Deck 11: Analysis of Variance: One-Way Classification

Question 1

The person responsible for developing analysis of variance was Karl Pearson.

Answer 1

False

Question 2

The numerator of an F ratio is a variance.

Answer 2

True

Question 3

In a one-way ANOVA, the total variability is divided into four portions.

Answer 3

False

Question 4

The F distribution is skewed.

Question 5

MS_treat is a good estimator of $\sigma$ ², even when the null hypothesis is false.

Question 6

A priori tests are those that are planned before an ANOVA is calculated.

Question 7

To compare two means from a three-group data set, use a Tukey Honestly Significant Difference test.

Question 8

The effect size index, d, is not appropriate for one-way ANOVA data.

Question 9

Analysis of variance is a null hypothesis statistical testing technique.

Question 10

The person responsible for developing analysis of variance was William Gosset.

Question 11

The denominator of an F ratio is a variance.

Question 12

In a one-way ANOVA, the total variability is divided into three portions.

Question 13

A sum of squares divided by degrees of freedom is a mean square.

Question 14

MS_error is a good estimator of $\sigma$ ², even when the null hypothesis is false.

Question 15

After an ANOVA is calculated and the group means examined, a post hoc test is appropriate.

Question 16

To compare two means from a three-group data set, use three t tests.

Question 17

Two effect size indexes, f and d, are appropriate for one-way ANOVA data.

Question 18

The one-way in one-way analysis of variance means that there is only one independent variable.

Question 19

The person responsible for developing analysis of variance was Francis Galton.

Question 20

F values are ratios of two variances.

Question 21

In a one-way ANOVA, the total variability is divided into two portions.

Question 22

The F distribution is not a normal distribution.

Question 23

A sum of squares is a mean square divided by degrees of freedom.

Question 24

MS_error is a good estimator of $\sigma$ ² when the null hypothesis is true.

Question 25

After an ANOVA is calculated and the group means examined, an a priori test is appropriate.

Question 26

A Tukey Honestly Significant Difference test can be used to compare two means from a four-group data set.

Question 27

The effect size index, f, is appropriate for one-way ANOVA data.

Question 28

The assumptions of analysis of variance are more numerous than those for the independent samples t test.

Question 29

Data Set 11-1: The baseline of each curve represents scores on the dependent variable (just like the curves in the book).


-Refer to Data Set 11-1. The null hypothesis should be rejected for an ANOVA on Experiment

A) X
B) Y
C) Z

Question 30

Data Set 11-1: The baseline of each curve represents scores on the dependent variable (just like the curves in the book).


-Refer to Data Set 11-1. The denominator of the F ratio would be smallest for an ANOVA on Experiment

A) X
B) Y
C) Z

Question 31

Data Set 11-1: The baseline of each curve represents scores on the dependent variable (just like the curves in the book).


-Refer to Data Set 11-1. The null hypothesis is true in Experiment

A) X
B) Y
C) Z

Question 32

Data Set 11-2: The baseline of each curve represents scores on the dependent variable (just like the curves in the book).


-Refer to Data Set 11-2. The null hypothesis should be rejected for an ANOVA on Experiment

A) X
B) Y
C) Z

Question 33

Data Set 11-2: The baseline of each curve represents scores on the dependent variable (just like the curves in the book).


-Refer to Data Set 11-2. The denominator of the F ratio would be largest for an ANOVA onExperiment

A) X
B) Y
C) Z

Question 34

Data Set 11-2: The baseline of each curve represents scores on the dependent variable (just like the curves in the book).


-Refer to Data Set 11-2. The null hypothesis is true in Experiment

A) X
B) Y
C) Z
D)X and Z

Question 35

Data Set 11-3: The baseline of each curve represents scores on the dependent variable (just like the curves in the book).


-Refer to Data Set 11-3. The null hypothesis should be rejected for an ANOVA in Experiment

A) X
B) Y
C) Z

Question 36

Data Set 11-3: The baseline of each curve represents scores on the dependent variable (just like the curves in the book).


-Refer to Data Set 11-3. The denominator of the F ratio would be largest for an ANOVA inExperiment

A) X
B) Y
C) Z
D)Y and Z

Question 37

Data Set 11-3: The baseline of each curve represents scores on the dependent variable (just like the curves in the book).


-Refer to Data Set 11-3. The null hypothesis is true in Experiment

A) X
B) Y
C) Z
D)Y and Z

Question 38

Data Set 11-4: The baseline of each curve represents scores on the dependent variable (just like the curves in the book).


-Refer to Data Set 11-4. The null hypothesis should be rejected for an ANOVA in Experiment

A) X
B) Y
C) Z

Question 39

Data Set 11-4: The baseline of each curve represents scores on the dependent variable (just like the curves in the book).


-Refer to Data Set 11-4. The denominator of the F ratio would be largest for an ANOVA in Experiment

A) X
B) Y
C) Z
D)Y and Z

Question 40

Data Set 11-4: The baseline of each curve represents scores on the dependent variable (just like the curves in the book).


-Refer to Data Set 11-4. The null hypothesis is true in Experiment

A) X
B) Y
C) Z
D) X and Y

Question 41

Data Set 11-5: $$\begin{array} { r r c } \text { Group A } & \text { Group B } & \text { Group C } \\\hline8 & 13 & 15 \\10 & 15 & 17\end{array}$$

-The three components of the error variance in Data Set 11-5 are

A) about equal
B) very unequal
C) some are equal and some are unequal
D) not enough information is given.

Question 42

Data Set 11-5: $$\begin{array} { r r c } \text { Group A } & \text { Group B } & \text { Group C } \\\hline8 & 13 & 15 \\10 & 15 & 17\end{array}$$

-Descriptions for Groups A, B, and C in Data Set 11-5 follow. For which would the ANOVA described in Chapter 11 not be appropriate?

A) 10 mg, 20 mg, and 100 mg of a new drug, 6 rats
B) Yale, Princeton, and Harvard, 6 students
C) before, after, and three months later, 2 rats
D) all of the descriptive alternatives are correct.

Question 43

Data Set 11-5: $$\begin{array} { r r c } \text { Group A } & \text { Group B } & \text { Group C } \\\hline8 & 13 & 15 \\10 & 15 & 17\end{array}$$

-The largest HSD in Data Set 11-5 would be found in comparing

A) A vs B
B) A vs C
C) B vs C
D) cannot be determined from the information given.

Question 44

Data Set 11-5: $$\begin{array} { r r c } \text { Group A } & \text { Group B } & \text { Group C } \\\hline8 & 13 & 15 \\10 & 15 & 17\end{array}$$

-Suppose each of the scores in Data Set 11-5 was changed by adding 1 to it. SS_error will then be

A) smaller
B) larger
C) the same size
D) cannot be determined from the information given.

Question 45

Data Set 11-6: Walking is valuable exercise. Does the size of the place you live have any relationship to how much walking you do? The following data (in miles per day) are entirely hypothetical, but represent a reasonable guess. (The place names for this problem are ordered from large to small and are from particular sources-can you identify a source or two?) $$\begin{array} { l c c c } & \text { Gotham } & \text { Middletown } & \text { Grovers Corners } \\ \Sigma \mathrm { X } & 16 & 24 & 32 \\\Sigma \mathrm { X } ^ { 2 } & 70 & 60 & 140 \\N & 4 & 12 & 8\end{array}$$

-For Data Set 11-6, the number of levels of the independent variable is

A) 1
B) 2
C) 3

Question 46

Data Set 11-6: Walking is valuable exercise. Does the size of the place you live have any relationship to how much walking you do? The following data (in miles per day) are entirely hypothetical, but represent a reasonable guess. (The place names for this problem are ordered from large to small and are from particular sources-can you identify a source or two?) $$\begin{array} { l c c c } & \text { Gotham } & \text { Middletown } & \text { Grovers Corners } \\ \Sigma \mathrm { X } & 16 & 24 & 32 \\\Sigma \mathrm { X } ^ { 2 } & 70 & 60 & 140 \\N & 4 & 12 & 8\end{array}$$

-The proper critical value for Data Set 11-6 with alpha at the .05 level is

A) 3.47
B) 3.40
C) 5.78

Question 47

Data Set 11-6: Walking is valuable exercise. Does the size of the place you live have any relationship to how much walking you do? The following data (in miles per day) are entirely hypothetical, but represent a reasonable guess. (The place names for this problem are ordered from large to small and are from particular sources-can you identify a source or two?) $$\begin{array} { l c c c } & \text { Gotham } & \text { Middletown } & \text { Grovers Corners } \\ \Sigma \mathrm { X } & 16 & 24 & 32 \\\Sigma \mathrm { X } ^ { 2 } & 70 & 60 & 140 \\N & 4 & 12 & 8\end{array}$$

-For Data Set 11-6, the proper conclusion is that there are

A) no significant differences the null hypothesis should be rejected
B) no significant differences the null hypothesis should be retained
C) significant differences the null hypothesis should be rejected
D) significant differences the null hypothesis should be retained.

Question 48

Data Set 11-7: As you may know, there has been some controversy about who the actual author was of plays we today attribute to Shakespeare. Suppose that three critics gave their judgments as to the likelihood (0 to 100%) that each of the three named below was the actual author. $$\begin{array} { l c c c } & \begin{array} { c } \text { William } \\\text { Shakespeare }\end{array} & \begin{array} { c } \text { Christopher } \\\text { Marlow }\end{array} & \begin{array} { c } \text { The Duke } \\\text { of Oxford }\end{array} \\ \text { Critic Smythe } & 75 & 25 & 50 \\\text { Critic Jones } & 40 & 10 & 75 \\\text { Critic Jonson } & 90 & 30 & 20\end{array}$$

-The scores in Data Set 11-7_____________ be analyzed using the techniques in Chapter 11 because

A) can, all the requirements for ANOVA are met
B) cannot, the same dependent variable was not used with each "author"
C) cannot, the independent variable is just names
D) cannot, the judgments are correlated measures.

Question 49

Data Set 11-7: As you may know, there has been some controversy about who the actual author was of plays we today attribute to Shakespeare. Suppose that three critics gave their judgments as to the likelihood (0 to 100%) that each of the three named below was the actual author. $$\begin{array} { l c c c } & \begin{array} { c } \text { William } \\\text { Shakespeare }\end{array} & \begin{array} { c } \text { Christopher } \\\text { Marlow }\end{array} & \begin{array} { c } \text { The Duke } \\\text { of Oxford }\end{array} \\ \text { Critic Smythe } & 75 & 25 & 50 \\\text { Critic Jones } & 40 & 10 & 75 \\\text { Critic Jonson } & 90 & 30 & 20\end{array}$$

-Regardless of your answer to the question above, the MS_treat for the numbers in Data Set 11-7 is

A) 6339
B) 3289
C) 2153
D) 1644
E) 508

Question 50

Data Set 11-7: As you may know, there has been some controversy about who the actual author was of plays we today attribute to Shakespeare. Suppose that three critics gave their judgments as to the likelihood (0 to 100%) that each of the three named below was the actual author. $$\begin{array} { l c c c } & \begin{array} { c } \text { William } \\\text { Shakespeare }\end{array} & \begin{array} { c } \text { Christopher } \\\text { Marlow }\end{array} & \begin{array} { c } \text { The Duke } \\\text { of Oxford }\end{array} \\ \text { Critic Smythe } & 75 & 25 & 50 \\\text { Critic Jones } & 40 & 10 & 75 \\\text { Critic Jonson } & 90 & 30 & 20\end{array}$$

-Regardless of your answer to the questions above, the df_error for the numbers in Data Set 11-7 is

A) 8
B) 6
C) 3

Question 51

Data Set 11-8: $$\begin{array} { c c c } \text { Group A } & \text { Group B } & \text { Group C } \\\hline 8 & 5 & 1 \\10 & 10 & 10 \\12 & 15 & 19\end{array}$$

-Consider the three components of the error variance in Data Set 11-8.

A) They are about equal
B) They are not equal
C) Two are equal and one is different
D) Not enough information is given.

Question 52

Data Set 11-8: $$\begin{array} { c c c } \text { Group A } & \text { Group B } & \text { Group C } \\\hline 8 & 5 & 1 \\10 & 10 & 10 \\12 & 15 & 19\end{array}$$

-Descriptions for Groups A, B, and C in Data Set 11-8 follow. For which would the ANOVA described in Chapter 11 not be appropriate?

A) New Yorkers, Bostonians, Chicagoers 9 political participants
B) age 16, age 20, age 24 3 female participants
C) freshmen, sophomores, seniors 9 student participants
D) all of the other alternatives are correct.

Question 53

Data Set 11-8: $$\begin{array} { c c c } \text { Group A } & \text { Group B } & \text { Group C } \\\hline 8 & 5 & 1 \\10 & 10 & 10 \\12 & 15 & 19\end{array}$$

-Suppose you performed HSD tests on the means of the groups in Data Set 11-8. The HSD values would be

A) all about equal and not significant
B) all about equal and significant
C) equal for two comparisons and larger for the other
D) equal for two comparisons and smaller for the other.

Question 54

The person who developed analysis of variance as a statistical technique was

A) Gosset
B) Quetelet
C) Tukey
D) none of the other alternatives are correct.

Question 55

The F distribution is called F

A) because it was the sixth statistical distribution discovered after 1900
B) because it is the only fixed statistical distribution
C) because the distribution is a theoretical frequency distribution
D) to honor a man whose name began with F.

Question 56

Credit for the development of ANOVA goes to

A) Francis Galton, a geneticist
B) Karl Pearson, a statistician
C) Ronald Fisher, a biologist
D) George Snedecor, a psychologist.

Question 57

The person who developed ANOVA was

A) W. S. Gosset, a businessman
B) John W. Tukey, a statistician
C) "student," a pseudonym
D) Ronald A. Fisher, a biologist.

Question 58

is credited with developing analysis of variance.

A) R. A. Fisher
B) George Snedecor
C) William S. Gosset ("student")
D) Karl Pearson.

Question 59

Ronald A. Fisher gets credit for developing

A) analysis of variance
B) the t distribution
C) both of the descriptive alternatives are correct
D) neither of the descriptive alternatives is correct

Question 60

Ronald A. Fisher made significant contributions to statistics and

A) psychology
B) chemistry
C) sociology
D) none of the other alternatives are correct.

Question 61

Ronald A. Fisher

A) discovered the exact sampling distribution of r
B) wrote Statistical Methods for Research Workers
C) invented analysis of variance
D) all of the descriptive alternatives are correct.

Question 62

The designs analyzed in Chapter 11 called for the samples to be

A) independent, as described for the independent-measures t test
B) related, as described for the paired-measures t test
C) either of the descriptive alternatives.

Question 63

The ANOVA technique as described in Chapter 11 cannot be used when

A) the number of scores in each group is unequal
B) subjects are randomly assigned to one of the groups before the independent variable is administered
C) samples are drawn from populations that have equal variances
D) subjects participate in every level of the independent variable.

Question 64

The ANOVA techniques described in Chapter 11 cannot be used to analyze an experiment with

A) two levels of the independent variable
B) three levels of the independent variable
C) paired samples designs:
D) independent samples designs.

Question 65

The techniques of Chapter 11 are not appropriate if the data come from

A) a paired-samples design
B) populations that do not have the same mean
C) both of the descriptive alternatives are correct
D) neither of the descriptive alternatives is correct.

Question 66

The ANOVA technique described in the text can be used on

A) paired-samples designs
B) independent-samples designs
C) both of the descriptive alternatives are correct
D) neither of the descriptive alternatives are correct.

Question 67

Suppose you found a way to redo a study so that the SS_error was reduced compared to the first time you ran the experiment. The SS_treat stayed the same as before. The effect of this will be to

A) increase the population variance
B) be more likely to detect population differences if there are any
C) increase the degrees of freedom
D) all of the descriptive alternatives are correct.

Question 68

Suppose MS_treat is calculated for three samples that are from a population with a mean = 10. Under which condition below would MS_treat certainly become larger?

A) the addition of a sample from a population with the a mean of 10
B) the addition of a sample from a population with a mean = 20
C) the removal of one of the three samples from the calculations
D) all of the other alternatives are correct.

Question 69

The larger the population variance, the larger________ is.

A) F
B) df
C) MS_error
D) all of the descriptive alternatives are correct.

Question 70

If the null hypothesis is true, an analysis of variance determines the probability that the samples

A) came from the same population
B) came from different populations
C) came from an F distribution
D) are random samples.

Question 71

If the null hypothesis is true, mean square__________ will be a good estimate of the population variance.

A) error
B) treatment
C) both of the descriptive alternatives are correct
D) neither of the descriptive alternatives is correct.

Question 72

If the null hypothesis is true,_______________ will be a good estimate of the population variance.

A) the error mean square
B) the treatment mean square
C) both of the descriptive alternatives are correct
D) neither of the descriptive alternatives is correct.

Question 73

If the null hypothesis is false,______________ will be a good estimate of the population variance.

A) the error mean square
B) the treatment mean square
C) both of the descriptive alternatives are correct
D) neither of the descriptive alternatives is correct.

Question 74

When the null hypothesis is true, which of the following is a good estimate of the population variance?

A) MS_treat
B) MS_error
C) both of the descriptive alternatives are correct
D) neither of the descriptive alternatives is correct.

Question 75

If the null hypothesis is not true, mean square______________ will be a good estimate of the population variance.

A) error
B) treatment
C) both of the descriptive alternatives are correct
D) neither of the descriptive alternatives is correct.

Question 76

The mean square error will be a good estimate of the population variance when

A) when the null hypothesis is true
B) when the null hypothesis is false
C) regardless of whether the null hypothesis is true or false

Question 77

MS_error will be a good estimate of the population variance

A) when the null hypothesis is true
B) when the null hypothesis is false
C) both of the descriptive alternatives are correct
D) never, MS_error is not an estimate of the population variance.

Question 78

When the null hypothesis is false, which of the following is a good estimate of the population variance?

A) MS_treat
B) MS_error
C) both of the descriptive alternatives are correct
D) neither of the descriptive alternatives is correct.

Question 79

"All of the samples in the study came from populations with identical means"is a statement of

A) an assumption about the data that is required if the F distribution is to be accurate
B) the null hypothesis
C) both of the descriptive alternatives are correct
D) neither of the descriptive alternatives are correct.

Question 80

The null hypothesis in an ANOVA problem is that

A) all the groups are drawn from the same population
B) none of the groups were drawn from the same population
C) one or more of the groups was drawn from a different population
D) any of the other alternatives, depending on how many levels of the independent variable there are.