Deck 11: Factorial Designs

Question 1

In a matrix representing the structure of a factorial design, the mean differences among the columns define ____.

A) the main effect for one factor
B) the interaction between the factors
C) the main effect and the interaction between the factors
D) the significance level

Answer 1

A

Question 2

A researcher who is examining the effects of temperature and humidity on the eating behavior of rats uses a factorial experiment comparing three different temperatures (70°, 80°, and 90°) and two humidity conditions (low and high). How many factors are in the experiment?

A) One
B) Two
C) Three
D) Six

Answer 2

B

Question 3

In a factorial design, an interaction between the factors occurs whenever ____.

A) the mean differences between the cells are not explained by the main effects
B) the mean differences between the cells are explained by the main effects
C) there are differences between the overall column means
D) there are differences between the overall row means

Answer 3

A

Question 4

The following data represent the means for each treatment condition in a two-factor experiment. What pattern of results is shown in the data? $\begin{array}{c}\begin{array}{lll}\text { B1 } \\\\\text { B2 } \end{array}\begin{array}{ | l | l| } \hline \\ \mathrm { M } = 30 & \mathrm { M } = 30 \\\\ \mathrm { M } = 40 & \mathrm { M } = 10 \\\hline\end{array}\end{array}$

A) Main effects for both factors and an interaction
B) Main effects for both factors and no interaction
C) A main effect for factor A, no main effect for factor B, and no interaction
D) A main effect for factor B, no main effect for factor A, and no interaction

Question 5

In a 3 × 4 factorial design, there are ____ main effect(s) and ____ interaction(s) possible.

A) three; four
B) two; three
C) two; one
D) one; two

Question 6

In order to determine whether factors influence or interact with each other, a researcher must use ____.

A) two experiments
B) a factorial design
C) a between-subjects design
D) a mixed design

Question 7

How many separate groups of participants would be needed for a between-subjects, two-factor study with three levels of factor A and four levels of factor B?

A) Three
B) Four
C) Seven
D) Twelve

Question 8

How many independent variables are there in an experimental two-factor design?

A) One
B) Two
C) Three
D) Four

Question 9

A researcher who is examining the effects of temperature and humidity on the eating behavior of rats uses a factorial experiment comparing three different temperatures (70°, 80°, and 90°) and two humidity conditions (low and high). The experiment has ____ level(s) for the temperature factor and a total of ____ treatment conditions.

A) one; three
B) three; six
C) six; six
D) three; two

Question 10

The advantage of a two-factor design compared to two single-factor designs is the ability to ____.

A) save time
B) evaluate the interaction
C) simplify the study
D) check the manipulation

Question 11

The following data represent the means for each treatment condition in a two-factor experiment. What pattern of results is shown in the data? $\begin{array}{c}\begin{array}{lll}\text { B1 } \\\\\text { B2 } \end{array}\begin{array}{ | l | l| } \hline \\ \mathrm { M } = 20 & \mathrm { M } = 20 \\\\ \mathrm { M } = 30 & \mathrm { M } = 50 \\\hline\end{array}\end{array}$

A) Main effects for both factors and an interaction
B) Main effects for both factors and no interaction
C) A main effect for factor A, no main effect for factor B, and no interaction
D) A main effect for factor A and an interaction but no main effect for factor B

Question 12

In a 2 × 2 between-subjects factorial experiment, there are a total of ____ treatment conditions in the experiment, and each participant serves in ____ condition(s).

A) 2; 1
B) 4; 1
C) 2; 2
D) 4; 2

Question 13

The following data show the means for four treatment conditions as well as the overall means for the columns and the rows. For these data, what numbers are compared to assess the main effect of factor A? $$\begin{array} {| l | l | l | l| } \hline \mathrm { B } 1 & \mathrm { M } = 20 & \mathrm { M } = 60 & \mathrm { M } = 40 \\\mathrm { B } 2 & \mathrm { M } = 30 & \mathrm { M } = 70 & \mathrm { M } = 50\\\hline\end{array}$$

A) 30; 70
B) 20; 30
C) 40; 50
D) 25; 65

Question 14

When the means for a two-factor study are displayed in a graph and the lines in the graph are perfectly parallel, what can you conclude about the main effects and interaction?

A) There is no main effect for either of the two factors.
B) There is a main effect for both of the two factors.
C) There is no interaction between factors.
D) There are no main effects and no interaction between factors.

Question 15

The following data represent the means for each treatment condition in a two-factor experiment. What pattern of results is shown in the data? $\begin{array}{c}\begin{array}{lll}\text { B1 } \\\\\text { B2 } \end{array}\begin{array}{ | l | l| } \hline \\ \mathrm { M } = 10 & \mathrm { M } =20 \\\\ \mathrm { M } = 10 & \mathrm { M } = 30 \\\hline\end{array}\end{array}$

A) Main effects for both factors and an interaction
B) Main effects for both factors and no interaction
C) A main effect for factor A, no main effect for factor B, and no interaction
D) A main effect for factor A and an interaction but no main effect for factor B

Question 16

How many main effects are there in a 2 × 3 factorial design?

A) Two
B) Three
C) Six
D) Nine

Question 17

In a 2 × 3 between-subjects factorial experiment, there are ____ groups of participants.

A) two
B) three
C) six
D) eight

Question 18

In a two-factor experiment with two levels of factor A and 2 levels of factor B, three of the treatment means are essentially identical and one is substantially different from the others. What result(s) would be produced by this pattern of treatment means?

A) A main effect for factor A only
B) A main effect for factor B only
C) An interaction between A and B
D) Main effects for both A and B, and an interaction

Question 19

How many independent variables are there in a 2 × 2 × 2 factorial design?

A) Two
B) Three
C) Four
D) Eight

Question 20

In an experiment examining the effects of task difficulty (easy/hard) for men and women, the factors are ____.

A) male and female
B) easy and hard
C) male, female, easy, and hard
D) difficulty and gender

Question 21

A researcher conducts a two-factor study to evaluate the effect of a medication for males and for females. If the results of the study show a 10-point main effect for the medication (participants taking the medicine average 10 points lower than those in the no-medication condition) and also show a significant interaction between medication and gender, then what can the researcher conclude about the effect of the medication?

A) The medication lowers scores by around 10 points and the effect is the same for males and females.
B) Although the average effect of the medication is to lower scores by 10 points, the exact effect depends on the gender of the participant.
C) Because there is an interaction, you cannot conclude that the medication has any effect.
D) Additional information is needed to come to a conclusion.

Question 22

How can order effects be measured and evaluated?

A) Limit the number of participants in each group.
B) Use a factorial design adding a participant variable (such as age) as a second factor.
C) Use a factorial design with the order of treatments as a second factor.
D) Randomize the order of the treatments.

Question 23

A clinician claims that the effectiveness of a new treatment varies depending on the gender of the client. Specifically, the new treatment has been shown to be very effective for females, but the treatment has little or no effect for males. In this example, ____.

A) there is an interaction between the treatment and client's gender
B) there is no interaction between the treatment and client's gender
C) there is no main effect of treatment
D) there is no main effect of gender

Question 24

The following data represent the means for each treatment condition in a two-factor experiment. Note that one mean is not given. What value for the missing mean would result in NO interaction between A and B? $\quad$$\quad$$\quad$$\quad$$\text {B1 }$$\quad$$\quad$$\quad$$\text {B2 }$
$\begin{array}{c}\begin{array}{lll}\text { A1 } \\\\\text {A2 } \end{array}\begin{array}{ | l | l| } \hline \\40\quad \quad&60\quad\quad \\\\20 & 40 \\\hline\end{array}\end{array}$

A) 0
B) 10
C) 20
D) 40

Question 25

A two-factor study with two levels of factor A and three levels of factor B uses a separate group of n = 5 participants in each treatment condition. How many participants are needed for the entire study?

A) 5
B) 10
C) 25
D) 30

Question 26

The following data represent the means for each treatment condition in a two-factor experiment. Note that one mean is not given. What value for the missing mean would result in no main effect for factor B? $\quad$$\quad$$\quad$$\quad$$\text {B1 }$$\quad$$\quad$$\quad$$\text {B2 }$
$\begin{array}{c}\begin{array}{lll}\text { A1 } \\\\\text {A2 } \end{array}\begin{array}{ | l | l| } \hline \\20\quad \quad&10\quad\quad \\\\40 & \\\hline\end{array}\end{array}$

A) 20
B) 30
C) 40
D) 50

Question 27

Which statement accurately describes a two-factor analysis of variance?

A) It conducts one hypothesis test and produces one F -ratio.
B) It conducts two separate hypothesis tests and produces two F -ratios.
C) It conducts three separate hypothesis tests and produces three F -ratios.
D) It conducts three separate hypothesis tests with the number of F -ratios produced depending on the number of levels.

Question 28

A factorial study measures allergy symptoms before and after taking medication for a group taking the real medication and a control group taking a placebo. What kind of design is being used?

A) Between-subjects design
B) Within-subjects design
C) Repeated measures design
D) Mixed design

Question 29

What statistical technique should be used to evaluate the results of a two-factor, between-subjects study?

A) A two-factor repeated-measures ANOVA
B) A two-factor independent-measures ANOVA
C) A two-factor mixed design ANOVA
D) A t -test

Question 30

The students in one gym class receive a self-esteem program as part of their sports training. To evaluate the program, a researcher measures self-esteem for the students before and after the program and compares their scores with those from another class that did not receive the program but was measured at the same two times. What kind of design is being used?

A) Between-subjects design
B) Within-subjects design
C) Repeated measures design
D) Mixed design

Question 31

What is the primary disadvantage of adding factors to investigate a four-way interaction?

A) It is difficult to interpret such a complex interaction.
B) It makes it nearly impossible to generate statistically significant results.
C) It reduces the differences between the groups too much.
D) It does not provide a complete picture of how the factor affects the dependent variable.

Question 32

The results from a two-factor ANOVA show no main effect for factor A but a significant interaction. What can you conclude based on this pattern of results?

A) Factor A has no effect on the participants' scores.
B) Factor A may have an effect but, if so, it depends on the levels of factor B.
C) Because the interaction is significant, factor A must also have an effect.
D) The effect of factor A is constant across all levels of factor B.

Question 33

Which outcome is possible in a 2 × 2 factorial design?

A) Two main effects and two interactions
B) A main effect for one factor, no main effect for the other factor, and two interactions
C) No main effect for either factor and one interaction
D) A four-way interaction

Question 34

A factorial study compares the effectiveness of two allergy medications by measuring symptoms immediately before taking the medication, 30 minutes after the medication, and 3 hours after the medication. Half of the participants take one of the medications and the rest take the second medication. Which statement accurately describes this study?

A) It is a between-subjects design that uses both the experimental and nonexperimental strategies.
B) It is a between-subjects experiment.
C) It is a nonexperimental between-subjects design.
D) It combines between- and within-subjects designs and uses both the experimental and nonexperimental strategies.

Question 35

A graph of a two-factor study indicates an interaction when the lines on the graph ____.

A) are parallel
B) cross or converge
C) are steep in slope
D) have the same slope

Question 36

How can variance be reduced in a between-subjects design?

A) Limit the number of participants in each group.
B) Use a factorial design adding a participant variable (such as age) as a second factor.
C) Reduce the number of treatments.
D) Reduce the strength of the treatment.

Question 37

If participating in treatment A before treatment B causes more fatigue than participating in treatment B before treatment A, then there are ________.

A) no interactions between the factors
B) no order effects
C) symmetrical order effects
D) nonsymmetrical order effects

Question 38

Why might a researcher add a factor when replicating a previously published study?

A) To see if the treatment effects are the same in a different situation
B) To turn a nonexperimental study into a true experiment
C) To turn a within-subjects study into a between-subjects study
D) To turn a between-subjects study into a within-subjects study

Question 39

What is the relationship between main effects and interactions?

A) At least one of the factors involved in the interaction must have a main effect.
B) None of the factors in the interaction can have a main effect.
C) All of the factors involved in the interaction must have main effects.
D) The existence of an interaction is independent of the main effects.

Question 40

The following data represent the means for each treatment condition in a two-factor experiment. Note that one mean is not given. What value would result in NO interaction between factors? $\begin{array}{c}\begin{array}{lll}\text { A1 } \\\\\text {A2 } \\\end{array}\begin{array}{ | l | l| } \hline \\20\quad \quad&60\quad\quad \\\\50 & \\\hline\end{array}\end{array}$

A) 60
B) 70
C) 80
D) 90

Question 41

A two-factor experimental design evaluates two main effects and one interaction.

Question 42

A two-factor study comparing task performance for males versus females (factor 1) for three different levels of task difficulty (factor 2) would be described as a 2 × 3 design.

Question 43

A two-factor study compares the effectiveness of two different treatments (factor 1) by measuring performance before treatment, immediately after treatment, and three months after treatment (factor 2) for each participant. There are 100 participants, 50 are randomly assigned to treatment A and 50 to treatment B. The results from this study should be evaluated with mixed-design two-factor analysis of variance.

Question 44

A researcher can replicate and expand a study by repeating the previous study in every way except adding an additional factor.

Question 45

It is possible for the results of a two-factor study to show an interaction even though there is no main effect for either factor.

Question 46

In a matrix representing the structure of a factorial design, the mean differences between the rows define the interaction between the factors.

Question 47

A two-factor study compares two different treatment conditions (factor 1) for males and females (factor 2). In this study, the males have an average score of 20 in the first treatment and an average of 25 in the second. The females average 35 in the first treatment and 45 in the second. For this study, there is no interaction.

Question 48

In a two-factor study, it is possible to have one experimental factor and one nonexperimental factor.

Question 49

If the A × B interaction is significant, then at least one of the two main effects also must be significant.

Question 50

A two-factor study compares three different treatment conditions (factor 1) for males and females (factor 2). In this study, the main effect for gender is determined by comparing the overall mean score for the males (averaged over the three treatments) and the corresponding overall mean score for the females (averaged over the three treatments).

Question 51

A two-factor study compares two levels of factor A and three levels of factor B with a separate sample of 5 participants in each treatment condition. This study will use a total of 25 participants.

Question 52

In a two-factor design, there are two separate interactions.

Question 53

In a two-factor design, an interaction means that the effect of one factor depends on the levels of the second factor.

Question 54

A doctor suspects that the effectiveness of a new cholesterol medication depends on the age of the patient. If the doctor is correct, the results from a two-factor study comparing medication versus no-medication for young versus old patients should produce an interaction.

Question 55

A two-factor experimental design must involve at least four different treatment conditions.

Question 56

In a two-factor experiment, an interaction can distort the main effects of either or both factors.

Question 57

In a two-factor study, it is possible to have one between-subjects factor and one within-subjects factor.

Question 58

It is often possible to reduce the variance in a between-subjects design by using a participant variable such as age or gender as a second factor.

Question 59

One advantage of a factorial research design is that is creates a more realistic situation in which to observe the relationship between variables.

Question 60

If a researcher adds order of treatment as a factor, and finds that the means are the same whether a treatment is presented first or second, then there are no order effects present in that study.

Question 61

For a two-factor design, describe what is meant by a "main effect" and an "interaction"?

Question 62

Describe how a second factor can be used to reduce the variance in a between-subjects experiment.

Question 63

Explain what it means to say that main effects and interactions are all independent.

Question 64

If the means from a two-factor study are displayed in a graph, how can you determine whether there is an interaction between factors?

Question 65

Explain how a researcher can create a factorial study that combines the experimental research strategy with either the quasi-experimental or nonexperimental strategies, and describe the two quasi-independent variables that are often used.

Question 66

Describe two situations in which factorial designs are commonly used.

Question 67

Explain how a factorial study can combine between-subjects and within-subjects designs and why a researcher might want a mixed-design study.