Deck 14: The Two-Way Analysis of Variance

Question 1

In a two-way ANOVA,the hypotheses for a Factor B that has four levels are

A) not all are equal.
B) not all are equal.
C)
D)

Answer 1

not all are equal.

Question 2

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)from all levels of that factor.
C)from each factor,ignoring which level they fall into.
D)from all the levels of all the factors.

Answer 2

from all levels of that factor.

Question 3

In a 2* 2 design with 40 participants equally distributed across the conditions,what are and

A) = 1; = 10
B) = 1; = 40
C) = 2; = 10
D) = 2; = 20

Answer 3

= 2; = 20

Question 4

When an experiment design has two factors and both factors are tested using related samples,we should perform a

A)two-way within-subjects ANOVA.
B)two-way between-subjects ANOVA.
C)two-way mixed-design ANOVA.
D)two-way dependent-factors ANOVA.

Question 5

A major reason for conducting a study with two factors is to

A)observe the interaction between the factors.
B)observe the main effects simultaneously.
C)conserve time and energy.
D)obtain more samples than can easily be obtained with one factor.

Question 6

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

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

Question 7

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.

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 that factor produces dependent variable scores different from those the other factor produced.
C)effect of changing the levels of that factor on the dependent variable scores,ignoring all other factors in the study.
D)effect of changing the levels of that factor on the dependent variable scores,taking into account all other factors in the study.

Question 9

The for a main effect of a two-way ANOVA is that differences in the sample means among the various levels are due to

A)heterogeneity.
B)sampling error.
C)treatment effect.
D)the interaction effect.

Question 10

A complete factorial design occurs when

A)all levels of one factor are combined with all levels of the other factor.
B)all levels of one factor are not combined with all levels of the other factor.
C)the researcher is finished collecting all the data from a two-factor study.
D)all statistical analyses,including post hoc comparisons and the calculation of , are completed.

Question 11

For Factor A,you have timed the rate at which 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 do you have?

A)A 2* 3 between-subjects,factorial design
B)A 3* 3 between-subjects,factorial design
C)A 3*2 between-subjects,factorial design
D)A 3* 3 between-subjects,incomplete factorial design

Question 12

For which of the three F-tests in a two-way ANOVA do you collapse across the levels of the other factor(s)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 13

In a two-way ANOVA,a cell represents

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

Question 14

When an experiment design has two factors but one factor involves related samples while the other factor involves independent samples,we should perform a

A)two-way within-subjects ANOVA.
B)two-way between-subjects ANOVA.
C)two-way mixed-design ANOVA.
D)two-way independent-related samples ANOVA.

Question 15

How many participants would be required for a completely randomized 4 *5 between-subjects design with three observations per cell?

A)18
B)20
C)27
D)60

Question 16

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.
B)The populations represented are normally distributed interval or ratio scores.
C)The variances of all the represented populations are homogeneous.
D)The means of all the populations represented are equal.

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,what kind of design do you have?

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

Question 18

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 you also want to include a factor for sex (boys vs.girls),what is the dependent variable?

A)The type of math instruction
B)The subjects' sex
C)The six-week unit
D)The scores on the math achievement test

Question 19

A two-way ANOVA contains

A)a main effect for each factor.
B)a main effect for each factor and an interaction.
C)an interaction for each factor and a main effect.
D)an interaction for each factor.

Question 20

Sarah Ann designed,conducted,analyzed,wrote,and published an experiment.In the 2 x 4 ANOVA,the F value for Art Medium was ,indicating a significant difference in the Time it took to produce works of art using different media.The F value for Size of the art work was ,indicating a nonsignificant finding.The interaction also was nonsignificant.What was the dependent variable?

A)Art Medium
B)Time
C)Size
D)Quality

Question 21

In a 4 * 2 design with 80 participants distributed equally across the conditions,what are and ?

A) = 4; = 20
B) = 6; = 10
C) = 8; = 10
D) = 8; = 80

Question 22

Sharon has conducted a study on the effectiveness of a drug for obsessive-compulsive disorder (OCD).Her drug levels are 0 mg. ,100 mg. ,and 500 mg.She also has included a second factor of therapy versus no therapy.Sharon already has computed the total of the scores in each treatment.These are given below,along with the sum of the scores for every measurement in the study ( ).Sharon had 10 participants in each treatment condition.What is her (drug level)?

A)7.25
B)34.64
C)45.60
D)87.01

Question 23

The denominator in all the F ratios in a two-way factorial ANOVA is

A)
B)
C)
D)different,depending on the number of cells.

Question 24

Sharon has conducted a study on the effectiveness of a drug for obsessive-compulsive disorder (OCD).Her drug levels are 0 mg. ,100 mg. ,and 500 mg.She also has included a second factor of therapy versus no therapy.Sharon already has computed the total of the scores in each treatment.These are given below,along with the sum of the scores for every measurement in the study ( ).Sharon had 10 participants in each treatment condition.What is her ?

A)7.25
B)34.64
C)45.60
D)87.01

Question 25

If and ,what is ?

A)4.97
B)23.97
C)52.47
D)311.53

Question 26

Sharon has conducted a study on the effectiveness of a drug for obsessive-compulsive disorder (OCD).Her drug levels are 0 mg. ,100 mg. ,and 500 mg.She also has included a second factor of therapy versus no therapy.Sharon already has computed the total of the scores in each treatment.These are given below,along with the sum of the scores for every measurement in the study ( ).Sharon had 10 participants in each treatment condition.What is her (therapy level)?

A)7.25
B)34.64
C)45.60
D)87.01

Question 27

A significant interaction effect indicates that

A)the influence of one factor is not the same for each level of the other factor.
B)the influence of one factor is the same for each level of the other factor.
C)the relationship between one factor and the dependent variable differs from the relationship between the other factor and the dependent variable.
D)the dependent variable differs depending on the level of a factor.

Question 28

If , ,and N = 30,what is ?

A)4.97
B)23.97
C)9.97
D)52.47

Question 29

For the following two-way ANOVA summary table,what are the appropriate MS values?

A)a
B)b
C)c
D)d

Question 30

If you have a two-way ANOVA with a 2 *3 design,and the A main effect is the only significant ,which of the following would you do?

A)Perform post hoc comparisons for the 3 levels of the B factor.
B)Perform post hoc comparisons for the 2 levels of the A factor.
C)Perform post hoc comparisons for the interaction effect.
D)Perform no post hoc comparisons.

Question 31

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

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

Question 32

An interaction effect that is not significant indicates that

A)the influence of one factor is not the same for each level of the other factor.
B)the influence of one factor is the same for each level of the other factor.
C)the relationship between one factor and the dependent variable differs from the relationship between the other factor and the dependent variable.
D)the dependent variable differs depending on the level of a factor.

Question 33

For the following mean square from an ANOVA summary table,what are the correct values?

A)a
B)b
C)c
D)d

Question 34

To graph a main effect from a two-way ANOVA,the _____ is (are)plotted along the X axis,the _____ is (are)plotted along the Y axis,and the _____ is (are)plotted in the graph.

A)levels of a factor;dependent variable;main effect means
B)dependent variable;levels of a factor;main effects means
C)levels of a factor;dependent variable;cell means
D)levels of one factor;levels of the other factor;dependent variable

Question 35

In any two-way ANOVA,if is significant,which of the following is true?

A) also has to be significant.
B) also has to be significant.
C)Both and
also must be significant.
D)A significant interaction does not tell us anything about the significance of the main effects.

Question 36

In a 3 * 4 design with four participants per cell,the degrees of freedom to use in looking up the for the interaction effect would be

A)2,36.
B)4,48.
C)6,36.
D)6,48.

Question 37

If , , and N = 30,what is ?

A)9.97
B)6.42
C)4.97
D)2.61

Question 38

If , ,and N = 30,what is ?

A)4.97
B)23.97
C)9.97
D)52.47

Question 39

If , , and N = 30,what is ?

A)9.97
B)6.42
C)4.97
D)2.61

Question 40

A professor and his graduate students conducted a study testing the effects of levels of collaborative learning (Factor A)and levels of constructivist instruction (Factor B)on student learning (dependent variable).Their partial summary table is shown here.What was ?

A)
B)
C)
D)

Question 41

When graphed,a significant interaction effect produces two or more lines that

A)slant upward from left to right.
B)slant downward from left to right.
C)are not parallel.
D)have either U shapes or inverted U shapes.

Question 42

A study investigated the influence of age and time pressure on creativity.Summary statistics are presented below.There was a significant main effect of time pressure.With = 2.89,compute the HSD for the difference between 30 seconds and 2 minutes.Use $\alpha$ = 0.05.

A)0.37
B)0.72
C)1.04
D)1.76

Question 43

The primary interpretation of a two-way ANOVA rests on the interpretation of the

A)main effects.
B)ANOVA summary table.
C)interaction effect,if it is significant.
D)means for the main effects.

Question 44

A study investigated whether taking a test in the same room in which a person studies helps performance on the test.The means are below.Which of the graphs correctly portrays the interaction?

A)Graph A
B)Graph B
C)Graph C
D)Graph D

Question 45

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 46

The "adjusted k" in Tukey's HSD is adjusted to take into account

A)the number of confounded comparisons we can make out of all the cell means in our interaction.
B)the number of unconfounded comparisons we can make out of all the cell means in our interaction.
C)the adjustment factor used when there are unequal ns in the cells.
D)the total number of cell means in a study.

Question 47

To graph an interaction,place the _____ on the X axis,place the _____ along the Y axis,and show the second factor by _____.

A)levels of one factor;levels of the other factor;plotting the cell means for the dependent variable
B)levels of one factor;dependent variable;drawing a separate line for each level of the second factor,with each line connecting the means for the levels
C)levels of one factor;levels of the other factor;creating a similar but separate graph for each cell mean
D)levels of one factor;dependent variable;creating a similar but separate graph for each level of the other factor

Question 48

In a two-way ANOVA,the HSDs for the two main effects will

A)always be the same.
B)never be the same.
C)be different if their values are different.
D)be different if their ks or ns are different.

Question 49

The larger the value of ,

A)the less consistent the relationship between the independent variable and the dependent variable.
B)the more important the manipulation (independent variable)is in determining participants' scores.
C)the less important the manipulation (independent variable)is in determining participants' scores.
D)the more variable the effects of the factor (independent variable)are on the participants' scores.

Question 50

A study investigated the influence of age and time pressure on creativity.The HSD for the interaction effect was 1.76.The table below shows the absolute differences between the cell means.Where are the significant differences?

A)Between the mean for participants Over 65 at the 30-sec time pressure and the mean for Over 65 at the 2-min time pressure.
B)(1)Between the mean for participants Over 65 at the 30-sec time pressure and the mean for Over 65 at the 2-min time pressure,and (2)between the mean for the College-Age group at the 30-sec time pressure and the mean for the Over 65 group at the 30-sec time pressure.
C)None of the cells are significantly different.
D)All of the cells are significantly different.

Question 51

An unconfounded comparison occurs in comparing two cell means when

A)there are unequal ns in the cells.
B)the two cells differ along one factor.
C)the two cells differ along more than one factor.
D)there are unequal ns in the factors.

Question 52

Usually the effect size for any significant effects in a two-way ANOVA is determined by computing ______,the proportion of variance accounted for in the sample.

A)
B)
C)
D)

Question 53

A study investigated the influence of relaxation training (relaxation training vs.no relaxation training)and type of sleep-inducing product (Brand X vs.Brand Y)on the amount of time it takes a person to fall asleep (in minutes).Partial results from the data analysis are in the table below.Compute the effect size for the relaxation factor.

A)0.14
B)0.30
C)0.37
D)0.70

Question 54

If for a factor is 0.09,

A)the importance of the factor should be emphasized in the interpretation of the overall experiment.
B)the importance of the factor should not be emphasized in the interpretation of the overall experiment.
C)the factor accounts for 90% of the variance in scores.
D)the factor accounts for 9% of the variance in scores.

Question 55

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 error variance.
C)even if the difference were significant,we could not tell where it came from.
D)if the difference were significant,it would cast doubt on the interpretation of other significant differences.

Question 56

A confounded comparison occurs in comparing two cell means when

A)there are unequal ns in the cells.
B)the two cells differ along one factor.
C)the two cells differ along more than one factor.
D)there are unequal ns in the factors.