Deck 16: One-Way Analysis of Variance

Question 1

The analysis of variance differs from a t test for two independent samples because

A) the t test is limited to 2 samples.
B) the analysis of variance can handle multiple samples.
C) they test different hypotheses.
D) both a and b

Answer 1

both a and b

Question 2

An important assumption in the one-way analysis of variance is that

A) observations are random.
B) observations are independent.
C) subjects are related.
D) there are equal numbers of observations in each group.

Answer 2

observations are independent.

Question 3

Which of the following is not a critical element of the analysis of variance?

A) the variance within each group
B) the variance of the means
C) the variance of the total sample
D) the difference between the means

Answer 3

the variance of the total sample

Question 4

The analysis of variance assumes that

A) the populations have no variance.
B) the samples have equal variances.
C) the populations have equal variances.
D) the variances are normally distributed.

Question 5

If we had the following pattern of population means (μ₁ = μ₂ = μ₃ ≠ μ₄) we would hope to conclude that

A) the null hypothesis is false.
B) the null hypothesis is true.
C) the null hypothesis is confused.
D) the experiment will have very little power.

Question 6

In the analysis of variance, the more the null hypothesis is false,

A) the larger the value of F .
B) the smaller the value of F .
C) the smaller the value of the correlation coefficient.
D) the harder it is to find a significant difference.

Question 7

We use the symbol
to represent

A) the variance of the individual observations.
B) the variance of the group totals.
C) the variance of the error scores.
D) the variance of the means.

Question 8

If the null hypothesis in the analysis of variance were true,

A) the variances would all be the same.
B) the sample means would all be the same.
C) the population means would all be the same.
D) every subject would have the same score.

Question 9

In evaluating the F in the analysis of variance, we need to know

A) the degrees of freedom for the Between Groups term.
B) the degrees of freedom for the Within Groups term.
C) only the total number of degrees of freedom.
D) both a and b

Question 10

In the Eysenck study of recall of lists of words, a significant F in the analysis of variance would at the least tell us that

A) greater processing leads to greater recall.
B) less processing leads to greater recall.
C) the recall means are different in the different groups.
D) none of the above

Question 11

In the analysis of variance we will assume that

A) the populations are normally distributed.
B) the populations follow a rectangular distribution.
C) the populations all have completely different shapes.
D) There is no assumption about the shape of the population.

Question 12

When we use the phrase "within group" we mean

A) the variability of the group means.
B) the variability within the group means.
C) the variability calculated for the scores within each group separately.
D) the variability within all of the data points.

Question 13

If we want to have faith in the results of our particular study, we will be most concerned with

A) random sampling.
B) random assignment.
C) equal sample sizes.
D) a significant F .

Question 14

The major difference between t tests and the analysis of variance is that the latter

A) deals with multiple groups.
B) compares group variances.
C) makes different assumptions about the populations from which we sample.
D) none of the above

Question 15

The analysis of variance compares

A) the total variance with the variance within groups.
B) the total variance with the variance between group means.
C) the variance between group means with the variance within groups.
D) the variance within groups with the variance among all data points.

Question 16

When we speak about error variance in the analysis of variance we are speaking of

A) differences between subjects in the same group.
B) differences between subjects in different groups.
C) the overall variability of scores in the experiment.
D) the misrecording of data.

Question 17

In the analysis of variance with three groups the null hypothesis is

A) the three population means are all different.
B) at least one of the population means is different from the others.
C) the three population means are equal to each other.
D) We can't tell from what is given here.

Question 18

In the analysis of variance, MS_error is

A) the average of the between group variances.
B) the average of the between group sums of squares.
C) the sum of squares of the within group variances.
D) the average of the within group variances.

Question 19

If the null hypothesis is true, we would expect the F in the analysis of variance to be

A) approximately 0.
B) somewhere around 1.
C) at least 10.
D) the value of F is not dependent on the status of the null hypothesis.

Question 20

When we reject the null hypothesis in the analysis of variance we can conclude that

A) all of the means are the same.
B) all of the means are different.
C) at least one of the means is different from at least one other mean.
D) only one mean is different from one other mean.

Question 21

If we run six independent comparisons among means, each at the five percent level, the overall familywise error rate will be approximately

A) .05.
B) .05/6.
C) .30.
D) .01.

Question 22

The major difference between η² (eta-squared) and ω² (omega-squared) is that

A) η² tends to overestimate the true value in the population.
B) ω² tends to overestimate the true value in the population.
C) calculation of η² uses the number of groups.
D) the calculation of ω² is quicker and easier.

Question 23

We can probably get away with violating assumptions if

A) the data are reasonably normal.
B) the variances are not too different.
C) the unequal variances are not paired with very unequal n s.
D) all of the above

Question 24

The magnitude of effect in a study was calculated to yield values for both η² and ω². Which of the following relationships between η² and ω² is likely?

A) η² = ω²
B) η² > ω²
C) η² ω ²
D) none of the above

Question 25

For an F value to be significant it must

A) be positive.
B) equal 1.0.
C) exceed the tabled value.
D) be less than the tabled value.

Question 26

The Bonferroni procedure controls error rates by

A) operating at a reduced level of α.
B) operating at an increased level of α.
C) not allowing you to make any comparisons unless the F is significant.
D) changing the error term.

Question 27

The following analysis of variance summary table applies to the next several questions.

In the experiment whose summary table is given above, the average standard deviation in each of the groups was approximately

A) 110.
B) 20.
C) 4.5.
D) 92.

Question 28

Which of the following is a possible null hypothesis in an analysis of variance with 5 groups?
( H ₁: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄ ≠ μ₅; H ₂: μ₁ ≠ μ₂ = μ₃ = μ₄ = μ₅)

A) the first one
B) the second one
C) both the first and second
D) Neither of these is a null hypothesis.

Question 29

The following analysis of variance summary table applies to the next several questions.

How many groups were there in this experiment?

A) 1
B) 2
C) 3
D) 4

Question 30

In a one-way analysis of variance we deal with unequal sample sizes by

A) not allowing them.
B) doing nothing different.
C) averaging the means.
D) multiplying each squared deviation by n _j as we go along.

Question 31

Fisher's LSD test is most useful when

A) you have only two means.
B) you have two or three means.
C) you have many means.
D) you have a nonsignificant overall F .

Question 32

The notation Σ( X - ..)² produces the term we call the

A) SS _between
B) SS _within
C) SS _total
D) MS _error

Question 33

Mean squares are closest to

A) means.
B) variances.
C) standard deviations.
D) F s.

Question 34

Unequal sample sizes in a one-way analysis of variance are generally

A) a major problem.
B) a minor inconvenience.
C) something to be avoided at all costs.
D) impossible.

Question 35

The column of mean squares in the analysis of variance is obtained by

A) dividing the sums of squares by the degrees of freedom.
B) multiplying the degrees of freedom times the sums of squares.
C) dividing the sum of squares for treatments by the sum of squares for error.
D) dividing the degrees of freedom by each other.

Question 36

The following analysis of variance summary table applies to the next several questions.

How many subjects were there in this experiment?

A) 100
B) 95
C) 93
D) 92

Question 37

The notation
 is used to calculate

A) SS _between
B) SS _within
C) SS _total
D) MS _error

Question 38

The familywise error rate is

A) the probability of at least one Type I error.
B) the probability of no Type I errors.
C) the number of Type I errors that you are likely to make.
D) the probability of a Type II error.

Question 39

The following analysis of variance summary table applies to the next several questions.

What would you conclude from the summary table above?

A) The difference "between groups" is significant by a one-tailed test of μ₁ μ ₂.
B) The difference "between groups" is not significant.
C) The difference "between groups" is significant.
D) We don't have enough information to draw a conclusion.

Question 40

In an analysis of variance summary table, the df for groups always equals

A) the number of groups.
B) the number of groups minus one.
C) the number of subjects per group.
D) the total number of subjects minus one.

Question 41

The post-hoc test which holds the familywise error rate at .05 by running each individual test at the c/alpha level (# comparisons/alpha) is the

A) Fisher's LSD.
B) Bonferroni.
C) Newmann Keuls.
D) Tukey test.

Question 42

What are our choices for effect size measures for a one-way ANOVA?

A)
B) η²
C) w ²
D) all of the above

Question 43

When looking at multiple comparisons, the more tests that you run, the more likely that you will have a _______.

A) Type I error
B) Type II error
C) mean squared error
D) random error

Question 44

You want to control the _______ when multiple comparisons are being made?

A) probability error rate
B) significance error rate
C) familywise error rate
D) test-retest error rate

Question 45

Which of the following is not a multiple comparison procedure we have discussed in class or seen in the texts.

A) Fisher's LSD test.
B) The Stroop test.
C) The Bonferroni test.
D) The Newman-Keuls test.

Question 46

The null hypothesis behind a simple multiple-group analysis of variance is of the form:

A)
B)
C)
D)

Question 47

Eysenck's study on recall as a function of level of processing showed

A) processing makes only minimal difference to recall.
B) old people don't learn anything.
C) just telling someone to learn a list of words doesn't work.
D) recall increases with the level of processing.

Question 48

A common criticism of Fisher's LSD test is that

A) it is sometimes too conservative.
B) it is sometimes too liberal.
C) it is too difficult.
D) it relies on a non-normal distribution.

Question 49

In the analysis of variance, MS_Groups measures how different group means are, and MS_error measures variability within each group. If the null hypothesis were false, what would we expect to find?

A) That MS_groups and MS_error would be roughly equal.
B) That MS_groups would be larger than MS_error.
C) That MS_error is larger than MS_groups.
D) That MS_error is close to zero.

Question 50

The familywise error rate is

A) the probability of at least one Type I error in a set of comparisons.
B) the probability of no Type I errors.
C) the number of Type I errors that you are likely to make.
D) the probability of a Type II error.

Question 51

A researcher found significant differences in the mean running speeds of sprinters wearing shoes made by Nike, Reebok, and Adidas using an analysis of variance. The η² calculated on the basis of group membership (based on which shoes were worn) equaled .16. The value of η² shows that

A) the r value would be .4.
B) 84% of the variability in running speed is attributed to shoe brand.
C) 16% of the variability in running speed is attributed to shoe brand.
D) most of the factors influencing running speed are contained in the brand of shoes worn by runners.

Question 52

We want to compare the scores of different groups on a measure of reaction time. Three different groups were studied: patients with recent head injuries, patients with old head injuries, and a control group of non-injured people. We want to know which group of people has the fastest reaction time. What is the best statistical test to use to find this out?

A) one-way ANOVA
B) factorial ANOVA
C) paired samples t -test
D) correlation

Question 53

What type of multiple comparison procedure should be used if we want to divide the familywise error rate among the number of comparisons that we are performing?

A) Fisher's LSD
B) Bonferroni procedure
C) factorial ANOVA
D) paired samples t-test

Question 54

The mean square error (MS_error) is a measure of

A) how different the group means are.
B) whether the dependent variable was measured incorrectly.
C) how much variability there is within each group.
D) whether the ANOVA is significant.

Question 55

When analyzing results of an ANOVA we are most interested in the _______.

A) F Statistic
B) t Statistic
C) R Squared
D) both a and c

Question 56

In multiple comparison procedures, post-hoc tests are completed after the ANOVA. Why are post-hoc tests preferred over running several t-tests?

A) They decrease the probability of a Type I error.
B) They do not control familywise error rate.
C) It increases the probability of a Type I error.
D) They are more likely to be significant.

Question 57

We want to compare the scores of different groups on a measure of reaction time. Three different groups were studied: patients with recent head injuries, patients with head injuries that occurred a year ago, and a control group of non-injured people. We want to know which group of people has the fastest reaction time. What is the best statistical test to use to find this out?

A) one way ANOVA
B) factorial ANOVA
C) paired samples t-test
D) correlation

Question 58

When we run a one-way ANOVA with four groups and obtain a significant F , the best effect-size measure to convey what that result tells us is

A) .
B) η².
C) w ² .
D) all of the above

Question 59

The book discusses an experiment by Merrell that examined the effects of Anthrax, Mozart, and no music on the amount of time it took a mouse to run a maze. To determine if there is an overall difference between the three groups, Merrell ran an ANOVA. To determine which means differed for each other, he ran a

A) regression.
B) repeated-measures t-test.
C) Bonferroni test.
D) chi-square.

Question 60

A student wanted to determine if the mean number of times a student missed class was different for sophomores, juniors, and seniors. After collecting attendance data, the student ran an ANOVA and found that MS_groups was much larger than MS_error. This student can conclude that

A) sophomores miss class more than juniors and seniors.
B) there is a difference in the mean number of times sophomores, juniors, and seniors miss class.
C) seniors miss class more than sophomores and juniors.
D) there is no difference between the groups.

Question 61

An overall ANOVA was significant. A student calculated t-tests between each of the groups. Each group consisted of 15 people. Which groups are significantly different from one another using a Bonferroni correction?

Question 62

If η² = .16, 4% of the variability in the dependent variable is attributable to group membership.

Question 63

Calculate η² and ω ² for the previous problem.

Question 64

Indicate whether or not each of the following F statistics are significant based on the following information, assuming α = .05.
a. F (4, 120) = 3.26
b. F (2, 60) = 3.10
c. F (6, 500) = 2.14

Question 65

Which of the following represents a measure of the magnitude of effect?

A) η²
B) ω²
C)
D) all of the above

Question 66

We have run a one-way ANOVA comparing three treatments for anorexia and found a significant difference. We now want to convey the most useful information to our reader about how effect one treatment is relative to one or more other treatments. The best statistic to use here to convey that information would most likely be

A)  computed on one or more pairs of groups.
B) η ² computed on all three groups.
C) w ²  computed on all three groups.
D) none of the above

Question 67

F is the ratio of MS_group divided by MS_error.

Question 68

df_group is the number of groups being compared in the ANOVA.

Question 69

The grand mean is the mean of all observations across all groups.

Question 70

We generally don't compute a confidence interval on the omnibus null hypothesis because

A) it is not clear what it would mean if we could do so.
B) we don't know how to do so.
C) it does not address the questions we are likely to want to answer.
D) all of the above

Question 71

Cohen's
is generally a better measure than η ² or w ²  because

A) it is more specific to individual treatments.
B) it is less biased than any other measure.
C) it pulls together information from all of the treatments.
D) It actually is a worse measure than the others.

Question 72

An ANOVA is used to compare the means of two or more groups.

Question 73

The larger the ratio of the more likely that the group means differ significantly one another significantly.

Question 74

Name 3 assumptions underlying a one-way ANOVA.

Question 75

The analysis of variance differs from a t test for two independent samples because

A) the t test is limited to 2 samples.
B) the analysis of variance can handle multiple samples.
C) they test different hypotheses.
D) both a and b

Question 76

When we use the phrase "omnibus null hypothesis" we are referring to

A) μ ₁ = μ ₂
B) μ ₁ = μ ₂ = μ ₃ = μ ₄
C) μ ₁ = μ ₂ ≠ μ ₃ = μ ₄
D) μ ₁ ≠ μ ₂

Question 77

Given the following information, calculate and interpret F.

Question 78

MS_group is the variability among subjects in the same group.

Question 79

MS_error is the variability among group means.

Question 80

In a Bonferrroni procedure, α is divided by the number of groups.