Analysis Of Variance (Two Factor) Chapter 18 Full Test Bank

MULTIPLE‑CHOICE TEST ITEMS

CHAPTER 18

ANALYSIS OF VARIANCE (TWO FACTOR)

18.1 Given the following data for the various mean "rehabilitation scores" earned by prison inmates,

NO. OF CELLMATES

0 1 2 Row Mean

__________________________

RECREATION 0 0 60 60 40

PRIVILEGES 2 60 60 60 60

4 120 60 60 80

__________________________

Column Mean 60 60 60 Grand Mean = 60

the three row means (40, 60, and 80) reflect the

a) main effect of cellmates.

b) main effect of privileges.

c) interaction of crowding and privileges.

d) total effect.

18.2 Given the following data for the various mean "rehabilitation scores" earned by prison inmates,

NO. OF CELLMATES

0 1 2 Row Mean

__________________________

RECREATION 0 0 60 60 40

PRIVILEGES 2 60 60 60 60

4 120 60 60 80

__________________________

Column Mean 60 60 60 Grand Mean = 60

it would appear that, among the null hypotheses for cellmates (#1), privileges (#2), and interaction (#3),

a) all probably should be rejected.

b) #1 probably should be rejected.

c) #1 and #2 probably should be rejected.

d) #2 and #3 probably should be rejected.

18.3 Interaction occurs whenever the effects of one factor are

a) not consistent.

b) not consistent for all values of the second factor.

c) consistent.

d) consistent for all values of the second factor.

18.4 In both one‑ and two-factor ANOVA, F ratios always consist of a numerator that reflects

a) random error.

b) a treatment effect.

c) both random error and a treatment effect.

d) random error and, if present, a treatment effect.

18.5 In both one‑ and two‑factor ANOVA, F ratios always consist of a denominator that reflects

a) random error.

b) a treatment effect.

c) both random error and a treatment effect.

d) random error and, if present, a treatment effect.

18.6 In two‑factor ANOVA, an F ratio is calculated for each different

a) sum of squares.

b) mean square.

c) factor.

d) null hypothesis.

18.7 In two‑factor ANOVA, most computational effort is devoted to the various

a) sum of squares terms.

b) degrees of freedom terms.

c) mean square terms.

d) F ratios.

18.8 Given that the total sum of squares equals 600, and that the column, row, and within sums of squares equal 200, 150, and 50, respectively, then the interaction sum of squares must equal

a) 200

b) 300

c) 400

d) 900

18.9 In a two-factor ANOVA design, with three values (or levels) for each factor, the interaction component has degrees of freedom equal to

a) 1

b) 3

c) 4

d) 6

18.10 In a two-factor design, with three values (or levels) for each factor and with five subjects in each of the resulting nine groups, the within group component has degrees of freedom equal to

a) 4

b) 9

c) 36

d) 45

18.11 Given the following incomplete ANOVA summary table,

SOURCE SS df MS F

_________________________________________________________

Column 100 2 50 0.50

Row 60 1 60 0.60

Interaction 80

Within 2400 24 100

Total 2640

it would be reasonable to conclude that for the null hypotheses corresponding to the two listed F values,

a) neither should be rejected.

b) at least one should be rejected.

c) one should be rejected.

d) both should be rejected.

18.12 Given the following incomplete ANOVA summary table,

SOURCE SS df MS F

_________________________________________________________

Column 100 2 50 0.50

Row 60 1 60 0.60

Interaction 80

Within 2400 24 100

Total 2640

the value of F for the above interaction equals

a) 0.33

b) 0.40

c) 0.80

d) 1.00

18.13 A partial squared curvilinear correlation coefficient can be used to estimate the size of the effect associated with

a) each F.

b) each nonsignificant F.

c) each significant F.

d) only the most significant F.

18.14 Excluded from the denominator of a partial squared curvilinear correlation are one or more sum of squares terms, namely, the sum of squares for

a) the two other treatments.

b) within cells.

c) both column and row treatments.

d) interaction.

18.15 (NOTE: This question requires Greek letters.) The introduction of additional statistical tests, such as and HSD, and estimates, such as and d, initially depends on a significant F test for

a) either main effect.

b) both main effects.

c) the interaction.

d) any one of the three treatments.

18.16 The occurrence of an interaction often

a) highlights pertinent issues for future research.

b) reflects a biased result.

c) eliminates the possibility of a significant main effect.

d) signifies a defect in the experimental design.

18.17 If an investigator reports that main effects exist for both factors, this implies

a) that an interaction probably is present.

b) that an interaction probably isn't present.

c) that an interaction could not possibly be present.

d) nothing whatsoever about the interaction.

18.18 When constructing a graph for a possible interaction, each dot in the graph should be based on the mean (or total) for

a) each subject.

b) each group of subjects that receives the same combination of treatments.

c) each group of subjects that receives the same treatment for one of the factors.

d) all subjects.

18.19 Given that the null hypothesis for interaction has been rejected, the corresponding graph of this interaction should contain two or more _______________________ lines.

a) straight

b) dissimilar

c) nonparallel

d) intersecting

18.20 If an investigator reports that factor A has an inconsistent effect for the various values of factor B, this implies that

a) the effect of factor A must be weak.

b) factor B also has an inconsistent effect for the various values of factor A.

c) the null hypothesis should be rejected for at least one of the two main effects.

d) the null hypothesis for the interaction should have been retained.

18.21 Given the following data for the various mean "rehabilitation scores" earned by prison inmates,

NO. OF CELLMATES

0 1 2 Row Mean

__________________________

RECREATION 0 0 60 60 40

PRIVILEGES 2 60 60 60 60

4 120 60 60 80

__________________________

Column Mean 60 60 60 Grand Mean = 60

the cell means in the first row (0, 60, and 60) represents the simple effect of

a) privileges at 1 cellmate.

b) privileges at 2 cellmates.

c) cellmates at 0 privileges.

d) cellmates at 2 privileges.

18.22 Given the following data for the various mean "rehabilitation scores" earned by prison inmates,

NO. OF CELLMATES

0 1 2 Row Mean

__________________________

RECREATION 0 0 60 60 40

PRIVILEGES 2 60 60 60 60

4 120 60 60 80

__________________________

Column Mean 60 60 60 Grand Mean = 60

the total number of simple effects equals

a) three.

b) four.

c) five.

d) six.

18.23 A modification of Tukey’s test can be used to pinpoint important differences between pairs of column or row means, given that (1) the corresponding null hypotheses have been rejected and (2) interpretations aren't compromised by inconsistencies associated with

a) the interaction.

b) the other factor.

c) small sample sizes.

d) test assumptions.

18.24 Consider using Cohen's d to estimate difference between pairs of means whenever an effect

a) is significant.

b) with more than two groups is significant.

c) is inconsistent.

d) is judged to be very important.

18.25 In two-factor ANOVA, it's important that the size of all groups be

a) equal.

b) approximately the same.

c) very small.

d) very large.

18.26 You needn't be too concerned about violations of assumptions for F tests in a two-factor ANOVA, particularly if all group sizes are equal and each is

a) very small.

b) small.

c) fairly large.

d) very large.

18.27 It's impossible to perform ANOVA for a two-factor experiment having only one observation per group (or cell) because

a) the assumption of normality can't be checked.

b) total variability is underestimated.

c) between group variability is exaggerated.

d) within group variability can't be estimated.