Deck 16: Introduction to the Two-Way Analysis of Variance

Question 1

The row variance estimate MS_rows and the column variance estimate MS_columns are used to measure _________.

A) the main effects of the independent variables
B) the interaction effects of the independent variables
C) the main effects of the independent variables and the interaction effects of the independent variables
D) none of these

Answer 1

the main effects of the independent variables

Question 2

An investigator collects the following data on variables A and B , using a two-way independent groups design. Use a = 0.05 in analyzing the data. F _obt for the interaction equals _________.

A) 2.66
B) 16.34
C) 29.11
D) 11.23

Answer 2

2.66

Question 3

A significant interaction effect occurs when _________.

A) there are no main effects
B) variable A has a main effect and variable B does not
C) the combined effects of variables A and B yield an unexpected effect
D) none of these

Answer 3

the combined effects of variables A and B yield an unexpected effect

Question 4

A main effect for variable A means that _________.

A) the effect of variable A is the same over all levels of variable B
B) the effect of variable A is significant when averaged over all levels of variable B
C) the effect of variable A is not the same over all levels of variable B
D) variable A has a greater effect than variable B

Question 5

In a two-way ANOVA, if there is a significant interaction between Factor A and Factor B , which of the following may be true?

A) the effect of Factor A is not the same at all levels of Factor B
B) The effect of Factor B is not the same at all levels of Factor A
C) the effects of the two Factors do not differ across levels
D) the effect of Factor A is not the same at all levels of Factor B and/or The effect of Factor B is not the same at all levels of Factor A

Question 6

If the null hypothesis is correct, which of the following is (are) an estimate of s 2 ?

A) MS _rows
B) MS _columns
C) MS _within-cells
D) MS _interaction
E) all of these

Question 7

Which of the following are called "main effects" in a two-way analysis of variance?

A) the effect of Factor A
B) the effect of Factor B
C) the interaction of Factors A and B
D) the effect of Factor A and B

Question 8

Which of the following increase(s) as the interaction effect increases?

A) MS _rows
B) MS _columns
C) MS _within-cells
D) MS _interaction

Question 9

The conclusion regarding the B variable is _________.

A) reject H ₀ ; variable B has no effect
B) retain H ₀ ; chance is a reasonable explanation
C) reject H ₀ ; there is a significant main effect for variable B
D) accept H ₀ ; chance is a reasonable explanation

Question 10

Which of the following increase(s) as the effect of the B variable increases?

A) MS _rows
B) MS _columns
C) MS _within-cells
D) MS _interaction

Question 11

An investigator collects the following data on variables A and B , using a two-way independent groups design. Use a = 0.05 in analyzing the data. F _crit for the A variable equals _________.

A) 3.40
B) 7.82
C) 5.81
D) 4.26

Question 12

The conclusion regarding the A variable is _________.

A) retain H ₀ ; chance is a reasonable explanation
B) reject H ₀ ; there is a significant main effect for variable A
C) accept H ₀ ; variable A has no real effect
D) reject H ₀ ; chance is a reasonable explanation

Question 13

An investigator collects the following data on variables A and B , using a two-way independent groups design. Use a = 0.05 in analyzing the data. F crit for the interaction equals _________.

A) 3.40
B) 7.82
C) 5.81
D) 4.26

Question 14

An investigator collects the following data on variables A and B , using a two-way independent groups design. Use a = 0.05 in analyzing the data. F _crit for the B variable equals _________.

A) 3.40
B) 7.82
C) 5.81
D) 4.26

Question 15

Which of the following increase(s) as the effect of the A variable increases?

A) MS _rows
B) MS _columns
C) MS _within-cells
D) MS _interaction

Question 16

An investigator collects the following data on variables A and B , using a two-way independent groups design. Use a = 0.05 in analyzing the data. F _obt for the A variable equals _________.

A) 2.66
B) 16.34
C) 29.11
D) 11.23

Question 17

The two-way analysis of variance _________.

A) assesses the effects of two independent variables in one experiment
B) allows an assessment of the interaction between two independent variables
C) results in calculation of three F ratio's
D) all of these

Question 18

An investigator collects the following data on variables A and B , using a two-way independent groups design. Use a = 0.05 in analyzing the data. F _obt for the B variable equals _________.

A) 2.66
B) 16.34
C) 29.11
D) 11.23

Question 19

If there are no main effects, then _________.

A) MS_columns / MS_within-cells is less than F _crit
B) MS_rows / MS_within-cells is less than F _crit
C) MS_interaction / MS_within-cells is less than F_crit
D) MS_columns / MS_within-cells is less than F _crit and MS_rows / MS_within-cells is less than F _crit

Question 20

If the A variable has a real effect, _________.

A) MS_columns / MS_within-cells must equal or exceed F _crit
B) MS_rows / MS_within-cells must equal or exceed F _crit
C) it is possible that MS_columns / MS_within-cells is less than F _crit
D) it is possible that MS_rows / MS_within-cells is less than F _crit

Question 21

Given the following data, collected from an independent groups design. When analyzing the data, assume that a = 0.05. The conclusion regarding the main effect of variable A is _________.

A) Retain H₀ . We cannot conclude variable A has main effect.
B) Accept H₀ . We cannot conclude variable A has main effect.
C) Reject H₀ . Variable A has a significant main effect.
D) Reject H₀ . Variable A has no effect.

Question 22

Consider the following graphic results from a 2 2 factorial experiment. These results show _________.

A) there is a significant main effect for factor A , no other significant effects
B) there is a significant main effect for factor B , no other significant effects
C) there is a significant interaction effect, no other significant effects
D) there is a significant main effect for factor A , a significant interaction effect, and no other significant effects
E) there is a significant main effect for factor B , a significant interaction effect, and no other significant effects

Question 23

The two-way analysis of variance _________.

A) assesses the effects of two independent variables in one experiment
B) allows an assessment of the interaction between two independent variables
C) results in calculation of three F ratio's
D) all of these

Question 24

Given the following data, collected from an independent groups design. When analyzing the data, assume that a = 0.05. The value of F _obt for evaluating the row column effect is _________.

A) 0.66
B) 6.23
C) 0.29
D) 5.28

Question 25

Consider the following graphic results from a 2 2 factorial experiment. These results show _________.

A) there are no significant main effects or interaction effects
B) there is a significant main effect for factor A , no other significant effects
C) there is a significant main effect for factor B , no other significant effects
D) there is a significant interaction effect, no other significant effects

Question 26

Given the following data, collected from an independent groups design. When analyzing the data, assume that a = 0.05. The value of F _crit for evaluating the column effect is _________.

A) 3.40
B) 7.82
C) 4.26
D) 5.61

Question 27

Given the following data, collected from an independent groups design. When analyzing the data, assume that a = 0.05. The conclusion regarding the main effect of variable B is _________.

A) Retain H₀ . We cannot conclude variable B has main effect.
B) Accept H₀ . We cannot conclude variable B has main effect.
C) Reject H₀ . Variable B has a significant main effect.
D) Reject H₀ . Variable B has no effect.

Question 28

Given the following data, collected from an independent groups design. When analyzing the data, assume that a = 0.05. The conclusion regarding the interaction effect of variables A and B is _________.

A) Retain H₀ . We cannot conclude there is a significant interaction
B) Accept H₀ . There is no interaction effect between A and B
C) Reject H₀ . There is a significant interaction effect.
D) Reject H₀ . There is no interaction effect between A and B

Question 29

Consider the following graphic results from a 2 2 factorial experiment. These results show _________.

A) there are no significant main effects or interaction effects
B) there is a significant main effect for factor A , no other significant effects
C) there is a significant main effect for factor B , no other significant effects
D) there is a significant interaction effect, no other significant effects

Question 30

The row variance estimate MS_rows and the column variance estimate MS_columns are used to measure _________.

A) the main effects of the independent variables
B) the interaction effects of the independent variables
C) the main effects of the independent variables and the interaction effects of the independent variables
D) none of these

Question 31

Which of the following are called "main effects" in a two-way analysis of variance?

A) the effect of Factor A
B) the effect of Factor B
C) the interaction of Factors A and B
D) all of these
E) the effect of Factor A and B

Question 32

Given the following data, collected from an independent groups design. When analyzing the data, assume that a = 0.05. The value of F _crit for evaluating the row effect is _________.

A) 3.40
B) 7.82
C) 4.26
D) 5.61

Question 33

Given the following data, collected from an independent groups design. When analyzing the data, assume that a = 0.05. The value of F _crit for evaluating the row column effect is _________.

A) 3.40
B) 7.82
C) 4.26
D) 5.61

Question 34

Consider the following graphic results from a 2 2 factorial experiment. These results show _________.

A) there are no significant main effects or interaction effects
B) there is a significant main effect for factor A , no other significant effects
C) there is a significant main effect for factor B , no other significant effects
D) there is a significant interaction effect, no other significant effects

Question 35

Consider the following graphic results from a 2 2 factorial experiment. These results show _________.

A) there are no significant main effects or interaction effects
B) there is a significant main effect for factor A , no other significant effects
C) there is a significant main effect for factor B , no other significant effects
D) there is a significant interaction effect, no other significant effects

Question 36

Given the following data, collected from an independent groups design. When analyzing the data, assume that a = 0.05. The value of F _obt for evaluating the column effect is _________.

A) 0.66
B) 6.23
C) 0.29
D) 5.28

Question 37

In a two-way ANOVA, if there is a significant interaction between Factor A and Factor B , which of the following may be true?

A) the effect of Factor A is not the same at all levels of Factor B
B) the effect of Factor B is not the same at all levels of Factor A
C) the effects of the two Factors do not differ across levels
D) the effect of Factor A is not the same at all levels of Factor B and/or The effect of Factor B is not the same at all levels of Factor A
E) need more information

Question 38

How many variance estimates are there in a 2 x 2 factorial design?

A) 1
B) 2
C) 3
D) 4

Question 39

Given the following data, collected from an independent groups design. When analyzing the data, assume that a = 0.05. The value of F _obt for evaluating the row effect is _________.

A) 0.66
B) 6.23
C) 0.29
D) 5.28

Question 40

The conclusion regarding the interaction is _________.

A) retain H ₀ ; chance is a reasonable explanation
B) accept H ₀ ; chance is a reasonable explanation
C) reject H ₀ ; there is a significant interaction between variables A and B
D) reject H ₀ ; there is no interaction between variables A and B

Question 41

ΣS_w for one-way ANOVA and ΣS_within-cells for two-way ANOVA are conceptually similar.

Question 42

ΣS_B for one-way ANOVA is conceptually similar to ΣS_rows and ΣS_columns for two-way ANOVA.

Question 43

In two-way ANOVA, ΣS_total is partitioned into ΣS_rows , ΣS_within-cells , ΣS_columns and ΣS_interaction .

Question 44

To answer this question, refer to the following two-way ANOVA summary table What is the value for df _within-cells ?

A) 2
B) 1
C) 34
D) 24

Question 45

Differences among cell means are used to assess the interaction effect.

Question 46

To answer this question, refer to the following two-way ANOVA summary table What is the value for MS_within-cells ?

A) 260.4
B) 130.2
C) 10.85
D) 8.98

Question 47

The row variance estimate does not change as the effect of independent variable A increases.

Question 48

A significant interaction effect occurs when the effects of one of the variables is not the same at all levels of the other variable.

Question 49

Differences among row means are used to assess the interaction effect.

Question 50

The within-cells variance estimate measures treatment effects.

Question 51

Differences among column means are used to assess the main effect of one of the variables

Question 52

Consider the following graphic results from a 2 x 2 factorial experiment. Do you think there is a significant A x B interaction?

A) Yes
B) No, it is not possible to have a significant interaction in a 2 x 2 factorial experiment.
C) No, the lines should be parallel for a significant interaction
D) none of these

Question 53

To answer this question, refer to the following two-way ANOVA summary table What is the value for MS_rows ?

A) 225.25
B) 450.5
C) 225.50
D) 9.39

Question 54

To answer this question, refer to the following two-way ANOVA summary table What is the value of F _obt for Rows?

A) 20.76
B) 195.87
C) 1.94
D) 22.53

Question 55

To answer this question, refer to the following two-way ANOVA summary table What is the value for ΣS_within-cells ?

A) 160.4
B) 260.4
C) 250.4
D) 150.4

Question 56

In the one-way ANOVA, the within-groups variance estimate is like _________ in two-way ANOVA.

A) the row variance estimate
B) the within-cells variance estimate
C) the column variance estimate
D) the interaction variance estimate

Question 57

To answer this question, refer to the following two-way ANOVA summary table What is the value of F _obt for Columns?

A) 11.64
B) 10.73
C) 4.85
D) 4.01

Question 58

Which of the following are not true statements?

A) The main effect of factor A is the effect of factor A averaged over the levels of factor B .
B) The main effect of factor B is the effect of factor B averaged over the levels of factor A .
C) An interaction effect occurs when the effect of one factor is the same for all levels of the other factor.
D) All of these statements are false.

Question 59

The column variance estimate increases as the effect of independent variable B increases.

Question 60

ΣS _total = ΣS_rows + ΣS_columns + ΣS_within-cells.

Question 61

MS_within-cells is sensitive to the effects of variable A or B .

Question 62

It is not possible to have an interaction effect unless one of the variables also has a main effect.

Question 63

A factorial experiment is one in which the effect of two or more factors is assessed in one experiment.

Question 64

In a two-way ANOVA, we do three F tests.

Question 65

In general, the alternative hypothesis for two-way ANOVA can be directional.

Question 66

It is not possible to have a significant interaction effect unless one of the variables also has a significant main effect.

Question 67

A two factor experiment yields no more information than two single factor experiments.

Question 68

MS_total = MS_rows + MS_columns + MS_interaction + MS_within-cells .

Question 69

The sum of df _rows , df _columns , df _interaction , and df _within-cells is N - 1.

Question 70

A main effect refers to the average effect of the variable.

Question 71

If there is an interaction between the variables of "activity level" and "time of day," this means that activity level does not have the same effect at different times of day.

Question 72

Two-way ANOVA is like two one-way ANOVA experiments, plus it gives us the ability to analyze the interaction of the two variables.

Question 73

A "mean square" is the same thing as a "variance estimate".

Question 74

A 2 * 4 factorial experiment has 2 levels of one variable and 4 levels of the other variable.

Question 75

MS_rows is sensitive to the effects of variable A .

Question 76

The homogeneity of variance assumption assumes the population scores from which each of the samples are drawn are normally distributed.

Question 77

In a two-way ANOVA, it is possible to have significant main effects without a significant interaction.

Question 78

In a two-way ANOVA, there are three possible main effects and one interaction.

Question 79

ΣS_total = ΣS_rows + ΣS_columns + ΣS_interaction + ΣS_within-cells .

Question 80

MS_columns is a measure of only s 2 , regardless of whether the variables have a main effect.