Exam 4 Psych Stats

Statistic used in ANOVAs

F=

An independent-measures t test produced a t statistic with df = 20. If the same data had been evaluated with an analysis of variance, what would be the df values for the F-ratio? a. 1, 20 b. 2, 20 c. 1, 19 d. 2, 19

a. 1, 20

The following data represent the means for each treatment condition in a two-factor experiment. Note that one mean is not given. What value for the missing mean would result in no AxB interaction? a. 10 b. 20 c. 30 d. 40

a. 10

The results from a repeated-measures ANOVA are reported as, "F(2, 24) = 3.75, p < .05." For this study, how many treatment conditions were compared? a. 3 b. 2 c. 22 d. 25

a. 3

A researcher reports an F ratio with df = 3, 36 for an independent-measures experiment. How many individual subjects participated in the experiment? a. 40 b. 39 c. 36 d. Cannot be determined from the information given

a. 40

The following table shows the results of a two-factor ANOVA. Based on this table, what is the value for η2 for factor A? a. 12/108 b. 12/84 c. 12/72 d. 12 /36

b. 12/84

After an analysis of variance comparing three treatment means, a researcher uses a Scheffé test to evaluate the difference between treatment #1 and treatment #1. If the original ANOVA produced F(2, 36) = 4.36, then what are the df values for the Scheffé test? a. 1, 24 b. 2, 24 c. 2, 36 d. 1, 36

c. 2, 36

The test statistic for an analysis of variance is an F-ratio, which divides the between-treatment variance by the within-treatment variance. The F-ratio has two values for df, one for the numerator (between) and one for the denominator (within). For example, with df = 2 for the numerator and df = 12 for the denominator, the F-ratio has df = 2, 12. If an F-ratio has df = 3, 24, then what is dftotal? a. 28 b. 25 c. 27 d. 26

c. 27

A repeated-measures study comparing two treatment conditions can be evaluated using a repeated-measures t test or a repeated-measures ANOVA. If a repeated-measures t test produces t(12) = 2.50, then what would be the df values for the F-ratio if an ANOVA had been used for the same data? a. 2, 11 b. 2, 12 c. 1, 11 d. 1, 12

d. 1, 12

An analysis of variances produces SSbetween treatments = 20 with dfbetween treatments = 2, and SSwithin treatments = 30 with dfwithin treatments = 15. For this analysis, what is the F-ratio? a. 20/30 = 0.67 b. 30/20 = 1.50 c. 2/10 = 0.20 d. 10/2 = 5.00

d. 10/2 = 5.00

The following table shows the results of a two-factor analysis of variance with two levels of factor A, three levels of factor B, and a separate sample of n = 8 participants in each of the treatment conditions. Note that several values are missing in the table. What is the missing value for the F-ratio for the AxB interaction? a. 10 b. 12.5 c. 5 d. 15

d. 15

In analysis of variance, what is the effect of increasing the sample variances? a. increase SSwithin treatments and increase the size of the F-ratio b. increase SSbetween treatments and decrease the size of the F-ratio c. increase SSbetween treatments and increase the size of the F-ratio d. increase SSwithin treatments and decrease the size of the F-ratio

d. increase SSwithin treatments and decrease the size of the F-ratio

In an ANOVA, which of the following is most likely to produce a large value for the F-ratio? a. small mean differences and large sample variances b. large mean differences and large sample variances c. small mean differences and small sample variances d. large mean differences and small sample variances

d. large mean differences and small sample variances

experimentwise alpha level

probability of all type 1 errors accumulated from all he tests in an experiment

error term

the difference between an individual value of the dependent variable and the corresponding mean value of the dependent variable random unsystematic differences

testwise alpha level

the risk of a type 1 error for an individual hypothesis test

The two-factor ANOVA involves 3 separate hypothesis tests and three separate F-ratios. One of the tests evaluates the mean differences attributed to factor A. If factor A defines the rows of the matrix, then this test uses the sample means for the rows of the to evaluate a hypothesis about he corresponding population means. The row means are used to compute a SS and df value for factor A. For a two-factor study with 2 levels of factor A and 3 levels of factor B, with a sample of n = 8 in each treatment condition, then what is the value for dfA? a. 1 b. 7 c. 2 d. 3

a. 1

For a research study comparing two treatment conditions, the significance of the mean difference can be evaluated with an independent-measures t test or with an analysis of variance. If a researcher obtains t = 4.50 with df = 18 for a t test, then what would the df be for the F-ratio if an analysis of variance had been used? a. 1, 18 b. 2, 17 c. 1, 17 d. 2, 18

a. 1, 18

A research report concludes that there are significant differences among treatments, with "F(2, 27) = 8.62, p < .01." If the same number of participants was used in all of the treatment conditions, then how many individuals were in each treatment? a. 10 b. 7 c. 9 d. Cannot determine without additional information

a. 10

The results of a repeated-measures ANOVA are reported as follows, F(3, 27) = 1.12, p > .05. How many subjects participated in the study? a. 10 b. 36 c. 9 d. 40

a. 10

A repeated-measures study uses a sample of n = 20 participants to evaluate the mean differences among three treatment conditions. In the analysis of variance for this study, what is the value for dfbetween treatments? a. 2 b. 57 c. 59 d. 19

a. 2

Analysis: of variance (ANOVA) measures the size of the sample mean differences by computing a variance for the set of sample means. The variance is computed by first finding a SS value and a df value for the set of sample means. What is the SS value for a group of three sample means consisting of M1 = 2, M2 = 3, and M3 = 4? a. 2 b. 0 c. 3 d. 1

a. 2

The repeated-measures ANVOA begins exactly the same as a independent-measures ANOVA by computing the total SS and df and then dividing these totals into between-treatments SS and df and within-treatments SS and df. For a repeated-measures study comparing 3 treatment conditions with a sample of n = 8 participants, what is the value for dfbetween treatments? a. 2 b. 7 c. 6 d. 3

a. 2

The two-factor ANOVA involves 3 separate hypothesis tests and three separate F-ratios. One test evaluates the mean differences attributed to factor A, one evaluates mean differences for factor B, and third evaluates the interaction between A and B, which is defined as the extra mean differences that are not accounted for by the two factors. All three F-ratios have MSbetween treatments as the denominator. For a study with 2 levels of factor A, 3 levels of factor B, and a sample of n = 10 in each treatment condition, what are the df values for the F-ratio evaluating factor B? a. 2, 54 b. 1, 59 c. 2, 59 d. 1, 54

a. 2, 54

The repeated-measures ANVOA begins exactly the same as a independent-measures ANOVA by computing the total SS and df and then dividing these totals into between-treatments SS and df and within-treatments SS and df. For a repeated-measures study comparing 3 treatment conditions with a sample of n = 8 participants, what is the value for dfwithin? a. 21 b. 6 c. 7 d. 23

a. 21

In an experiment with 2 levels of factor A, 3 levels of factor B, and n = 5 in each treatment condition, what is the correct value for the degrees of freedom within treatments? a. 24 b. 8 c. 29 d. 30

a. 24

A two-factor research study has two levels of factor A and two levels of factor B with n = 10 participants in each treatment condition. For this study, what is the value for dfbetween treatments? a. 3 b. 9 c. 36 d. 4

a. 3

The two-factor ANOVA involves 3 separate hypothesis tests and three separate F-ratios. One of the tests evaluates the mean differences attributed to factor A. If factor A defines the rows of the matrix, then this test uses the sample means for the rows of the to evaluate a hypothesis about he corresponding population means. If the F-ratio for factor A has df = 2, 24, then how many levels of factor A are being compared? a. 3 b. 25 c. 2 d. 1

a. 3

A two-factor study with two levels of factor A and three levels of factor B uses a separate sample of n = 5 participants in each treatment condition. How many participants are needed for the entire study? a. 30 b. 5 c. 25 d. 10

a. 30

For analysis of variance, the variance within treatments is used to measure the differences that exist when there are no treatment effects. This value is determined by adding the SS values in each treatment and dividing by the sum of the df values in each treatment. A study comparing three treatments with a sample of n = 6 in each treatment produces SS1 = 11, SS2 = 12, and SS3 = 7 in the three treatments. For this study, what is the value for the variance within treatments? a. 30/15 = 2 b. 30/2 = 15 c. 30/6 = 5 d. 30/5 = 6

a. 30/15 = 2

A researcher reports an F ratio with df = 3, 36 for an independent-measures experiment. How many treatment conditions were compared in this experiment? a. 4 b. 3 c. 36 d. 39

a. 4

The test statistic for an analysis of variance is an F-ratio, which divides the between-treatment variance by the within-treatment variance. The F-ratio has two values for df, one for the numerator (between) and one for the denominator (within). For example, with df = 2 for the numerator and df = 12 for the denominator, the F-ratio has df = 2, 12. If an F-ratio has df = 3, 36, then how many treatments were compared in the analysis of variance? a. 4 b. 3 c. 2 d. 1

a. 4

The test statistic for an analysis of variance is an F-ratio, which divides the between-treatment variance by the within-treatment variance. The F-ratio has two values for df, one for the numerator (between) and one for the denominator (within). For example, with df = 2 for the numerator and df = 12 for the denominator, the F-ratio has df = 2, 12. If an F-ratio has df = 3, 36, then what is the total number of participants in the research study? a. 40 b. 38 c. 39 d. 37

a. 40

A two-factor study can be represented as a matrix with the levels of one factor defining the rows and the levels of the second factor defining the columns. The two-factor ANOVA begins exactly the same as a single-factor ANOVA by computing the total SS and df and then dividing these totals into between-treatments SS and df and within-treatments SS and df with each cell in the matrix viewed as a separate treatment condition. For a study with 2 levels of factor A, 3 levels of factor B, and a sample of n = 10 in each treatment condition, what is the value of dfbetween treatments? a. 5 b. 2 c. 1 d. 6

a. 5

A two-factor study can be represented as a matrix with the levels of one factor defining the rows and the levels of the second factor defining the columns. The two-factor ANOVA begins exactly the same as a single-factor ANOVA by computing the total SS and df and then dividing these totals into between-treatments SS and df and within-treatments SS and df with each cell in the matrix viewed as a separate treatment condition. For a study with 2 levels of factor A and 3 levels of factor B, dfwithin treatments = 30. If each treatment condition has the same number of participants, then how many individuals are in each treatment? a. 6 b. 28 c. 5 d. 29

a. 6

In a repeated-measures ANOVA the between-treatment differences in the numerator of the F-ratio cannot be caused by individual differences because the same individuals are in every treatment. To balance the F-ratio the individual differences must also be removed from the denominator. This is done by first computing a between-subjects SS and df using the totals for each person exactly like the between-treatments SS and df are computing using the totals for each treatment. If the totals for n = 4 people in a repeated-measures study comparing 3 treatments are 3, 6, 6, and 9, then what is the value for SSbetween subjects? a. 6 b. 54 c. 24 d. 48

a. 6

In a two-factor analysis of variance, the F-ratio for factor A has df = 2, 60 and the F-ratio for factor B has df = 3, 60. Based on this information, what are the df values for the F-ratio for the interaction? a. 6, 60 b. Cannot be determined without additional information c. 3, 60 d. 5, 60

a. 6, 60

A repeated-measures analysis of variance with a sample of n = 8 participants, produces dfwithin treatments = 14. What is the value for dferror for this analysis? a. 7 b. 21 c. Cannot determine without additional information d. 6

a. 7

For an experiment comparing more than two treatment conditions you should use analysis of variance rather than separate t tests because ______. a. ANOVA has less risk of a Type I Error because several means are compared in one test b. ANOVA has less risk of a Type II Error because several means are compared in one test c. a test based on variances is more sensitive than a test based on means d. you are less likely to make a mistake in the computations of ANOVA

a. ANOVA has less risk of a Type I Error because several means are compared in one test

In a repeated-measures ANOVA, which of the following is not computed directly but rather is obtained by a process of subtraction? a. SS error b. SSbetween subjects c. SSwithin treatments d. SSbetween treatments

a. SS error

In the F-ratio for a repeated-measures ANOVA, variability due to individual differences ________. a. is automatically eliminated from the numerator but must be computed and subtracted out of the denominator b. is automatically eliminated from both the numerator and the denominator c. must be computed and subtracted out of the numerator and the denominator d. is automatically eliminated from the denominator but must be computed and subtracted out of the numerator

a. is automatically eliminated from the numerator but must be computed and subtracted out of the denominator

In a two-factor analysis of variance, the F-ratios for factor A, factor B, and the AxB interaction ________. a. may have different df values but they all have the same denominator b. all have the same df values but they may have different denominators c. all have the same df values and they all have the same denominator d. may have different df values and may have different denominators

a. may have different df values but they all have the same denominator

A treatment effect refers to differences between scores that are caused by the different treatment conditions. The differences (or variability) produced by treatment effects will contribute to ________. a. the numerator of the F-ratio b. Treatment effects do not contribute to the F-ratio because they are removed before the F-ratio is computed. c. the denominator of the F-ratio d. both the numerator and the denominator of the F-ratio

a. the numerator of the F-ratio

What is the appropriate denominator for the F-ratio for a repeated-measures ANOVA? a. the variance that remains after the variance between subjects is subtracted from the variance within treatments. b. variance between subjects. c. the variance that remains after the variance within treatments is subtracted from the variance between subjects. d. variance within treatments.

a. the variance that remains after the variance between subjects is subtracted from the variance within treatments.

For a repeated-measures ANOVA, how is the value dferror computed? a. (N − 1) b. (N − k) − (n − 1) c. k − 1 d. n − 1

b. (N − k) − (n − 1)

In an independent-measures experiment with three treatment conditions, all three treatments have the same mean, M1 = M2 = M3. For these data, what is the value for SSbetween treatments? a. 3(5.50) b. 0 c. 1.00 d. Cannot be determined from the information given

b. 0

For an independent-measures experiment comparing two treatment conditions with a sample of n = 10 in each treatment, the F ratio would have df equal to ______. a. 1, 19 b. 1, 18 c. 19 d. 18

b. 1, 18

The following table shows the results of an analysis of variance comparing three treatment conditions with a sample of n = 10 participants in each treatment. Note that several values are missing in the table. What is the missing value for SStotal? a. 81 b. 111 c. 121 d. 51

b. 111

The following data represent the means for each treatment condition in a two-factor experiment. Note that one mean is not given. What value for the missing mean would result in no main effect for factor A? a. 10 b. 2 c. 14 d. 12

b. 2

The results of a two-factor analysis of variance produce df = 2, 28 for the F-ratio for factor A, and df = 2, 28 for the F-ratio for the A×B interaction. Based on this information, how many levels of factor B were compared in the study? a. 3 b. 2 c. Cannot be determined without additional information d. 1

b. 2

If k = 3 and n = 5, then what are the df values for the repeated measures F-ratio? a. 2, 4 b. 2, 8 c. 2, 12 d. 3, 5

b. 2, 8

The following table shows the results of a repeated-measures ANOVA. Based on this table, what is the value for η2, the percentage of variance accounted for by the treatments a. 22/32 b. 22/54 c. 22/80 d. 22/58

b. 22/54

An analysis of variance is used to evaluate the mean differences for a research study comparing four treatment conditions with a separate sample of n = 5 in each treatment. The analysis produces SSwithin treatments = 32, SSbetween treatments = 40, and SStotal = 72. For this analysis, what is MSwithin treatments? a. 32/5 b. 32/16 c. 32/20 d. 32/4

b. 32/16

For an F-ratio with df = 2, 10, what is the critical value for a hypothesis test using α = .05? a. 99.40 b. 4.10 c. 7.56 d. 19.39

b. 4.10

A repeated-measures ANOVA has SSwithin treatments = 20 and SSbetween subjects = 12. For this analysis, what is the value for SSerror? a. 20 b. 8 c. 12 d. 32

b. 8

To balance the F-ratio for a repeated-measures ANOVA, the denominator is computed by first calculating the between-subjects SS and df and then subtracting these values from the within-treatments SS and df. The results, identified as SSerror and dferror, provide a measure of random, unsystematic variability without any individual differences or treatment effects. For a repeated-measures study comparing 3 treatments with a sample of n = 5, what is the value of dferror? a. 7 b. 8 c. 4 d. 12

b. 8

Post hoc tests are necessary after an ANOVA whenever ________. a. H0 is rejected b. H0 is rejected and there are more than two treatments c. You always should do post hoc tests after an ANOVA. d. There are more than two treatments

b. H0 is rejected and there are more than two treatments

For the repeated-measures ANOVA, SSerror is found by ________. a. SSbetween treatments − SSbetween subjects b. SSwithin − SSbetween subjects c. SSbetween treatments − SSwithin d. SStotal − SSbetween treatments

b. SSwithin − SSbetween subjects

In an analysis of variance, what is the effect of increasing the size of the sample mean differences? a. increase SSwithin treatments and decrease the size of the F-ratio b. increase SSbetween treatments and increase the size of the F-ratio

b. increase SSbetween treatments and increase the size of the F-ratio

In general the distribution of F ratios is ________. a. symmetrical with a mean equal to dfbetween b. positively skewed with all values greater than or equal to zero c. negatively skewed with all values greater than or equal to zero d. symmetrical with a mean of zero

b. positively skewed with all values greater than or equal to zero

What is the purpose of a post hoc test? a. to determine whether or not a Type I Error was made in the ANOVA b. to determine which treatments are different c. to determine how much difference there is between treatments d. to determine whether or not a complete ANOVA is justified

b. to determine which treatments are different

Which of the following are sources of variability that contribute to SSbetween treatments in a repeated ANOVA? a. treatment effect, individual differences, and chance/error b. treatment effect and chance/error c. treatment effect and individual differences d. individual differences and chance/erro

b. treatment effect and chance/error

In analysis of variance, the F-ratio is a ratio of ________. a. sample means divided by sample variances b. two variances c. two (or more) sample means d. None of the other 3 choices is correct.

b. two variances

Analysis: of variance (ANOVA) measures the actual differences between sample means by computing a variance for the set of sample means. The analysis also computes a variance within the treatments to obtain a measure of the differences that exist if there are no treatment effects. The two variances are then compared with an F-ratio, which equals the variance between treatments divided by the variance within treatments. If the null hypothesis is true, what value is expected for the F-ratio? a. 0 b. greater than 1.00 c. 1 d. less than 1.00

c. 1

When the null hypothesis is true for an ANOVA, what is the expected value for the F ratio? a. N-k b. 0 c. 1.00 d. k-1

c. 1.00

The following table shows the results of a repeated-measures analysis of variance comparing three treatment conditions with a sample of n = 12 participants. Note that several values are missing in the table. What is the missing value for SStotal? a. 88 b. 108 c. 144 d. 94

c. 144

The two-factor ANOVA involves 3 separate hypothesis tests and three separate F-ratios. One test evaluates the mean differences attributed to factor A, one evaluates mean differences for factor B, and third evaluates the interaction between A and B, which is defined as the extra mean differences that are not accounted for by the two factors. The numerators for the 3 F-ratios are obtained by separating the between-treatments SS and df into 3 components, one for factor A, one for B, and one for the interaction. If SSbetween treatments = 90, SSA = 30, and SSB = 40, then what is the value of SS for the interaction? a. 50 b. 60 c. 20 d. 40

c. 20

For a research study comparing two treatment conditions, the significance of the mean difference can be evaluated with an independent-measures t test or with an analysis of variance. If a researcher obtains F = 6.30 with df = 1, 28 for an analysis of variance, then what would the df be for the independent-measures t if a t test had been used? a. 26 b. 27 c. 28 d. 29

c. 28

A two-factor study examines the effects of two independent (or quasi-independent) variables within the same study. The structure of a two factor study can be viewed as a matrix with the levels of one factor defining the rows and the levels of the second factor defining the columns. Each cell in the matrix is a treatment condition defined by a unique combination of the two factors. If the factors are identified as A and B, with 2 levels of factor A, 3 levels of factor B, and a sample of n = 5 participants in each treatment condition, then how many participants are in the study? a. 25 b. 15 c. 30 d. 10

c. 30

Analysis of variance begins by computing SS and df for the entire set of scores and then dividing the total SS into SSbetween treatments and SSwithin treatments and dividing the total df into dfbetween treatments and dfwithin treatments. If an analysis of variance produces dfbetween treatments = 3 and dfwithin treatments = 28, then what is dftotal? a. 25 b. 28 c. 31 d. 3

c. 31

The following table shows the results of an analysis of variance comparing four treatment conditions with a sample of n = 11 participants in each treatment. Note that several values are missing in the table. What is the missing value for the F-ratio? a. 10 b. 4 c. 5 d. 2

c. 5

An analysis of variance produces SStotal = 90 and SSwithin treatments = 40. For this analysis, what is SSbetween treatments? a. 3600 b. 130 c. 50 d. Cannot be determined without additional information

c. 50

Analysis of variance begins by computing SS and df for the entire set of scores and then dividing the total SS into SSbetween treatments and SSwithin treatments and dividing the total df into dfbetween treatments and dfwithin treatments. If an analysis of variance produces SStotal = 80 and SSwithin treatments = 30, then what is SSbetween treatments? a. 80 b. 30 c. 50 d. 110

c. 50

A two-factor study examines the effects of two independent (or quasi-independent) variables within the same study. The structure of a two factor study can be viewed as a matrix with the levels of one factor defining the rows and the levels of the second factor defining the columns. Each cell in the matrix is a treatment condition defined by a unique combination of the two factors. If the factors are identified as A and B, with 2 levels of factor A and 3 levels of factor B, then how many different treatment conditions are being compared? a. 5 b. 3 c. 6 d. 2

c. 6

A repeated-measures study uses a sample of n = 10 participants to evaluate the mean differences among four treatment conditions. In the analysis of variance for this study, what is the value for dfbetween subjects? a. 39 b. 36 c. 9 d. 27

c. 9

A repeated-measures analysis of variance produces SSwithin treatments = 24 and SSbetween treatments = 40. For this analysis, what is the value of SSerror? a. 64 b. 24 c. Cannot be determined from the information provided d. 16

c. Cannot be determined from the information provided

An analysis of variance is used to evaluate the mean differences for a research study comparing four treatments with a separate sample of n = 5 in each treatment. If the data produce an F-ratio of F = 3.15, then which of the following is the correct statistical decision? a. Reject the null hypothesis with either α = .05 or α = .01. b. Reject the null hypothesis with α = .05 but not with α = .01. c. Fail to reject the null hypothesis with either α = .05 or α = .01. d. There is not enough information to make a statistical decision.

c. Fail to reject the null hypothesis with either α = .05 or α = .01.

In a two-factor ANOVA, which of the following is not computed directly but rather is found by subtraction? a. SSB b. SSbetween treatments c. SSAxB d. SSA

c. SSAxB

The results from a two-factor analysis of variance show that both main effects are significant. What can you conclude from this information? a. that the interaction cannot be significant b. there must be an interaction but it may not be statistically significant c. You can make no conclusions about the significance of the interaction. d. that the interaction also must be significant

c. You can make no conclusions about the significance of the interaction.

A two-factor research study is used to evaluate the effectiveness of a new blood-pressure medication. In this two-factor study, Factor A is medication versus no medication and factor B is male versus female. The medicine is expected to reduce blood pressure for both males and females, but it is expected to have a much greater effect for males. This expectation should result in a. a significant main effect for factor A (medication). b. neither a significant main effect for factor A (medication) and a significant interaction. c. both a significant main effect for factor A (medication) and a significant interaction. d. a significant interaction.

c. both a significant main effect for factor A (medication) and a significant interaction.

If an analysis of variance is used for the following data, what would be the effect of changing the value of M2 to 35?Sample Data:M1 = 15 M2 = 25SS1 = 90 SS2 = 70 a. increase SSbetween and decrease the size of the F-ratio b. decrease SSbetween and increase the size of the F-ratio c. increase SSbetween and increase the size of the F-ratio d. decrease SSbetween and decrease the size of the F-ratio

c. increase SSbetween and increase the size of the F-ratio

The null hypothesis for an ANOVA states that ________. a. all of the population means are different from each other b. None of the other 3 choices is correct. c. there are no differences between any of the population means d. at least one of the population means is different from the others

c. there are no differences between any of the population means

The distinction between the "testwise" alpha level and the "experimentwise" alpha level is important ________. a. when the study is comparing exactly two treatments b. only when there are fewer than 30 scores in each treatment c. when the study is comparing more than two treatments d. whenever you do an analysis of variance

c. when the study is comparing more than two treatments

Analysis: of variance (ANOVA) is a hypothesis testing technique that uses the data from two or more samples to test hypotheses about the means for two or more populations. For a research study comparing three populations, what is the null hypothesis for an analysis of variance? a. M1 ≠ M2 ≠ M3 b. M1 = M2 = M3 c. μ1 = μ2 = μ3 d. μ1 ≠ μ2 ≠ μ3

c. μ1 = μ2 = μ3

Analysis: of variance (ANOVA) measures the size of the sample mean differences by computing a variance for the set of sample means. The variance is computed by first finding a SS value and a df value for the set of sample means. What is the df value for the variance for a group of three sample means consisting of M1 = 1, M2 = 2, and M3 = 6? a. 0 b. 1 c. 3 d. 2

d. 2

For analysis of variance, the variance within treatments is used to measure the differences that exist when there are no treatment effects. This value is determined by adding the SS values in each treatment and dividing by the sum of the df values in each treatment. A study comparing three treatments with a sample of n = 10 in each treatment produces SS1 = 12, SS2 = 15, and SS3 = 12 in the three treatments. For this study, what is the value for dfwithin treatments? a. 9 b. 2 c. 29 d. 27

d. 27

An analysis of variance produced an F-ratio of F = 9 with df = 1, 12. If the same data had been evaluated with an independent-measures t test, what value would have been obtained for t? a. 18 b. 9 c. 81 d. 3

d. 3

In a repeated-measures ANOVA the between-treatment differences in the numerator of the F-ratio cannot be caused by individual differences because the same individuals are in every treatment. To balance the F-ratio the individual differences must also be removed from the denominator. This is done by first computing a between-subjects SS and df using the totals for each person exactly like the between-treatments SS and df are computing using the totals for each treatment. If the totals for n = 4 people in a repeated-measures study comparing three treatments are 3, 6, 6, and 9, then what is the value for dfbetween subjects ? a. 2 b. 11 c. 9 d. 3

d. 3

The following data represent the means for each treatment condition in a two-factor study with 2 levels of factor A and 2 levels of factor B. Note that one mean is not given. What value for the missing mean would result in no effect for factor A? a. 40 b. 10 c. 20 d. 30

d. 30

The repeated-measures ANVOA begins exactly the same as a independent-measures ANOVA by computing the total SS and df and then dividing these totals into between-treatments SS and df and within-treatments SS and df. For a repeated-measures study with SSwithin treatments = 20 and SSbetween treatments = 12, what is the value for SStotal? a. 240 b. 0.60 c. 8 d. 32

d. 32

An experiment compares two treatment conditions with a sample of n = 20 in each treatment. If the data are analyzed with ANOVA, the analysis would have dftotal = ________. a. 18 b. 38 c. 19 d. 39

d. 39

For analysis of variance, the variance within treatments is used to measure the differences that exist when there are no treatment effects. This value is determined by adding the SS values in each treatment and dividing by the sum of the df values in each treatment. A study comparing three treatments with a sample of n = 10 in each treatment produces SS1 = 12, SS2 = 15, and SS3 = 12 in the three treatments. For this study, what is the value for SSwithin treatments? a. 2 b. 13 c. 3 d. 39

d. 39

An analysis of variance produces SSbetween = 40 and SSwithin = 60. Based on this information, what is the value for, η2, the percentage of variance accounted? a. 60/100 = 60% b. 60/40 = 150% c. 40/60 = 67% d. 40/100 = 40%

d. 40/100 = 40%

For two-factor study with 3 levels of factor A and 4 levels of factor B with a sample of n = 5 in each treatment condition, what is the value for dfwithin? a. 24 b. 12 c. 60 d. 48

d. 48

An analysis of variance produces SSbetween treatments = 40 and MSbetween treatments = 10. In this analysis, how many treatment conditions are being compared? a. 4 b. 30 c. 50 d. 5

d. 5

A two-factor study can be represented as a matrix with the levels of one factor defining the rows and the levels of the second factor defining the columns. The two-factor ANOVA begins exactly the same as a single-factor ANOVA by computing the total SS and df and then dividing these totals into between-treatments SS and df and within-treatments SS and df with each cell in the matrix viewed as a separate treatment condition. For a study with 2 levels of factor A, 3 levels of factor B, and a sample of n = 10 in each treatment condition, what is the value of dfwithin treatments? a. 9 b. 59 c. 19 d. 54

d. 54

Analysis: of variance (ANOVA) measures the size of the sample mean differences by computing a variance for the set of sample means. What is the variance for a group of three sample means consisting of M1 = 1, M2 = 2, and M3 = 6? a. 2 b. 14 c. 3 d. 7

d. 7

An analysis of variance is used to evaluate the mean differences for a research study comparing three treatments with a separate sample of n = 6 in each treatment. If the data produce an F-ratio of F = 4.10, then which of the following is the correct statistical decision? a. Fail to reject the null hypothesis with either α = .05 or α = .01. b. Reject the null hypothesis with either α = .05 or α = .01. c. There is not enough information to make a statistical decision. d. Reject the null hypothesis with α = .05 but not with α = .01.

d. Reject the null hypothesis with α = .05 but not with α = .01.

Which of the following accurately describes the two stages of a repeated-measures analysis of variance? a. The first stage is identical to the independent-measures analysis and the second stage removes individual differences from the numerator of the F-ratio. b. The first stage removes individual differences from the numerator of the F-ratio and the second stage is identical to the independent-measures analysis. c. The first stage removes individual differences from the denominator of the F-ratio and the second stage is identical to the independent-measures analysis. d. The first stage is identical to the independent-measures analysis and the second stage removes individual differences from the denominator of the F-ratio.

d. The first stage is identical to the independent-measures analysis and the second stage removes individual differences from the denominator of the F-ratio.

In a two-factor experiment with 2 levels of factor A and 2 levels of factor B, three of the treatment means are essentially identical and one is substantially different from the others. What result(s) would be produced by this pattern of treatment means? a. a main effect for factor A b. an interaction between A and B c. a main effect for factor B d. The pattern would produce main effects for both A and B, and an interaction.

d. The pattern would produce main effects for both A and B, and an interaction.

In analysis of variance, the term factor refers to ________. a. a dependent variable b. a treatment total c. a treatment mean d. an independent (or quasi-independent) variable

d. an independent (or quasi-independent) variable

If an analysis of variance is used for the following data, what would be the effect of changing the value of SS1 to 50?Sample Data:M1 = 15 M2 = 25SS1 = 90 SS2 = 70 a. increase SSbetween and increase the size of the F-ratio b. increase SSbetween and decrease the size of the F-ratio c. decrease SSwithin and decrease the size of the F-ratio d. decrease SSwithin and increase the size of the F-ratio

d. decrease SSwithin and increase the size of the F-ratio

Analysis: of variance (ANOVA) measures the actual differences between sample means by computing a variance for the set of sample means. The analysis also computes a variance within the treatments to obtain a measure of the differences that exist if there are no treatment effects. The two variances are then compared with an F-ratio, which equals the variance between treatments divided by the variance within treatments. If the null hypothesis is false, what value is expected for the F-ratio? a. less than 1.00 b. 1 c. 0 d. greater than 1.00

d. greater than 1.00

In a repeated-measures design, each individual in one sample is measured in several treatment conditions or at several different times. The repeated-measures analysis of variance uses the sample data to test a hypothesis about the corresponding populations. For a study comparing three treatments, what is the null hypothesis for a repeated-measures ANVOA? a. M1 ≠ M2 ≠ M3 b. μ1 ≠ μ2 ≠ μ3 c. M1 = M2 = M3 d. μ1 = μ2 = μ3

d. μ1 = μ2 = μ3

levels

individual conditions or values that makes up a factor

residual variance

measurement of expected variability, given no contribution by systematic treatment effects or individual differences

main effect

result of the mean differences among the levels of one factor

post hoc tests or posttests

trails of additional hypotheses completes after an ANOVA to determine which mean differences are significant

factor

variable that designated the groups being compared in ANOVA