Deck 14: Factorial Analysis of Variance

Question 1

Factorial ANOVA allows us to

A) determine which means differ significantly when there are more than two groups.
B) examine the effects of more than one independent variable.
C) conduct repeated t tests using only one alpha level.
D) All of the above are true.

Answer 1

B

Question 2

In research, a factor is

A) a level of an independent variable.
B) an extraneous variable that has to be controlled.
C) experiment-wise alpha level.
D) an independent variable.

Answer 2

D

Question 3

Which is the correct notation for a factorial ANOVA with two independent variables, each presented at three levels?

A) 2 x 2 x 2
B) 2 x 3
C) 3 x 3
D) 2 x 2 x 3

Answer 3

C

Question 4

A 4 x 4 ANOVA has __________ independent variables, each presented at ___________ levels.

A) two; four
B) four; two
C) two; sixteen
D) four; eight

Question 5

How many independent variables are involved in a 4 x 3 x 2 study?

A) four
B) three
C) two
D) twenty four

Question 6

In factorial analysis of variance, main effects

A) provide the same kind of information that would be obtained by conducting separate one-way ANOVAs.
B) refer to how the independent variables are affected by the dependent variable.
C) refer to any effects that are statistically significant.
D) All of the above are true.

Question 7

How many total participants would be involved in a 3 x 3 ANOVA if each group is made up of four participants?

A) 9
B) 18
C) 24
D) 36

Question 8

How many main effects are possible in a 3 x 2 x 3 ANOVA?

A) nine
B) eighteen
C) three
D) eight

Question 9

Main effects refer to

A) any interactions among the independent variables in a factorial ANOVA.
B) the effects due to the independent variables in a factorial ANOVA.
C) the effects due to the dependent variables in a factorial ANOVA.
D) significant effects.

Question 10

In a factorial ANOVA, the effects created by the different levels of an independent variable are referred to as

A) level effects.
B) variance.
C) interaction effects.
D) main effects.

Question 11

In a factorial ANOVA, interaction effects refer to

A) the effects due the different levels of an independent variable.
B) the case in which there is more than one main effect.
C) the case in which one independent variable is affected by different levels of other independent variables.
D) how the dependent variable is influenced by an independent variable.

Question 12

The information provided by a factorial ANOVA includes

A) the effect of a single independent variable.
B) the separate effects of more than one independent variable.
C) the combined effects of more than one independent variable.
D) All of the above are true.

Question 13

The results of two factors can be examined using a

A) two sample t test, independent samples design.
B) two sample t test, between samples design.
C) two-way ANOVA.
D) one-way ANOVA, between samples design.

Question 14

Reaction time is measured after a weight lifting exercise for six different groups. Factor A was the amount of the weights lifted (5, 10, or 15 pounds). Factor B was age group (teenager or adult). The researchers found that the reaction time for the different age groups did not depend on the amount of weights lifted. Based on this information, the researchers can conclude that

A) Factor A was not significant.
B) Factor B was not significant.
C) There was no interaction between Factors A and B.
D) All of the above are true.

Question 15

In the line graph of a two-way ANOVA, no significant interaction would be suggested by lines that

A) are parallel.
B) intersect.
C) have data points that are equidistant apart.
D) Both "a" and "c" are true.

Question 16

In the line graph of a two-way ANOVA, if the lines for Factors A and B cross like an X,

A) a main effect is suggested for Factor A.
B) a main effect is suggested for Factor B.
C) an interaction between Factors A and B is suggested.
D) All of the above are true.

Question 17

In a two-way ANOVA, there are __________ sources of between-treatments variance.

A) two
B) three
C) four
D) five

Question 18

In the line graph of a two-way ANOVA, lines that have data points that are equidistant apart suggest

A) main effects for Factors A and B.
B) no main effects for Factors A and B.
C) no significant interaction.
D) a significant interaction.

Question 19

How many significance tests would be conducted for a two-way ANOVA?

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

Question 20

The null hypothesis for Factor A of a two-way ANOVA is that

A) all of the means for Factor A are equal.
B) all of the variances for Factor A are equal.
C) all of the scores for the groups of Factor A are normally distributed.
D) some of the means for Factor A are not equal.

Question 21

The alternative hypothesis for Factor A of a two-way ANOVA is that

A) all of the means for Factor A are equal.
B) all of the variances for Factor A are equal.
C) all of the scores for the groups of Factor A are normally distributed.
D) some of the means for Factor A are not equal.

Question 22

The null hypothesis for the interaction between factors A and B of a two-way ANOVA is that

A) Factors A and B have a significant interaction.
B) Factors A and B do not have a significant interaction.
C) all of the means for Factors A and B are equal.
D) some of the means for Factors A and B are not equal.

Question 23

A cell in a factorial ANOVA

A) is a particular treatment group.
B) is identified by its own subscript.
C) represents a level of a particular independent variable.
D) All of the above are true.

Question 24

_______________ refers to the variability within each group due to individual differences and experimental error.

A) SS_wi
B) SS_bet
C) SS_total
D) SS_interaction

Question 25

______________ refers to the variability between the different groups due to Factor A, Factor B, and the interaction between Factors A and B.

A) SS_total
B) SS_wi
C) SS_bet
D) SS_interaction

Question 26

In a two-factor ANOVA, ____________ is broken down into SS_A, SS_B, and SS_AB.

A) SS_wi
B) SS_bet
C) SS_total
D) SS_interaction

Question 27

In a two-way ANOVA, SS_bet is made up of

A) SS_A, SS_B, and SS_wi.
B) SS_wi and S_interaction.
C) SS_wi and SS_total.
D) SS_A, SS_B, and SS_AB.

Question 28

How many mean square values are required for a 2 x 2 ANOVA?

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

Question 29

What is df_bet(AB) for a 3 x 4 ANOVA?

A) 2
B) 6
C) 12
D) 4

Question 30

What is df_wi for a 4 x 2 ANOVA with 5 participants in each group?

A) 32
B) 200
C) 30
D) 40

Question 31

If df_tot = 63, df_bet(A) = 3, df_bet(B) = 3, and df_bet(AB) = 9, what is df_wi?

A) 12
B) 16
C) 48
D) 56

Question 32

A 4 x 3 ANOVA has five participants in each cell. What is N_tot?

A) 60
B) 45
C) 20
D) 12

Question 33

In a factorial ANOVA with df_bet(A) = 5 and df_bet(B) = 4, k = _______.

A) 9
B) 20
C) 30
D) 40

Question 34

In a factorial ANOVA with df_bet(A) = 4, df_bet(B) = 3, and df_wi = 100, N_tot = _________.

A) 80
B) 88
C) 112
D) 120

Question 35

In a factorial ANOVA with df_bet(A) = 2, df_bet(B) = 4, df_wi = 30, k = _______ and N_tot = ________.

A) 8; 38
B) 15; 45
C) 8; 22
D) 15; 15

Question 36

How many F-statistics are required for a 3 x 4 ANOVA?

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

Question 37

A 4 x 3 factorial analysis of variance was conducted with results showing a significant interaction. In addition to the interaction, we can conclude that

A) at least one of the factors was also significant.
B) both of the factors were also significant.
C) neither of the factors alone was significant.
D) A significant interaction does not provide information about the significance of the individual factors alone.

Question 38

If the results of a 2 x 3 ANOVA produce a significant interaction as well as a significant main effect for one of the factors, then

A) caution should be exercised when interpreting the main effect due to the influence of the other factor.
B) the main effect can be interpreted in the same way as with a one-way ANOVA, using a post hoc test.
C) both the interaction and main effect can be interpreted directly at face value since both are significant.
D) the main effect can be interpreted directly since the main effect for the other factor was not significant.

Question 39

A supplement to the eta squared effect size is

A) gamma squared.
B) omega squared.
C) delta squared.
D) zeta squared.

Question 40

When interpreting a significant main effect in a factorial ANOVA

A) the effects of other independent variables are taken into account.
B) the effects of other independent variables are ignored.
C) the effects of the interaction between the independent variables are taken into account.
D) Both "a" and "c" are correct.

Question 41

What is the difference between a one-way ANOVA and a factorial ANOVA?

Question 42

A researcher is studying the effects of physical activity (low, moderate, and high), gender (male, female), and diet (low fat, low carb, intermittent fasting, and vegan) on blood cholesterol levels. What is the correct notation for this study?

Question 43

How many independent variables are involved in a 2 x 2 factorial ANOVA?

Question 44

Define the following terms:
• factor
• main effect
• interaction effects

Question 45

How can line graphs be used to identify main effects and interaction effects in a two-way ANOVA?

Question 46

Using symbolic notation, write the null hypotheses for a study that is examining the effects of three different kinds of incentives (Factor A) for males and females (Factor B) on purchasing decisions.

Question 47

A 3 x 3 ANOVA is conducted with 45 participants distributed equally across all conditions. How many groups were there and what was the sample size of each group?

Question 48

A factorial analysis was conducted with 80 participants distributed equally across the four levels of Factor A and five levels of Factor B. Determine df_bet(A), df_bet(B), df_bet(AB), and df_wi.

Question 49

In a two-way ANOVA, if df_bet(A) = 2, df_bet(B) = 3, and df_wi = 72, how many treatment groups were involved in the study and how many subjects participated?

Question 50

A researcher is studying the effects of room temperature and music on basic logic skills (dependent variable). Room temperature (Factor A) was varied at three levels: warm, moderate, and cool. Soft background music (Factor B) was either present or absent. Participants were given twenty minutes under these varying conditions to solve fifteen simple logic problems. Sum of squares and degrees of freedom values are provided in the table below. Assume an alpha level of α = .01.

A) Complete the table.
B) Determine F_crit for each of the main effects and the interaction effect.
C) Using words, write a statement of conclusion

Question 51

Suppose a study is examining the mean enjoyment ratings for different types of television programs (Factor A) according to gender (Factor B). In one study, females gave a mean enjoyment rating of 17 to cooking shows and 8 to westerns. Males gave a mean rating of 10 to cooking shows and 15 to westerns. Does there appear to be an interaction effect between Factors A and B? Create a line graph to help make this determination. Put Factor A along the horizontal axis.

Question 52

The annual Roundup B-B-Q Festival is underway. It is a huge event with thousands of attendees and various kinds of cook-offs. Attendees were randomly sampled to taste and rate the flavor of four variations of potato salad. Factor A, temperature, was varied at two levels (hot or cold). Factor B, bacon, was also varied at two levels (the potato salad either did or did not contain bacon). Summary values for the study are below. Draw a line graph representing the study with Factor A long the horizontal axis and write a statement of conclusion.