Deck 9: Introduction to the Analysis of Variance

Question 1

Analysis of variance should be conducted only when

A)sample sizes are greater than 30 per group.
B)sample sizes are smaller than 30 per group.
C)population variances can be assumed to be equal.
D)population sizes are approximately equal.

Answer 1

population variances can be assumed to be equal.

Question 2

In an analysis of variance,if the within-groups variance estimate is about the same as the between-groups variance estimate,then

A)the null hypothesis should be rejected.
B)any difference between sample means is probably due to random sampling error.
C)an error has been made in computing the between-groups and the within-groups variance estimates.
D)any difference between sample means is probably due to a real difference caused by experimental conditions.

Answer 2

any difference between sample means is probably due to random sampling error.

Question 3

When sample sizes are equal,MS_Within is figured by

A)summing the population variance estimates figured within each group and dividing by the total number of participants (over all groups).
B)summing the population variance estimates figured within each group and dividing this sum by the number of groups.
C)multiplying the within-groups sum of squares (SS_Within)by the size of each sample (n).
D)dividing the within-groups sum of squares (SS_Within)by the size of each sample (n).

Answer 3

summing the population variance estimates figured within each group and dividing this sum by the number of groups.

Question 4

When carrying out an analysis of variance with equal sample sizes,the estimated variance of the distribution of means is converted to an estimated variance of the population of individual scores by

A)multiplying the estimated variance of the distribution of means by the number of scores in each sample.
B)dividing the estimated variance between groups by the number of groups.
C)dividing the estimated variance of the distribution of means by the number of scores in each sample.
D)multiplying the estimated variance of the population of individual scores by the number of groups.

Question 5

An analysis of variance differs from a t test for independent means in that an analysis of variance

A)is usually used to compare two groups,while a t test for independent means can be used to compare two or more groups.
B)can be used to compare three or more groups,while a t test for independent means cannot be used to compare more than two groups.
C)is conducted before the experiment,while a t test for independent means is conducted after the experiment.
D)includes computation of group variances as part of the analysis,while a t test does not include these computations.

Question 6

In the formula,Σ(M-GM)²/df_Between,"GM" is the

A)general multiple.
B)grand mean.
C)group mean.
D)group median.

Question 7

In a one-way analysis of variance,if the null hypothesis is true,then

A)the analysis of variance can never produce a significant F ratio.
B)estimates of the population variance will be easier to figure.
C)the variance between sample means will be larger than the variance within each sample.
D)any difference among sample means reflects variance within the populations.

Question 8

Ann conducts a study,and finds that the estimated population variances for the groups are 12.8,16.3,15.1,and 19.9.What is the within-groups estimate of the population variance?

A)(12.8² + 16.3² + 15.1² + 19.9²)/ (4 - 1)= 351.18.
B)(12.8² + 16.3² + 15.1² + 19.9²)/ 4 = 263.39.
C)(12.8 + 16.3 + 15.1 + 19.9)/ (4 - 1)= 21.37.
D)(12.8 + 16.3 + 15.1 + 19.9)/ 4 = 16.03.

Question 9

The formula "Σ(M-GM)²/df_Between" is used to compute

A)the F ratio for a repeated measures design.
B)the between-groups sum of squared deviations.
C)the estimated variance of the distribution of means.
D)the between-groups estimate of the population variance.

Question 10

The most serious violation of an assumption for an analysis of variance occurs when

A)the populations are strongly skewed in the positive direction.
B)the scores between and within groups are dependent.
C)the variance estimate of the group with the largest estimate is twice that of the smallest.
D)the number of scores in each group is less than 10.

Question 11

Because of the assumption that the population variances are equal,when conducting an analysis of variance

A)fewer degrees of freedom are required.
B)sample variances are not important.
C)an average estimate of the population variance is computed.
D)population parameters are used instead of sample statistics.

Question 12

Given four populations with equal means and equal variances,an F distribution for situations with samples of 10 scores each could be created by

A)applying the t test formula to each pair of samples,squaring the results to obtain F ratios,then repeating this process a large number of times.
B)applying the analysis of variance formula to a set of four samples (one from each of the four populations)of 10 scores each,determining the degrees of freedom,and repeating this process a large number of times.
C)taking 10 samples from each of the four populations,figuring the F ratio,and repeating this process a large number of times.
D)taking samples of 10 scores from each of the four populations,figuring an F ratio for each set of samples,and repeating this process a large number of times.

Question 13

In an analysis of variance,you reject the null hypothesis when the F ratio is

A)negative.
B)much larger than 1.
C)equal to the t score.
D)smaller than 1.

Question 14

In an analysis of variance,if the null hypothesis is false,then

A)the variation between sample means reflects the variation within the populations as well as the variation between the population means.
B)the within-groups variance is significantly larger than the between-groups variance.
C)the variance within each sample is larger than if the null hypothesis were true.
D)the variance between sample means is no greater than the variance within the population with the largest variance.

Question 15

"S²_Within" equals

A)the sum of squares within each group.
B)the square root of the standard within-groups deviations from the mean.
C)the squared variance within groups.
D)the population variance estimate based on the variation within each of the groups.

Question 16

In an analysis of variance with a between-groups population variance estimate of 30 and a within-groups estimate of 25,the F ratio is

A)25 / (30-25)= 5.00
B)(30-25)/ 30 = 0.17
C)25 / 30 = 0.83
D)30 / 25 = 1.20

Question 17

In an analysis of variance with a within-groups variance estimate of 8.5 and a between-groups variance estimate of 5.3,the F ratio is

A)5.3 / 8.5 = 0.62
B)8.5 / 5.3 = 1.60
C)√5.3 / 8.5 = 0.27
D)√8.5 / 5.3 = 0.55

Question 18

In an analysis of variance,if the null hypothesis is true,then

A)the research hypothesis can also be true.
B)fewer participants can be included in the experiment.
C)there is less variance among means of samples than if the null hypothesis were not true.
D)the within-groups estimate of the population variance is smaller than the between-groups estimate.

Question 19

Joe conducts an analysis of variance.If he rejected the null hypothesis,the most likely F value is

A)0.64
B)1.01
C)3.57
D)-5.12

Question 20

A characteristic of an F ratio is that

A)the cutoff F equals the calculated F divided by 2.
B)it can never be less than 0.
C)it is negatively skewed.
D)the t distribution for ∞ df is the comparison distribution.

Question 21

In general,using the Bonferroni procedure as a post-hoc comparison procedure means that

A)important interactions would be overlooked in fewer studies.
B)the .05 alpha will be divided into such small parts that finding any significant comparisons will be a long shot.
C)fewer subjects will be required per group to detect significant results.
D)an overall .10 significance level will guarantee that each comparison can be conducted at the .05 level.

Question 22

A planned comparison comparing two means involves figuring an F ratio in which the numerator

A)depends on which pair of means is being compared.
B)has exactly 2 degrees of freedom.
C)is the overall between-groups population variance estimate,regardless of the pair of means being compared.
D)does not involve figuring an F ratio for any planned comparison.

Question 23

According to Cohen's conventions,an R² of .14 would represent a

A)small effect
B)medium effect
C)large effect
D)none of the above,as there are no standards for interpreting R²

Question 24

The Scheffé test requires first figuring the F for the comparison as if a planned comparison is being conducting,then adjusting the F from that comparison by

A)dividing that F by the study's overall df_Within.
B)multiplying that F by the study's overall df_Within.
C)dividing that F by the study's overall df_Between.
D)multiplying that F by the study's overall df_Between.

Question 25

The cutoff F used to evaluate the significance of the Scheffé test for any particular comparison between two group means is

A)the same cutoff F used for the overall study.
B)the cutoff based on df = 1 for the numerator and the overall df_Between for the denominator.
C)the cutoff based on df = 2 for the numerator and the overall df_Within for the denominator.
D)the cutoff based on df = 1 for the numerator and df = overall df_Within / 2 for the denominator.

Question 26

Advanced topic: One disadvantage of using the structural model to understand the analysis of variance (as opposed to the method which involves averaging the variances of each group)is that

A)it provides less accurate results.
B)it makes analyzing the results more difficult when group sizes are equal.
C)it is more structured,and therefore more rigid.
D)it is not as intuitive or easy to grasp.

Question 27

"Proportion of variance accounted for" is also referred to as all of the following EXCEPT

A)R²
B)the correlation ratio
C)eta-squared
D)chi-squared

Question 28

If a research article does not report the variance estimates,R²

A)can be figured by [(F)(df_Between)]/[(F)(df_Between)+ df_Within].
B)can be figured by F/df_Within.
C)can be estimated by S_M/S_Within.
D)cannot be figured.

Question 29

Which statistical procedure ensures that the alpha level for any given planned contrast will not exceed .05?

A)Tukey
B)Scheffé
C)Bonferroni
D)Gosset

Question 30

If a research article presented the results of an analysis of variance as,"F (2,38)= 3.60,p < .05," then how many groups were there in the study?

A)2
B)3
C)40
D)41

Question 31

The overall test of the significance of the difference among groups in an analysis of variance is called

A)an omnibus test.
B)a planned comparison.
C)an absolute contrast.
D)a post-hoc test.

Question 32

The correct order of post hoc comparison procedures following an analysis of variance from the least conservative to the most conservative is

A)Bonferroni,Scheffé,Tukey.
B)Scheffé,Tukey,Bonferroni.
C)Tukey,Scheffé,Bonferroni.
D)Bonferroni,Tukey,Scheffé.

Question 33

[(S²_Between)(df_Between)]/[(S²_Between)(df_Between)+ (S²_Within)(df_Within)] =

A)R²
B)F
C)f
D)t

Question 34

Advanced topic: One advantage of using the structural model to understand the analysis of variance (as opposed to the method which involves averaging the variances of each group)is that

A)it provides more accurate results.
B)it makes analyzing the results easier when group sizes are different.
C)it is more structured,and therefore more rigid.
D)it is more robust to violations of assumptions of normal population distributions.

Question 35

The power of an analysis of variance can be increased by all of the following EXCEPT

A)having more participants in each group.
B)using more groups in an experiment.
C)using the .01 significance level instead of the .05 significance level.
D)having equal numbers of participants in the groups.

Question 36

The results of an analysis of variance would be reported in a research article as

A)F (44)= 3.40,significant
B)F (2,44)< .05
C)F (2,44)= 3.40,p < .05
D)F = 3.40,p < .05

Question 37

If a research article reports that "The mean performance scores for the Normal Sleep,Reduced Sleep,and No Sleep groups were 18.0,16.6,and 15.6,respectively,F (2,36)= 2.95,p < .05," the most accurate conclusion is that

A)people who get no sleep perform significantly worse than people who sleep a reduced amount.
B)people who get no sleep perform significantly better than people who sleep a normal amount.
C)the three groups do not all come from populations with the same mean,although it is not clear which population means are different.
D)conclusions about the relationship between amount of sleep and performance cannot be drawn from these results.

Question 38

If a research article reports "F (2,36)= 2.95,p < .05," you know that

A)there were two groups.
B)there were 39 participants.
C)there were 36 participants.
D)there were 36 participants per group.

Question 39

A planned comparison comparing two means involves figuring an F ratio in which the denominator

A)depends on the pair of means being compared.
B)has degrees of freedom equal to the total within-groups degrees of freedom of the two groups being compared.
C)is the overall within-groups population variance estimate,regardless of the pair of means being compared.
D)does not involve figuring an F ratio for any planned comparison.

Question 40

A crucial feature of planned comparisons is that they are

A)planned before the study is conducted.
B)planned after the study is conducted,but before the analysis of variance is conducted.
C)tests of power,conducted before the study is conducted.
D)only conducted if power is greater than .80.

Question 41

The null hypothesis of an analysis of variance is that the __________ means are equal.

Question 42

Advanced topic: The sum of the squared deviations of each score from the mean of its group plus the sum of the squared deviations of each score's group's mean from the grand mean equals

A)the grand mean divided by df_Total.
B)the portion of the grand mean's deviation accounted for by the score itself.
C)the portion of the grand mean's deviation accounted for by the score's group.
D)the sum of squared deviations of each score from the grand mean.

Question 43

In a one-way analysis of variance,when sample sizes are equal,"(S²_M)(n)" is the formula for __________.(Do not give a symbol.)

Question 44

An experimenter "fishing for results" once a study is completed is conducting __________.

Question 45

The F ratio was invented by __________.

Question 46

In an analysis of variance,if the null hypothesis is false,then the __________- groups estimate of the population variance is larger than if the null hypothesis were true.

Question 47

A planned comparison involving more than two means,such as the average of two groups versus a third,is called a(n)__________ comparison.

Question 48

In an analysis of variance,if the null hypothesis is false,then the __________- groups estimate of the population variance is much smaller than the __________- groups estimate.

Question 49

In a planned comparison of two particular means,a between-groups population variance estimate,based on the two groups being compared,is divided by a within-groups population variance estimate,based on __________.

Question 50

If a researcher conducted six t tests,each at the .05 significance level,the chance that at least one test would reach significance would be about __________,even if the null hypothesis were true.(Give a number.)

Question 51

The between-groups population variance estimate divided by the within-groups population variance estimate is called __________.

Question 52

The method used to make planned comparisons that involves dividing the total significance level by the number of comparisons to be made is the __________.

Question 53

In a one-way analysis of variance,"(S²₁ + S²₂ + … + S²_last)/ N_groups" is the formula for __________.(Do not give a symbol.)

Question 54

Advanced topic: Σ(X-GM)²

A)equals the sum of squared deviations of scores from their group's mean.
B)ignores the group a score is in.
C)is always smaller than Σ(X-M)².
D)is used to determine the grand mean.

Question 55

When conducting an analysis of variance,one assumption is that each population distribution is __________.

Question 56

Advanced topic: Each score's deviation from the grand mean represents

A)true variation.
B)measurement error.
C)both true variation and measurement error.
D)neither true variation nor measurement error.

Question 57

Advanced topic: If you were to use a "signal-noise" analogy to explain the structural model,you could say that "signal" represents

A)the between-groups population variance estimate.
B)the within-groups population variance estimate.
C)the total population variance estimate.
D)degrees of freedom.

Question 58

A priori comparisons are also known as __________.

Question 59

Advanced topic: In an analysis of variance table,which of the following can be used to refer to "within-groups"?

A)treatment
B)model
C)group
D)error

Question 60

Conducting an analysis of variance involves comparing __________ different estimates of the population variance.(Give a number.)

Question 61

To study the effectiveness of possible treatments for insomnia,a sleep researcher conducted a study in which four participants were instructed to count sheep (the Sheep Condition),four were told to concentrate on their breathing (the Breathing Condition),and four were not given any special instructions (the Control Condition).The average number of minutes taken for participants to fall asleep over the next seven days were 39,33,42,and 38 minutes for the Sheep condition; 33,25,31,and 27 minutes for the Breathing condition; and 44,41,38,and 41 for the Control condition.Using the .01 significance level,did the different techniques have different effects?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Figure the effect size of this study and indicate whether it is nearer to small,medium,or large.
d.Figure a planned contrast between the means for those in the Sheep Condition versus those in the Breathing Condition using the .05 significance level.
e.Conduct Scheffé's test for the groups in (d)and indicate the F cutoff,the F you would use for the comparison,and the hypothesis-testing decision (reject or do not reject).
f.Explain the logic of what you did to a person who is familiar with the t test for independent means,but who knows nothing about the analysis of variance.(Be sure your explanation includes the logic of comparing within-groups to between-groups population variance estimates,the logic of how each of these is figured,the F distribution,and the F table.)

Question 62

based on the following tables.

Advanced topic: SS_Total = __________.(Give a number.)

Question 63

based on the following tables.

Advanced topic: SS_Within = __________.(Give a number.)

Question 64

based on the following tables.

Advanced topic: Complete the ANOVA summary table,replacing the letters (a)to (i)with the appropriate number.

Question 65

Prior to eating breakfast,25 participants were randomly assigned to eat a large meal,25 to eat a small meal,and 25 to eat nothing.Immediately following the meal,all participants took a memory test.The means and estimated population variances for the three groups on the memory test were: Large: M = 2.1,S² = 1.0; Small: M = 2.5,S² = 1.2; Nothing: M = 2.9,S² = 0.8.Using the .05 significance level,does amount of breakfast eaten affect memory?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Figure the effect size of this study and indicate whether it is nearer to small,medium,or large.
d.Conduct a planned contrast for Large Meal versus Small Meal (using the .05 level).
e.Conduct Scheffé's test for the groups in (d)and indicate the F cutoff,the F you would use for the comparison,and the hypothesis-testing decision (reject or do not reject).
f.Explain the logic of what you did to a person who is familiar with the t test for independent means,but who knows nothing about the analysis of variance.(Be sure your explanation includes the logic of comparing within-groups to between-groups population variance estimates,the logic of how each of these is figured,the F distribution,and the F table.)

Question 66

Advanced topic: Thinking of each score in an analysis of variance in terms of its overall deviation being divided into two parts is the core idea of __________.

Question 67

If a study has 3 groups,each with 20 participants,and a one-way analysis of variance produced an F ratio of 6.21 that was significant at the .01 level,the results would be reported in a research article as __________.

Question 68

Rosnow and Rosenthal propose that analyses of variance can often be replaced with __________.

Question 69

based on the following tables.

Advanced topic: At the .01 significance level,the null hypothesis __________.(Provide hypothesis testing decision.)

Question 70

According to Cohen's conventions,an R² of 14% (.14)is considered a(n)__________ effect size.

Question 71

based on the following tables.

Advanced topic: df_Between = __________.

Question 72

R² is never greater than __________.(Give a number.)

Question 73

based on the following tables.

Advanced topic: SS_Between = __________.(Give a number.)

Question 74

In research articles,post-hoc comparisons are often displayed in tables with __________ placed by the means to indicate whether the means are alike or different.

Question 75

High school juniors planning to attend college were randomly assigned to view one of four videos that emphasized social life,athletics,scholarship,or artistic/cultural opportunities at a particular college.After viewing the videos,the participants took a test of their desire to attend this college,with the following results.Using the .05 significance level,did the type of activity emphasized in the video affect the participants' desire to attend the college? a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Figure the effect size of this study and indicate whether it is nearer to small,medium,or large.
d.Conduct a planned contrast for the Social Life versus Scholarship films (using the .05 level).
e.Conduct Scheffé's test for the groups in (d)and indicate the F cutoff,the F you would use for the comparison,and the hypothesis-testing decision (reject or do not reject).
f.Explain the logic of what you did to a person who is familiar with the t test for independent means,but who knows nothing about the analysis of variance.(Be sure your explanation includes the logic of comparing within-groups to between-groups population variance estimates,the logic of how each of these is figured,the F distribution,and the F table.)

Question 76

based on the following tables.

Advanced topic: R² = __________.

Question 77

There are four determinants of the power of a one-way analysis of variance: effect size,sample size,significance level,and the __________.

Question 78

Forty-five participants (15 per group)were randomly assigned to do a series of math tasks while listening to soft-gentle music,while listening to loud-intense music,or while in silence.The means and estimated population variances for the three groups were: Soft-Gentle: M = 37,S² = 28; Loud-Intense: M = 33,S² = 25; Silence: M = 41,S² = 22.Using the .05 significance level,is there a difference in performance on this kind of math task under these three conditions?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Figure the effect size of this study and indicate whether it is nearer to small,medium,or large.
d.Conduct a planned contrast for the Soft-Gentle versus Silence conditions (using the .05 level).
e.Conduct Scheffé's test for the groups in (d)and indicate the F cutoff,the F you would use for the comparison,and the hypothesis-testing decision (reject or do not reject).
f.Explain the logic of what you did to a person who is familiar with the t test for independent means,but who knows nothing about the analysis of variance.(Be sure your explanation includes the logic of comparing within-groups to between-groups population variance estimates,the logic of how each of these is figured,the F distribution,and the F table.)

Question 79

based on the following tables.

Advanced topic: df_Within = __________.

Question 80

A sports psychologist gave a questionnaire about healthy eating habits to randomly selected professional athletes.The results are displayed below.Using the .05 significance level,is there a difference in healthy eating habits among professionals in the three sports? a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Figure the effect size of this study and indicate whether it is nearer to small,medium,or large.
d.Conduct a planned contrast for Baseball versus Football players (using the .05 level).
e.Conduct Scheffé's test for the groups in (d)and indicate the F cutoff,the F you would use for the comparison,and the hypothesis-testing decision (reject or do not reject).
f.Explain the logic of what you did to a person who is familiar with the t test for independent means,but who knows nothing about the analysis of variance.(Be sure your explanation includes the logic of comparing within-groups to between-groups population variance estimates,the logic of how each of these is figured,the F distribution,and the F table.)