Deck 10: Introduction to the Analysis of Variance

Question 1

Because of the assumption that the population variances are equal, when you do an analysis of variance:

A)you need fewer degrees of freedom
B)sample variances are not important
C)you figure an averaged estimate of the population variance
D)you use actual population parameters in place of sample statistics

Answer 1

you figure an averaged estimate of the population variance

Question 2

An analysis of variance (ANOVA)differs from a test for independent means (t test)in that an ANOVA:

A)is usually used to compare the means of two groups but a t test is used to compare three groups
B)is used to compare the means of three or more groups whereas a t test is used to compare two groups
C)is conducted before the experiment whereas a t test is conducted after the experiment
D)figures variances as part of the analysis whereas a t test does not figure variances

Answer 2

is used to compare the means of three or more groups whereas a t test is used to compare two groups

Question 3

" S²Within" equals:

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

Answer 3

the population variance estimate based on the variation within each of the groups

Question 4

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

A)the variation between sample means reflects the variation within the populations and the variation between the population means
B)the within-group variance is significantly larger than the between-group 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 5

How do you figure S²Within "assuming sample sizes are equal"?

A)Add up the population variance estimates figured from within each group, then divide by the total number of participants
B)Add up the population variance estimates figured from within each group, then divide by the number of groups
C)Multiply the within-group sum of squares by the size of each sample (n)
D)Divide the within-group sum of squares by the size of each sample (n)

Question 6

If the null hypothesis is false, the between-groups estimate of population variance will not give an accurate estimate of the variation within the populations because it also will be affected by:

A)the difference between the variances of the two distributions of means
B)the sum of the variances of the two distributions of means
C)the difference between the two estimated population variances
D)the variation among the populations

Question 7

What does the formula Σ (M-GM)²/ df_Between provide?

A)The t score for a t test for dependent means
B)The between-group sum of squared deviations
C)The estimated variance of the distribution of means
D)The within-group estimate of the population variance

Question 8

If three samples have means of 10, 20, and 15, respectively, what is their grand mean?

A)5
B)10
C)15
D)20

Question 9

If the null hypothesis is true, __________ gives an accurate indication of the variation within the populations (i.e., the variation due to chance factors)

A)the estimated mean of the distribution of variances of Population 1
B)the variance of the difference scores for Population 1
C)the between-groups estimate of the population variance
D)the estimated mean of the distribution of variances of Population 2

Question 10

Analysis of variance should only be done when:

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

Question 11

When you do an analysis of variance:

A)you need fewer participants than for a t test for independent means
B)you compare two estimates of the population variance
C)you figure difference scores, as in a t test for dependent means
D)all of the above

Question 12

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

A)general multiple
B)grand mean
C)group mean
D)guess of maturation

Question 13

A procedure used to compare more than two groups of scores, each of which is from an entirely separate group of people, is called a(n):

A)analysis of variance
B)analysis of mean scores
C)t test for independent means
D)Z test for three groups

Question 14

In an analysis of variance, when the null hypothesis is true, then all of the following are true EXCEPT:

A)occasionally an F ratio will be significant anyway
B)within-group and between-group variances are estimating the same population variance
C)the F ratio will generally be significantly larger than 1
D)the variance between samples is due entirely to random sampling variance

Question 15

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

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

Question 16

When the research hypothesis is true, the means of the samples are spread out for what reason(s)?

A)Because of variation within each of the populations (due to unknown chance factors)
B)Because of variation among the means of the population (a treatment effect)
C)Because of variation in the level of significance set by the experimenter
D)Both A and B

Question 17

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

A)the research hypothesis is also true
B)you will need fewer participants for the experiment
C)there is less variance among the sample means than if the null hypothesis was not true
D)the within-group estimate of population variance is smaller than the between-group estimate

Question 18

When conducting an ANOVA, the within-groups population variance estimate is the sum of the population variance estimates based on each sample, divided by the:

A)sample size
B)number of groups
C)degrees of freedom
D)number of groups minus 1

Question 19

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

A)the null hypothesis should be rejected
B)any difference between sample means is probably due to random sampling
C)an error in the figuring was made, because a within-group variance estimate must always be smaller than the between-group variance estimate
D)any difference between sample means is probably due to a real difference caused by the experimental conditions

Question 20

In an ANOVA, if the between-group variance estimate is 640 and the within-group variance estimate is 110, what is the F ratio?

A)5)82
B) .17
C)6)82
D)704

Question 21

When using the F table, one must pay attention to:

A)significance level
B)between-groups degrees of freedom
C)within-groups degrees of freedom
D)all of the above

Question 22

The within-groups degrees of freedom is also known as the:

A)sample size degrees of freedom
B)numerator degrees of freedom
C)denominator degrees of freedom
D)ANOVA test degrees of freedom

Question 23

In ANOVA, the ratio of the between-groups population variance estimate to the within-groups population variance estimate is known as the:

A)F ratio
B)T ratio
C)ANOVA ratio
D)distribution

Question 24

As a general rule, in an ANOVA if the variance estimate of the group with the largest estimate is no more than __________ that of the smallest and the sample sizes are equal, the conclusions using the F distribution should be adequately accurate.

A)1 or 2
B)4 or 5
C)around 10
D)around 25

Question 25

In an analysis of variance, the between-group estimate of the population variance is 30 and the within-group estimate is 25. What is the F ratio?

A)25/(30-25)= 5.00
B)(30-25)/30 = 0.17
C)25/30 = .83
D)30/25 = 1.20

Question 26

In an analysis of variance, the within-group population variance estimate is 8.5 and the between-group estimate is 5.3. What is the F ratio?

A)5)3/8.5 = 0.62
B)8)5/5.3 = 1.60
C)square root of (5.3/8.5)= 0.79
D)square root of (8.5/5.3)= 1.27

Question 27

Typically, after getting a significant result with an ANOVA, researchers will go on to compare:

A)each population to each other population (using a protected t test)
B)the attained Z scores for each population
C)the attained F scores for each population
D)the modal scores in addition to the mean scores (using a nonparametric procedure)

Question 28

For analysis of variance, an approach to effect size is to calculate the:

A)size of the groups multiplied by the sample means
B)proportion of variance accounted for (R²)
C)difference between the two means divided by the pooled population variance
D)difference between the two means divided by the pooled population standard deviation

Question 29

Suppose you had four populations with equal means and equal variances. You could make an F distribution for situations with samples of 10 each by:

A)applying the test formula to each pair of samples and squaring, then repeating this process a large number of times
B)applying the ANOVA formula to a set of four samples (one from each of the four populations)of 10 each, figuring df, and repeating this process a large number of times
C)taking 10 samples from one of the populations, figuring the F ratio, and repeating this a large number of times
D)taking samples of 10 from each of the four populations, figuring an F ratio for each set of samples, and repeating this a large number of times

Question 30

In an analysis of variance where sample sizes are equal, when you go from the estimated variance of the distribution of means to an estimated variance of the population of individual scores you:

A)multiply the estimated variance of the distribution of means by the number of participants in each sample
B)divide the estimated variance between groups by the number of groups
C)divide the estimated variance of the distribution of means by the number of participants in each sample
D)divide the estimated variance of the population of individuals by the number of groups

Question 31

The conventions for R² are as follows for small, medium, and large effect sizes, respectively:

A) .2, .5, .8
B) .1, .4, .9
C) .01, .06, .14
D) .001, .5, .1

Question 32

The F distribution/ratio:

A)is symmetrical
B)has a long tail on the right
C)cannot be a very high number
D)tends to result in numbers that pile up near -1

Question 33

A mathematically defined curve that is the comparison distribution used in ANOVA is called the:

A)normal distribution
B)chi square distribution
C)F distribution
D)T distribution

Question 34

An important characteristic of an F ratio is that:

A)when looking up the cutoff on a table, the degrees of freedom are needed from the numerator, denominator, and the sum of squares calculation
B)it is never less than 0
C)it is negatively skewed (the long tail to the left)
D)the standard t distribution (for 30 df)is used as a comparison distribution

Question 35

Suppose you were conducting an ANOVA with 6 groups of 10 participants each. What are your between-groups and within-groups degrees of freedom, respectively?

A)6; 60
B)60; 6
C)54; 6
D)5; 54

Question 36

When using the value of R² to calculate effect size for an ANOVA, R² represents the proportion of the total variation of scores from the __________ that is accounted for by variation between the means of the groups.

A)median of group 1
B)mode of groups 2 and 3
C)grand mean
D)protected t tests

Question 37

In analysis of variance procedures, special t tests conducted among pairs of means after finding a significant overall F value are called:

A)t tests for post ANOVA
B)t tests for dependent ANOVA pairs
C)protected t tests
D)preferred t tests

Question 38

Tukey's HSD test is a type of:

A)power coefficient
B)pooled estimate
C)protected t test
D)independent t score

Question 39

A study has three groups, each with an equal number of participants. The population variance is estimated from the variance within each group, giving three estimates, 54.4, 48.6, and 50.9. What is the within-group estimate of the population variance?

A)(54.4 + 48.6 + 50.9)/(3-1)= 76.95
B)(54.4 + 48.6 + 50.9)/3 = 51.3
C)(54.4 + 48.6 + 50.9)/(3 + 1)= 38.48
D)(54.4 + 48.6 + 50.9)/(3 + 2)= 30.78

Question 40

Suppose you were conducting an ANOVA with four groups of five participants each. What are your within-groups and between-groups degrees of freedom, respectively?

A)16; 4
B)12; 3
C)20; 3
D)16; 3

Question 41

What is the main advantage of using a factorial design instead of doing separate studies of each variable?

A)Speed: with a factorial design you are able to carry out a study at twice the speed of other designs.
B)Effect size: with a factorial design you can increase the effect size by a factor of 2-4.
C)Efficiency: with a factorial design you study both variables at once without needing twice as many participants.
D)Both A and B.

Question 42

A consumer researcher is interested in the effects of Annual Income and Motivations to Shop on shopping patterns of consumers. If Annual Income (broken into two levels: High and Moderate)and Motivation to Shop (with three levels: Escape, Necessity, and Socializing)are considered in one study, how many cells will there be?

A)2
B)3
C)4
D)6

Question 43

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

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

Question 44

Before carrying out a study, a researcher can calculate approximate power for the .05 significance level for small, medium, and large effect sizes if one has access to a power table and knows the __________.

A)estimated effect size
B)outcome of the hypothesis-testing procedure
C)multiple correlation
D)degrees of freedom within

Question 45

When carrying out an ANOVA, what is the approximate number of participants needed in each group (assuming equal sample sizes)for 80% power when you anticipate a medium effect size and have four groups in the study?

A)16
B)18
C)21
D)45

Question 46

All of the following are true about the creator of the analysis of variance EXCEPT:

A)his name was Karl Pearson
B)he supported the idea of eugenics
C)he wrote 300 papers and 7 books
D)his work was first popularized in agriculture

Question 47

In a two-way factorial design, you are testing:

A)one interaction and one main effect
B)one interaction and two main effects
C)two interactions and one main effect
D)two interactions and two main effects

Question 48

The main advantage of a factorial design is that it lets you study:

A)the correlation between two or more variables
B)the predictive validity of several variables
C)the effects of combining two or more variables
D)nominal variables with parametric tests

Question 49

What is the approximate level of power for a study using ANOVA at the .05 significance level with four groups of 30 participants each (expected effect size is medium).

A) .13
B) .61
C) .96
D) .55

Question 50

A research article reports the following: "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." Based on this information, which conclusion is most accurate?

A)People who get no sleep perform significantly worse than people who sleep a reduced amount.
B)People who sleep a reduced amount perform significantly worse 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)This null hypothesis cannot be rejected.

Question 51

__________ is a way of organizing a study in which the effect of two or more variables is examined at once by making groupings of every combination of the variables.

A)Factorial research design
B)Repeated measures research design
C)Multiple research design
D)Influential research design

Question 52

An interaction effect in a two-way factorial research design:

A)is the effect of one variable, ignoring the influence of other variables
B)occurs when the influence of one variable changes according to the level of another variable
C)almost never occurs when more than one variable is considered at a time
D)is rare in a well-designed study, and usually indicates some error in computation

Question 53

A two-way factorial design:

A)is "two-way" because the influence of two separate variables is being studied
B)varies only in name from a one-way analysis of variance
C)considers two levels of a single variable
D)considers a single level of two variables

Question 54

Which of the following would be most likely to appear in a research article?

A)F(22)= 3.40, significant
B)F(2,55)< .05
C)F(2,44)= 3.4, p < .05
D)F = 3.40, p < .05

Question 55

Which of the following shows how the results of an analysis of variance would usually be reported in a research article?

A)F < p(.01)
B)F(3,50)= 4.33, p < .01
C)F(4.33)= p(.01)
D)F = 4.33, significant

Question 56

Suppose you are planning a study involving five groups and you expect a medium effect size (and will use the .05 level). For 80% power, how many participants will you need in each group?

A)240
B)52
C)16
D)39

Question 57

According to the effect size conventions for ANOVA, .14 is considered to be a __________ effect.

A)very small
B)small
C)medium
D)large

Question 58

Ronald A. Fisher was noted for:

A)the creation of the t test for independent means
B)his charming personality, which inadvertently helped popularize various statistical tests
C)the creation of the analysis of variance
D)his overcoming of great physical disabilities

Question 59

You conduct an ANOVA in which you expect a small effect size. What is your approximate level of power if you plan to use five groups with 20 participants in each group?

A) .01
B) .10
C) .13
D) .17

Question 60

Suppose you are planning a study involving three groups and you expect a large effect size (and will use the .05 level). For 80% power, how many participants will you need in total?

A)52
B)18
C)63
D)156

Question 61

In a factorial design, a "cell" is:

A)each combination of levels of the variables
B)the combination of different levels of one variable, ignoring any other variables
C)a study with a single two-level variable
D)the same thing as a main effect

Question 62

Which of the following statements is consistent with Scenario C?

A)Those who shop a long time spend four times as much as those who shop for less time.
B)Taken on their own, the marginal means indicate that there is an interaction effect.
C)Younger shoppers were not affected by the amount of time they shopped, but older people bought more if they just shopped for a short time.
D)Regardless of how long they shopped, younger people bought the same amount. However, older people bought more if they shopped a longer time.

Question 63

Scenarios A, B, and C each show:

A)an interaction effect
B)main effects
C)marginal means
D)both B and C

Question 64

A store manager said, "How much money people spend isn't related to age. All that matters is how long they shop." If she said that after seeing the results of one of these studies, which scenario was she probably looking at?

A)Scenario A
B)Scenario B
C)Scenario C
D)None of the above

Question 65

Which statement is true about Scenario A?

A)There is a moderate interaction effect.
B)Older buyers spend more in general, and the longer people shop, regardless of age, the more money they spend.
C)Old buyers who shop a long time buy more than young buyers who shop a long time, but old buyers who shop a short time buy less than young buyers who shop a short time.
D)The general trend is for buyers to buy more and shop for less time.

Question 66

Results of a two-way ANOVA are usually shown with:

A)a pie graph
B)a frequency polygon
C)a bar graph
D)a scatter diagram

Question 67

You conduct a study to assess the relative effectiveness of three different medications for depressive symptoms in patients with major depressive disorder. Three randomly selected groups of participants receive one of the three medications and their level of depression is measured before and after treatment. In this study, level of depression is the:

A)interaction effect
B)marginal mean
C)independent variable
D)dependent variable

Question 68

In a factorial design, the mean score for all participants at a particular level of one of the variables is a(n):

A)interaction effect
B)cell mode
C)cell mean
D)marginal mean

Question 69

For the following question(s): The scenarios below are possible results of a study in which participants completed a measure that assessed how important religion is to them personally. Participants are either from a rural or an urban area and are either poor or rich.
Which statement is TRUE about Scenario A?

A)There is a moderate interaction effect.
B)Religion is consistently more important for rich people than for poor people, regardless of where they live.
C)Religion is more important to people who live in an urban areas, regardless of wealth.
D)Religion is particularly important to people who are both poor and live in rural areas.

Question 70

A situation in a factorial analysis of variance in which the combination of variables has an effect that could not be predicted from the effects of two variables individually is known as:

A)a main effect
B)a marginal effect
C)an interaction effect
D)a grouping effect

Question 71

You can identify an interaction effect by:

A)comparing the pattern of cell means across one row to the pattern of cell means across another row
B)conducting a series of t tests
C)dividing each cell mean by its marginal mean
D)dividing each cell mean by a weighted marginal mean

Question 72

In a research study, a variable that is measured and represents the effect of the experimental procedure is known as the:

A)independent variable
B)dependent variable
C)main effect
D)main variable

Question 73

Which of the following interpretations are consistent with Scenario B?

A)People who spend more time shopping buy more if they are old than if they are young.
B)When there is a long time to shop, young shoppers outspend old shoppers; but if there is only a short time to shop, age makes no difference.
C)When older people shop quickly, they know what they want and spend a lot; when they shop slowly, they usually do not spend as much.
D)Older shoppers enjoy browsing (which means taking a long time)and when they take a long time, they end up purchasing a lot more than young shoppers.

Question 74

For the following question(s): The scenarios below are possible results of a study in which participants completed a measure that assessed how important religion is to them personally. Participants are either from a rural or an urban area and are either poor or rich.
Which of the following is most consistent with Scenario B?

A)Religion is more important to poor people when they live in rural areas.
B)Rich people, regardless of where they live, belong to a cultural elite that values religion moderately. Poor people value religion more in urban centers than in rural areas.
C)People who live in the city need religion more than people in the country, regardless of how rich or poor they are.
D)Rich people who move to the country are trying to get away from their materialistic lifestyle and tend to be more religious.

Question 75

Which of the scenarios has an interaction effect?

A)Scenario A
B)Scenario B
C)Scenario C
D)Both B and C

Question 76

In a two-way analysis, the result for a variable, averaging across the levels of the other grouping variable, is known as:

A)a main effect
B)a marginal effect
C)an interaction effect
D)a grouping effect

Question 77

A sociologist said, "As far as how important religion is to people, it doesn't matter where they live. What matters is how much money they make." If her conclusion was based on one of these scenarios, which one was she probably looking at?

A)Scenario A
B)Scenario B
C)Scenario C
D)None of the above

Question 78

Which of the scenarios has a main effect of wealth status?

A)Scenario A
B)Scenario B
C)Scenario C
D)All three of the above

Question 79

For the following question(s): The scenarios below are possible results of a study in which participants completed a measure that assessed how important religion is to them personally. Participants are either from a rural or an urban area and are either poor or rich.
Which of the following statements is true, based on Scenario C?

A)On the average, religion is more important to rich people than to poor people.
B)Religion is more important to the rural poor than to the urban poor.
C)There is no difference between rich and poor in their average interest in religion.
D)Poor people value religion more in urban areas while rich value it more in rural areas.

Question 80

You can identify interaction effects in all of the following ways EXCEPT:

A)through inspecting cell means
B)through inspecting marginal means
C)by using graphs
D)by a verbal description of results