that divides the groups in a study changes according to the level of another variable that divides the groups,a(n)__________ is present.

Question 54

If the top row of a 3 × 2 table of cell means consists of an 8,a 7,and a 6,and the bottom row of a 6,a 7,and an 8,the pattern of means indicates the presence of a(n)__________ effect.

Question 55

If the top row of a 2 × 2 table of cell means consists of a 6 and a 6,and the bottom row of a 4 and a 4,the pattern of means indicates the presence of a(n)__________ effect.

Question 56

The controversial process of using the mean or median of a numeric variable to place participants in two groups,one with high scores on the variable and one with low scores on the variable,is __________.

Question 57

In a two-way analysis of variance,the component of the F ratio that is always the same is the __________.

Question 58

In a two-way analysis of variance,a difference between the means on one variable,ignoring the effects of the other variable,is a(n)__________.

Question 59

An interaction effect can be seen numerically by examining the pattern of __________ means.

Question 60

In a factorial analysis of variance,the numerator for the row main effect is based on the variation among __________.

Question 61

Advanced topic: An analysis of variance table for a two-way analysis of variance has columns for Source,__________,df,MS,and F.(Give a symbol.)

Question 62

Based on the means in the following table: a.Make a graph.
b.Figure marginal means.
c.Assuming all numerical differences are statistically significant,identify which effects are significant and which effects are not significant.

Question 63

Advanced topic: When figuring the effect size for the main and interaction effects in a factorial analysis of variance,the denominator includes a term in which the within-cell population variance estimate is multiplied by the __________.(Do not give a symbol or symbols; say it in words.)

Question 64

Advanced topic: Drug K is thought to heighten the ability of smell.Twenty-four volunteers were randomly assigned to receive one of four dosages of Drug K (no,low,medium,or high)and to either be exposed to competing smells or not exposed to competing smells (present or absent).Their ability to smell was then tested,and the results were as follows. a.Make a chart and graph of the cell and marginal means.
b.Analyze these data using a factorial analysis of variance,testing each effect at the .05 level,and including R² for each effect.
c.Explain your analysis and conclusions to a person who is familiar with one-way analysis of variance (including the structural model),but who does not know anything about factorial designs or the two-way analysis of variance.

Question 65

Advanced topic: N_Cells - df_Columns - df_Rows - 1 = __________.

Question 66

A child psychologist interested in the joint effects of parental marital status (divorced or married)and child disposition (social or shy)asked 12 children to report how many times they had been bullied in the past month.The results were as follows: a.Make a chart and graph of the cell and marginal means.
b.Analyze these data using a factorial analysis of variance,testing each effect at the .01 level,and including R² for each effect.
c.Explain your analysis and conclusions to a person who is familiar with one-way analysis of variance (including the structural model),but who does not know anything about factorial designs or the two-way analysis of variance.

Question 67

Advanced topic: In a factorial analysis of variance,the effect size,the number of participants,and the overall structure of the design influence the __________ of each effect.

Question 68

Advanced topic: If there are four degrees of freedom for the column main effect in a factorial analysis of variance,then there are __________ levels of that variable.

Question 69

Advanced topic: A group of first-year college students at a large state university was asked to rate the importance of school in relation to the rest of their lives.Students were selected from different ethnic groups (type 1,type 2,or type 3)and different socioeconomic status groups (SES; low or high).The results were as follows: a.Make a chart and graph of the cell and marginal means.
b.Analyze these data using a factorial analysis of variance,testing each effect at the .05 level,and including R² for each effect.
c.Explain your analysis and conclusions to a person who is familiar with one-way analysis of variance (including the structural model),but who does not know anything about factorial designs or the two-way analysis of variance.

Question 70

A researcher is interested in the effects of sleep deprivation and caffeine intake on mood.Participants were randomly assigned to a sleep condition (normal or deprived)and a caffeine condition (0 cups,2 cups,or 4 cups).After the manipulations,mood was measured (such that higher numbers indicated better mood).The results were as follows: a.Make a chart and graph of the cell and marginal means.
b.Analyze these data using a factorial analysis of variance,testing each effect at the .01 level,and including R² for each effect.
c.Explain your analysis and conclusions to a person who is familiar with one-way analysis of variance (including the structural model),but who does not know anything about factorial designs or the two-way analysis of variance.