Deck 12: Understanding the Two-Way Analysis of Variance

Question 1

A two-way analysis of variance involves

A)two dependent variables.
B)two levels of one dependent variable.
C)two independent variables.
D)two levels of one independent variable.

Answer 1

C

Question 2

In a two-way ANOVA, an F involving a comparison among the means of the cells is referred to as a test for the significance of

A)a main effect.
B)the interaction effect.
C)a factorial design.
D)a level effect.

Answer 2

B

Question 3

If there are 4 participants per cell, in a 5 x 3 ANOVA, what is N?

A)60
B)32
C)15
D)120

Answer 3

A

Question 4

The $H_{0}$ for a main effect of a two-way ANOVA is the samples in the various levels are drawn from populations where there are

A)equal means.
B)unequal means.
C)equal variances.
D)unequal variances.

Question 5

In a two-way ANOVA, a cell represents

A)one level of the A independent variable and one level of the B independent variable.
B)one level of the dependent variable.
C)one level of the A independent variable.
D)all the subjects in the experiment.

Question 6

In a 5 x 3 ANOVA, how many factors are present?

A)2
B)15
C)5
D)3

Question 7

In a two-way ANOVA, the values of n and k

A)may be different for each factor.
B)may be different for each level within a factor.
C)will always be the same for each factor.
D)will never be the same for different factors.

Question 8

In a two-way ANOVA, the main effect of a factor is the

A)extent to which its effect depends on the action of the other factor.
B)extent to which the factor produces dependent variable scores different from those the other factor produced.
C)effect of changing the levels of the factor on the dependent variable scores, ignoring all other factors in the study.
D)effect of changing the levels of the factor on the dependent variable scores, taking into account all other factors in the study.

Question 9

In a 5 x 3 ANOVA, how many cells are present?

A)15
B)3
C)5
D)8

Question 10

A way to understand a two-way ANOVA is to treat it as if it contained

A)two one-way ANOVAs.
B)two one-way ANOVAs and an interaction ANOVA.
C)an interaction ANOVA and three one-way ANOVAs.
D)two two-way ANOVAs.

Question 11

In a two-way ANOVA, an F involving a comparison among the level means of a factor is referred to as a test for the significance of an) effect.

A)main
B)interaction
C)within
D)between

Question 12

If you are interested in how well students perform on a standardized math-achievement test after they have completed a six-week math unit in either a computer-assisted class, a videotaped course, or a regular classroom, what kind of design do you have?

A)A 2 × 2 between-subjects, factorial design
B)A 3 × 2 between-subjects, factorial design
C)A 3 × 3 between-subjects, incomplete factorial design
D)A one-way design

Question 13

In statistical terminology, when we "collapse across a factor," we average together all the scores

A)from all the cells, ignoring which level of either factor they fall into.
B)within each level of a factor, ignoring which level of the other factor they fall into.
C)from each factor, ignoring which level they fall into.
D)from all the levels of all the factors.

Question 14

In a two-way ANOVA, the interaction effect is the

A)effect of changing the levels of a factor on the dependent scores.
B)effect of changing the levels of a factor on the dependent scores, ignoring all other factors in the study.
C)extent to which the effect of one factor depends on the action of the other factor.
D)effect on the independent variables of changing the levels of a factor.

Question 15

In a 5 x 3 ANOVA, how many levels are present in Factor B?

A)3
B)15
C)5
D)2

Question 16

For which of the three F-tests in a two-way ANOVA do you collapse across the levels of the other factors) in computing the means?

A)The A main effect
B)The B main effect
C)The interaction effect
D)Both the A main effect and the B main effect

Question 17

If you are interested in how well students perform on a standardized math-achievement test after they have completed a six-week math unit in either a computer-assisted class, a videotaped course, or a regular classroom, and also taking into consideration whether they are in the fourth or the fifth grade, what kind of design do you have?

A)A 2 × 2 between-subjects, factorial design
B)A 3 × 2 between-subjects, factorial design
C)A 3 × 3 between-subjects, incomplete factorial design
D)A one-way design

Question 18

Which of the following is not one of the assumptions we must satisfy when conducting a two-way, between-subjects ANOVA?

A)Each cell is an independent sample of interval or ratio scores.
B)The populations represented are normally distributed.
C)The variances of all the represented populations are homogeneous.
D)The means of all the populations represented are equal.

Question 19

When analyzing a two-way ANOVA, we make comparisons where two cells differ along __________________ factor.

A)unconfounded; only one
B)unconfounded; at least one
C)confounded; only one
D)confounded; at least one

Question 20

We do not compare cell means in post hoc analysis when the cells are confounded because

A)confounded cell means cannot differ significantly.
B)confounded cell means contain too much sampling error.
C)even if the difference were significant, we could not tell where the difference came from.
D)if the difference were significant, it would cast doubt on the interpretation of other significant differences.

Question 21

How many participants would be required for a complete factorial 4 × 5 between-subjects design with three observations per cell?

Question 22

For Factor A, you have timed the rate at which three groups of participants can solve puzzles under three conditions of noise: high, medium, and low.In addition, for Factor B the participants have received either no caffeine or a high level of caffeine equivalent to 4 cups of coffee).What kind of design is this called?

Question 23

Professor Blake has completed an experiment where all subjects were asked to give assessments of three different hypothetical individuals as a function of their age.Prior to making these assessments, half of all subjects were randomly assigned to be first presented with a film designed to promote the challenges of aging whereas the other half purposely did not view this film.What type of research design would this study be and why?

Question 24

For a two-way ANOVA, state the null and alternative hypotheses for Factor B that has 4 levels.

Question 25

When you are comparing pairs of cell means for the Tukey HSD Test, which comparisons are confounded and unconfounded?

Question 26

In a 3 x 4 design with four participants per cell, what degrees of freedom would you use in looking up the for the interaction effect?

Question 27

Suppose you have done a two-way ANOVA where the interaction was not significant.How should you next proceed?

Question 28

When performing the Tukey HSD Test on an interaction, why must we use an adjusted value of k ?

Question 29

The following table contains the cell means for a study involving two types of dashboard displays and three types of drive seat designs.
a.Graph these means.
b.Does this graph indicate the presence of an interaction or not? Explain.

Question 30

A researcher has done a pilot study where she recruited a small sample of men and women and then assessed their reaction time to a certain stimuli measured in seconds and listed below in the table) after either playing music or not.Calculate and state the main effects for the two factors.
Factor A: Playing Music? Factor B: Gender

Question 31

In a 2 × 2 design with 40 participants equally distributed across the conditions:
a.How many levels of Factor A are there?
b.How many participants are in Factor A?

Question 32

Suppose you perform a 2 x 3 ANOVA on 18 participants equally divided across all cells.Your for Factor A is
9.15.This is a significant .What is the correct way to report this finding?

Question 33

In a 4 × 2 design with 80 participants distributed equally across the conditions:
a.How many cells are there?
b.How many participants are in each cell?

Question 34

Suppose you are interested in how well students perform on a standardized math-achievement test after they have completed a six-week math unit in either a computer-assisted class, a videotaped course, or a regular classroom and comparing the performance of male students against that of female students.
a.What is the dependent variable?
b.What are the independent variables?
c.How many levels does each independent variable have?