Deck 12: One-Way Between-Groups Anova

Question 1

The z, t, and F distributions have something in common-the denominator of the test statistic:

A) contains a measure of difference among group means.
B) contains a measure of difference within the various groups.
C) is a squared number.
D) represents what would be expected if the null hypothesis were true.

Answer 1

contains a measure of difference within the various groups.

Question 2

The z, t, and F distributions have something in common-the numerator of the test statistic:

A) contains a measure of difference among group means.
B) contains a measure of difference within the various groups.
C) is a squared number.
D) represents what would be expected to happen by chance.

Answer 2

contains a measure of difference among group means.

Question 3

Interested in the effects of different kinds of instruction on video game performance, Martin asks 30 college freshmen to each play one hour of Ratchet and Klank.Participants are randomly assigned to one of three instruction groups: (1) complete the tasks as quickly as possible, (2) conserve as much health as possible find gold bolts (worth lots of money in equipment and ammunition).If Martin averages the scores for each instruction group and then compares them, any differences in the means of the instruction groups reflect:

A) individual differences in hand-eye coordination.
B) inherent differences in the ability of the college freshmen to play video games.
C) within-groups variance.
D) between-groups variance.

Answer 3

between-groups variance.

Question 4

If there are only two samples, then the F distribution is the:

A) sum of the two samples.
B) square of the t distribution.
C) square of the z distribution.
D) null hypothesis distribution for N = 2.

Question 5

Given a scale dependent variable and a nominal independent variable with three or more levels, a(n) _____ could be used to analyze the data.

A) PRE test
B) z test
C) t test
D) ANOVA

Question 6

A researcher can't just run multiple t tests when the independent variable has more than two levels because as more statistical tests are run:

A) it becomes harder and harder to reject the null hypothesis.
B) the probability of making a Type I error in one of the tests increases.
C) degrees of freedom are lost.
D) the probability of making a Type III error in one of the tests increases.

Question 7

If the p level is.0.05 and the null hypothesis is true, what is the probability of NOT making a Type I error (i.e., one will correctly fail to reject the null hypothesis)?

A) 0.05
B) 0.90
C) 0.95
D) 0.00

Question 8

Interested in the effects of different kinds of instruction on video game performance, Martin asks 30 college freshmen to each play one hour of Ratchet and Klank..Participants are randomly assigned to one of three instruction groups: (1) complete the tasks as quickly as possible, (2) conserve as much health as possible find gold bolts (worth lots of money in equipment and ammunition).Obviously, even in a single instruction group, not all players will obtain the same final score.These differences in an instruction group reflect:

A) between-groups variance.
B) within-groups variance.
C) effects of instruction.
D) effects of confounding variables.

Question 9

If between-groups variance is much larger than within-groups variance, we infer that the sample means are _____ one another, and we _____ the null hypothesis.

A) different from; reject
B) similar to; fail to reject
C) different from; fail to reject
D) similar to; reject

Question 10

Within-groups variance reflects the:

A) amount of difference between means that we would expect to occur as a result of experimental manipulation.
B) average of the sample variances.
C) mean averages.
D) total amount of difference we would expect to occur, given both chance and experimental manipulation.

Question 11

In which situation would it be necessary to use a between-groups ANOVA?

A) A researcher is interested in a longitudinal study that follows a group of kindergarten children through high school and assesses their body mass index at four time points.
B) A researcher classifies a group of college students on the basis of their political leanings as liberal, conservative, libertarian, or green.
C) A researcher is interested in the effects of distraction on driving performance and randomly assigns participants to one of three distraction groups.
D) A researcher is interested in whether a sensitivity training class changes attitudes toward minority populations.The researcher assesses these attitudes before and after the sensitivity training class.

Question 12

If the p level is.0.05 and the null hypothesis is true, the probability of making a Type I error when performing a single hypothesis test is _____, but if three hypothesis tests are performed, then the probability of NOT making a Type I error is _____, which means that the probability of making a Type I error at least once in these three hypothesis tests is _____.

A) 0.05; 0.857; 0.143
B) 0.95; 0.85; 0.15
C) 0.05; 0.95; 0.15
D) 0.00; 0.95; 0.85

Question 13

If the p level is 0.05 and the null hypothesis is true, what is the probability of making a Type I error (i.e., that one will fail to reject the null hypothesis)?

A) 0.05
B) 0.90
C) 0.95
D) 0.00

Question 14

With two groups, the square root of F is equal to:

A) t.
B) 0.0.
C) 1.0.
D) 2t.

Question 15

In which situation would it be necessary to use a within-groups ANOVA?

A) A researcher is interested in a longitudinal study that follows a group of kindergarten children through high school and assesses their body mass index at four time points.
B) A researcher classifies a group of college students on the basis of their political leanings as liberal, conservative, libertarian, or green.
C) A researcher is interested in the effects of distraction on driving performance and randomly assigns participants to one of three distraction groups.
D) A researcher is interested in whether a sensitivity training class changes attitudes toward minority populations.The researcher assesses these attitudes before and after the sensitivity training class.

Question 16

The F ratio is calculated by:

A) dividing a measure of within-groups variability by a measure of between-groups variability.
B) averaging the results from the t tests for all possible two-group comparisons.
C) dividing a measure of between-groups variability by a measure of within-groups variability.
D) squaring all the scores.

Question 17

There is a different F distribution for every:

A) sample size.
B) level of the independent variable.
C) combination of sample size and number of samples.
D) within-groups degrees of freedom.

Question 18

If there are only two samples and sample size is infinity, then the F distribution is the:

A) sum of the two samples.
B) t distribution.
C) null hypothesis distribution for N = 2.
D) square of the z distribution.

Question 19

A measure of the differences among group means is:

A) the z score.
B) between-groups variance.
C) within-groups variance.
D) the proportionate reduction in error.

Question 20

A measure of variability that is essentially an average of the sample variances is:

A) the z score.
B) between-groups variance.
C) within-groups variance.
D) the proportionate reduction in error.

Question 21

A one-way ANOVA includes:

A) one nominal dependent variable with more than two levels and a scale independent variable.
B) one nominal independent variable with more than two levels and a scale dependent variable.
C) one nominal dependent variable with more than three levels and a scale independent variable.
D) one nominal independent variable with more than three levels and a scale dependent variable.

Question 22

The grand mean is the:

A) mean of every score in the study, regardless of the sample.
B) average of each of the group means.
C) mean of all the scores in the study squared.
D) average difference of each of the group means.

Question 23

Changes in between-groups variance result in changes in the _____ of the F ratio.

A) denominator
B) numerator
C) sign
D) significance

Question 24

MS_between is obtained by dividing:

A) SS_between by df_between.
B) SS_between by SS_within.
C) df_between by SS_between.
D) SS_within by SS_within.

Question 25

Within-groups degrees of freedom is calculated by:

A) subtracting 1 from the total number of groups in the study.
B) multiplying the number of subjects by the number of conditions in the study and then subtracting 1.
C) subtracting 1 from the total number of subjects in the study.
D) for each condition, subtracting 1 from the number of subjects in that group and then adding together the totals for all the groups.

Question 26

Violation of the assumption that samples are randomly selected affects researchers' ability to:

A) generalize the results of a study beyond the sample.
B) differentiate between-groups variance and within-groups variance.
C) meet the homogeneity of variance assumption.
D) reject the null hypothesis.

Question 27

Changes in within-groups variance result in changes in the _____ of the F ratio.

A) denominator
B) numerator
C) sign
D) significance

Question 28

If an F statistic is negative, which of these is true?

A) The within-groups variance exceeds the between-groups variance.
B) The difference among the group means is greater than what would have occurred by chance.
C) There has been a calculation error.
D) The difference among the group means is less than what would have occurred by chance.

Question 29

The assumptions of ANOVA are that samples are selected:

A) randomly and that the samples come from populations with unequal variances.
B) randomly, the population distribution is normal, and the samples come from populations with equal variances.
C) randomly and the population distribution is normal.
D) from populations that are heteroscedastic and normally distributed.

Question 30

The less overlap there is among sample distributions, the:

A) less confounding variability there is in the groups.
B) less confident we are that the samples represent true differences in the population.
C) more confident we are that the samples represent true differences in the population.
D) less likely it is that we will reject the null hypothesis.

Question 31

In which situation would it NOT be appropriate to use a one-way ANOVA?

A) A researcher is interested in a longitudinal study that follows a group of kindergarten children through high school and assesses their body mass index at four time points.
B) A researcher classifies a group of college students on the basis of their political leanings as liberal, conservative, libertarian, or green.
C) A researcher is interested in the effects of distraction on driving performance and randomly assigns participants to one of three distraction groups.
D) A researcher is interested in whether a sensitivity training class changes attitudes toward minority populations.The researcher assesses these attitudes before, immediately after, and 6 months after the sensitivity training class.

Question 32

Which of the following is NOT an assumption of an ANOVA?

A) random selection
B) independent variable has only three levels
C) normally distributed population
D) samples come from populations with the same variances

Question 33

Between-groups degrees of freedom is calculated by:

A) subtracting 1 from the total number of groups in the study.
B) multiplying the number of subjects by the number of conditions in the study and then subtracting 1.
C) subtracting 1 from the total number of subjects in the study.
D) subtracting 1 from the number of subjects within each group and then adding those numbers together.

Question 34

In a z test and a t test, when there is no difference between groups, the test statistic is equal to _____, but in the ANOVA, when there are no differences among groups, the test statistic is equal to _____.

A) 0; 1
B) 1; 0
C) 1; 2
D) 2; 1

Question 35

Homoscedasticity can be tested for by:

A) making sure that the within-groups variance is no more than two times the between-groups variance.
B) making sure that the largest sample variance is no more than two times the smallest variance.
C) using ANOVA.
D) making sure that the largest sample variance is no more than five times the smallest sample variance.

Question 36

The symbol for variance in ANOVA is:

A) s², which stands for standard deviation squared.
B) MS, which stands for mean squared.
C) SD², which stands for standard deviation squared.
D) MS², which stands for means squared.

Question 37

F is obtained by dividing _____ by _____.

A) SS_between; df_between
B) MS_between; MS_within
C) df_between; SS_between
D) SS_between; SS_within

Question 38

The F ratio is a ratio of:

A) two (or more) sample means.
B) two variances.
C) sample means divided by sample variances.
D) two sum-of-squares estimates.

Question 39

The F statistic increases when:

A) within-groups variance decreases.
B) between-groups variance decreases.
C) between-groups variance increases.
D) within-groups variance decreases and between-groups variance increases.

Question 40

MS_within is obtained by dividing:

A) SS_between by df_between.
B) SS_between by SS_within.
C) df_between by SS_within.
D) SS_within by df_within.

Question 41

The F statistic is more versatile than the t test.

Question 42

An F statistic calculated on 3 and 48 degrees of freedom equals 2.70.Which decision should be made about a hypothesis tested at the p = 0.05 level?

A) Fail to reject the null hypothesis and conclude there are differences among the groups.
B) Fail to reject the null hypothesis and conclude no significant differences are indicated among the groups.
C) Reject the null hypothesis and conclude there are differences among the groups.
D) Reject the null hypothesis and conclude no significant differences are indicated among the groups.

Question 43

R², the effect size for ANOVA, is calculated as a ratio of:

A) total sum of squares to within-groups sum of squares.
B) within-groups mean squares to between-groups mean squares.
C) total mean squares to total sum of squares.
D) between-groups sums of squares to total sum of squares.

Question 44

A post hoc test is warranted when one:

A) rejects the null hypothesis and there are more than two groups.
B) fails to reject the null hypothesis in an ANOVA.
C) rejects the null hypothesis when performing an independent-groups t test.
D) has an a priori prediction about which group means will differ.

Question 45

The Bonferroni, Scheffé, and Tukey are all examples of:

A) hypothesis tests.
B) post hoc tests.
C) effect size statistics.
D) confidence intervals.

Question 46

Cohen's d cannot be used as a measure of effect size for ANOVA because:

A) there is no effect size measure for ANOVA.
B) its values no longer have meaning when more than two groups are compared.
C) it can only compare two means.
D) it must be saved to compute effect size for the post hoc tests.

Question 47

If the cutoff q statistic is 4.96, with a p level of 0.05, which of these would be significant?

A) an HSD of 4.8
B) a group mean difference of 5.2
C) an F of 5.2
D) an HSD of 5.2

Question 48

When computing Tukey HSD with samples of different sizes, what additional step must be performed?

A) Calculate a weighted sample size called a harmonic mean.
B) Calculate HSD for each pair of means.
C) Compare the means of all groups using Bonferroni first.
D) Compute R².

Question 49

Lucille is interested in the effects of alcohol consumption on style of play while playing the video game Sims.She asks a group of 15 college students to play Sims under one of the following conditions: no alcohol, 1 ounce of alcohol, 2 ounces of alcohol, or 3 ounces of alcohol.Lucille measures on a scale of 1 to 10 how prosocial the students' style of play is.After collecting the data, Lucille performs an ANOVA and finds that she can reject the null hypothesis.On this basis, what does Lucille know?

A) She knows that greater levels of alcohol consumption are associated with a more prosocial style of play.
B) She knows that there is a difference among the groups somewhere, but she does not know where.
C) She knows that moderate alcohol consumption is associated with prosocial play, but that greater alcohol consumption is associated with an antisocial style of play.
D) She knows that drinking any amount of alcohol affects the style of play.

Question 50

An F statistic calculated on 2 and 26 degrees of freedom equals 3.41.Which decision should be made about a hypothesis tested at the p = 0.05 level?

A) Fail to reject the null hypothesis and conclude there are differences among the groups.
B) Fail to reject the null hypothesis and conclude no significant differences are indicated among the groups.
C) Reject the null hypothesis and conclude there are differences among the groups.
D) Reject the null hypothesis and conclude no significant differences are indicated among the groups.

Question 51

According to Cohen's conventions, an R² of 0.15 is considered to be a(n) _____ effect size.

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

Question 52

According to Cohen's conventions, an R² of 0.01 is considered to be a(n) _____ effect size.

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

Question 53

The proportion of variance in the dependent variable that is accounted for by the independent variable is _____.

A) t
B) Cohen's d
C) R²
D) z

Question 54

In Tukey's HSD post hoc test, the HSD stands for:

A) honorary standardized description.
B) honorary standardized difference.
C) honestly significant difference.
D) honestly standardized difference.

Question 55

Using the Bonferroni post hoc test, the overall probability of making a Type I error can be kept at a p level of 0.05 by:

A) dividing 0.05 by the number of comparisons you plan to make and using the result as the p level for each comparison.
B) dividing 0.05 by 2 and using the result as the p level for each comparison.
C) determining the amount of difference you should have between each of your means based on a p level of 0.01.
D) finding the honestly significant difference.

Question 56

The critical cutoffs for a two-tailed Tukey HSD test comparing two group means with 12 within-groups degrees of freedom are:

A) -3.08 and 3.08.
B) -3.77 and 3.77.
C) -3.82 and 3.82.
D) -5.05 and 5.05.

Question 57

When F is significant:

A) the values of the means that are closest together are the only ones that are significant.
B) the values of the means that are farthest apart are the only ones that are significant.
C) we do not know which specific means differ significantly.
D) we fail to reject the null hypothesis.

Question 58

According to Cohen's conventions, an R² of 0.05 is considered to be a(n) _____ effect size.

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

Question 59

Using the Bonferroni post hoc test, to make all possible comparisons between the means of three groups while keeping the overall p level at 0.05, what should the p level be for each comparison?

A) 0.050
B) 0.001
C) 0.017
D) 0.008

Question 60

To evaluate Tukey's HSD, consult the _____ table.

A) z
B) F
C) q
D) R

Question 61

When the null hypothesis is true, the F ratio for analysis of variance is expected, on average, to be 0.

Question 62

An ANOVA is typically used when the independent variable is nominal with more than two groups.

Question 63

An ANOVA is typically used when the dependent variable is nominal with more than two groups.

Question 64

When the F statistic is less than the critical cutoff value, additional follow-up analyses are needed.

Question 65

As the number of t tests increases, the risk of a Type I error decreases.

Question 66

As the variability of between-groups means increases, the F statistic increases.

Question 67

Populations that have the same variance are referred to as homoscedastic.

Question 68

To test the assumption of homoscedasticity, check to see if the largest variance is not more than twice the smallest variance.

Question 69

The values observed on the F table under two samples are the same as those on the t table.

Question 70

When the null hypothesis is true, the F ratio for analysis of variance is expected, on average, to be 1.

Question 71

Populations that have the same variance are referred to as heteroscedastic.

Question 72

As the variability of between-groups means increases, the F statistic decreases.

Question 73

R² is the proportion of variance in the independent variable accounted for by the dependent variable.

Question 74

When the F statistic is more than the critical cutoff value, additional follow-up analyses are needed.

Question 75

If between-groups variability increases, within-groups variability necessarily increases.

Question 76

R² is the proportion of variance in the dependent variable accounted for by the independent variable.

Question 77

Populations that have different variances are referred to as homoscedastic.

Question 78

The values observed on the F table under two samples is the square of those on the t table.

Question 79

The F ratio measures two sources of variability: within-groups variance and between-groups variance.

Question 80

Populations that have different variances are referred to as heteroscedastic.