Discovering statistics using ibm spss statistics 4th edition field test bank

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Discovering Statistics Using IBM SPSS Statistics 4th edition

Andy Field Multiple Choice Testbank for Chapter 11 Comparing Several Means: ANOVA (GLM 1)

Using this testbank: This testbank is designed to be used in conjunction with Field, A. P. (2013). Discovering Statistics Using IBM SPSS Statistics, 4th edition. London: SAGE. Please note, that in this testbank the first choice is always the correct answer. Additionally, each multiple choice question comes with suggested feedback to further support your students.

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Exercise

FieldStat4 11.MC.001.

A researcher testing the effects of two treatments for anxiety computed a 95% confidence interval for the difference between the mean of treatment 1 and the mean of treatment 2. If this confidence interval includes the value of zero, then she should reject the null hypothesis that the two population means are equal: true or false?

Author’s Notes

Multiple Choice Options (correct choice comes first)

Feedback (rejoinder) for this choice

False

Yes, this is correct. If the confidence interval contains zero, it means that the difference between the two population means could be zero (i.e., they are the same). In this situation, we would accept the null hypothesis that there is no difference between the population means (see Section 2.5.2).

True

This is incorrect. If the confidence interval contains zero, it means that the difference between the two population means could be zero (i.e., they are the same). In this situation, we would accept the null hypothesis that there is no difference between the population means (see Section 2.5.2).

Exercise

FieldStat4 11.MC.002.

A researcher wanted to see the effects of different learning strategies. A control group simply read the book Discovering Statistics (Book), a second group read the book and completed the ‘end of chapter exercises’ (Book & Exercises), and a third group read the book, did the end of chapter exercises and also completed the web materials (All Activities). The researcher predicted that the ‘all activities’ and ‘book and exercises’ groups would perform better than the book group on a subsequent test, but that the ‘book and exercises’ group would perform worse than the ‘all activities’ group. Which coding scheme would test these hypotheses in a set of planned comparisons? (Hint: The sum of weights for a comparison should be zero. If you add up the weights for a given contrast the result should be zero.)

Author’s Notes

Multiple Choice Options (correct choice comes first)

Feedback (rejoinder) for this choice Yes, this is correct (see Section 11.4.2).

Case Summ ariesa

1 2

Contras t Contras t 1 Contras t 2

Book -2 0

Book & Exercises 1 1

All Activities 1 -1

a. Limited to firs t 100 cas es .

Case Summ ariesa

1 2

Contras t Contras t 1 Contras t 2

Book 0 0

Book & Exercises 1 1

All Activities 1 -1

a. Limited to firs t 100 cas es .

Case Summ ariesa

1 2

Contras t Contras t 1 Contras t 2

Book

a. Limited to firs t 100 cas es .

2 0

Book & Exercises 1 1

All Activities 1 1

This is incorrect. The sum of weights for each contrast should equal zero. Also, the variable ‘Book’ has not been included in either of the contrasts as it has been given a weight of zero for both contrasts (see Section 11.4.2).

This is incorrect. Groups coded with positive weights will be compared against groups coded with negative weights. So, you need to assign one chunk of variation positive weights and the opposite chunk negative weights (see Section 11.4.2).

Case Summ ariesa

1 2

Contras t Contras t 1 Contras t 2

Book

a. Limited to firs t 100 cas es .

2 0

Book & Exercises -1 -1

All Activities -1 -1

This is incorrect. The sum of weights for each contrast should equal zero. Groups coded with positive weights will be compared against groups coded with negative weights (see Section 11.4.2).

Exercise

FieldStat4 11.MC.003.

A psychologist was looking at the effects of an intervention on depression levels. Three groups were used: waiting list control, treatment and post-treatment (a group who had had the treatment 6 months before). The SPSS output is below. Based on this output, what should the researcher report?

Test of Homogeneity of Variances BDIDIF Levene Statistic 4.246

df1

df2 2

Sig. .020

45

ANOVA BDIDIF

Betw een Groups Within Groups Total

Sum of Squares 529.437 2331.135 2860.572

df 2 45 47

Mean Square 264.719 51.803

F 5.110

Sig. .010

Robust Tests of Equality of Means BDIDIF a

Welch Brown-Forsythe

Statis tic 4.345 5.110

df1 2 2

df2 26.436 35.104

Sig. .023 .011

a. Asymptotically F dis tributed.

Author’s Notes

Multiple Choice Options (correct choice comes first)

Feedback (rejoinder) for this choice

The treatment groups had a significant effect on the depression levels, F(2, 26.44) = 4.35.

Yes, this is correct. Levene’s test is significant, indicating that the assumption of homogeneity of variance has been violated. Therefore, we need to look at Welch’s F and the Brown–Forsythe F (see Section 11.7.1).

The treatment groups did not have a significant effect on depression levels, F(2, 26.44) = 4.35.

This is incorrect. You were right to look at Welch’s F because the assumption of homogeneity of variances has been violated. However, the value in the box labelled Sig. is .023, which is less than .05, so we would conclude that the treatment groups did have a significant effect on the change in depression levels (see Section 11.7.1).

The treatment groups had a significant effect on depression levels, F(2, 45) = 5.11.

This is incorrect. Levene’s test is significant, indicating that the assumption of homogeneity of variance has been violated. Therefore, we need to look at Welch’s F and the Brown–Forsythe F (see Section 11.7.1).

The treatment groups did not have a significant effect on the change in depression levels, F(2, 35.10) = 5.11.

This is incorrect. Levene’s test is significant, indicating that the assumption of homogeneity of variance has been violated. Therefore, we need to look at Welch’s F and the Brown–Forsythe F (see Section 11.7.1).

Exercise

FieldStat4 11.MC.004.

A psychologist was looking at the effects of an intervention on depression levels. Three groups were used: waiting list control, treatment and post-treatment (a group who had had the treatment 6 months before).

Based on the output for these tests, what should the researcher conclude?

Test of Homogeneity of Variances BDIDIF Levene Statistic 4.246

df1

df2 2

45

Sig. .020

Multiple Comparisons Dependent Variable: BDIDIF

Bonferroni

(I) Group treatment Post Treatment Control

Games-Howell

treatment Post Treatment Control

(J) Group Post Treatment Control treatment Control treatment Post Treatment Post Treatment Control treatment Control treatment Post Treatment

Mean Difference (I-J) -2.4421 -7.9413* 2.4421 -5.4992 7.9413* 5.4992 -2.4421 -7.9413* 2.4421 -5.4992* 7.9413* 5.4992*

Std. Error 2.54468 2.54468 2.54468 2.54468 2.54468 2.54468 2.48536 2.95195 2.48536 2.12958 2.95195 2.12958

Sig. 1.000 .009 1.000 .108 .009 .108 .596 .031 .596 .043 .031 .043

95% Confidence Interval Lower Bound Upper Bound -8.7702 3.8859 -14.2694 -1.6133 -3.8859 8.7702 -11.8272 .8289 1.6133 14.2694 -.8289 11.8272 -8.7162 3.8319 -15.2320 -.6506 -3.8319 8.7162 -10.8347 -.1636 .6506 15.2320 .1636 10.8347

*. The mean difference is significant at the .05 level.

Author’s Notes

Multiple Choice Options (correct choice comes first)

Feedback (rejoinder) for this choice

The treatment group was significantly different from the control group but not the post-treatment group, and the post-treatment group was significantly different from the control group.

Yes, this is correct. Both the Bonferroni and Games–Howell tests indicate the same results, although the Games–Howell procedure is more conservative (see Section 11.7.3).

The treatment group was significantly different from the post-treatment and control group, and the post-treatment group was significantly different from the control group.

This is incorrect. Look at the values in the column labelled Sig. If the value is less than .05 then the effect is significant, and if the value is greater than .05 then the effect is nonsignificant (see Section 11.7.3).

The treatment group was significantly different from the control group but not the post-treatment group, and the post-treatment group was not significantly different from the control group.

This is incorrect. Look at the values in the column labelled Sig. If the value is less than .05 then the effect is significant, and if the value is greater than .05 then the effect is nonsignificant (see Section 11.7.3).

The post hoc tests are inconclusive.

This is incorrect. Look at the values in the column labelled Sig. If the value is less than .05 then the effect is significant, and if the value is greater than .05 then the effect is nonsignificant (see Section 11.7.3).

Exercise

FieldStat4 11.MC.005.

What kind of trend does the following graph show? ●

14

12

Outcome

10

8

●

6 ●

4 ●

2 ●

1

2

3

4

5

Group

Author’s Notes

Multiple Choice Options (correct choice comes first)

Feedback (rejoinder) for this choice

Quadratic

Yes, this is correct. To find a quadratic trend you need at least three groups, because with two groups the means of the dependent variable can’t be connected by anything other than a straight line (see Section 11.4.5).

Linear

This is incorrect. A linear trend is indicated by a straight line (see Section 11.4.5).

Cubic

This is incorrect. A cubic trend is where there are two changes in the direction of the trend. So, for example, the mean of the dependent variable at first goes up across the first couple of categories of the independent variable, then across the succeeding categories the mean goes down, but then across the last few categories the mean rises again (see Section 11.4.5).

Quartic

This is incorrect. This trend has three changes of direction, so you need at least five categories of the independent variable (see Section 11.4.5).

Exercise

FieldStat4 11.MC.006.

The student welfare office was interested in trying to enhance students’ exam performance by investigating the effects of various interventions. They took five groups of students before their statistics exams and gave them one of five interventions: (1) a control group just sat in a room contemplating the task ahead; (2) the second group had a yoga class to relax them; (3) the third group were told they would get monetary rewards contingent upon the grade they received in the exam; (4) the fourth group were given beta-blockers to calm their nerves; and (5) the fifth group were encouraged to sit around winding each other up about how much revision they had/hadn’t done (a bit like what usually happens). The final percentage obtained in the exam was the dependent variable. Using the critical values for F, how would you report the result in the table below?

Model Residual Total

SS 1213.6 707.9 1921.5

Df 4 29 33

MS 303.4 21.4

F 12.43**

Author’s Notes

Multiple Choice Options (correct choice comes first)

Feedback (rejoinder) for this choice

Type of intervention had a significant effect on levels of exam performance, F(4, 29) = 12.43, p < .01.

Yes, this is correct (see Section 11.7.1).

Type of intervention did not have a significant effect on levels of exam performance, F(4, 29) = 12.43, p > .05.

This is incorrect. The two asterisks next to the value of F indicate that the effect is significant at the .01 level (see Section 11.7.1).

Type of intervention did not have a significant effect on levels of exam performance, F(4, 33) = 12.43, p > .01.

This is incorrect. When reporting the Fratio, you need to use the model and residual degrees of freedom. Also, the two asterisks next to the value of F indicate that the effect is significant at the .01 level (see Section 11.7.1)

Type of intervention had a significant effect on levels of exam performance, F(4, 33) = 12.43, p < .01.

This is incorrect. When reporting the Fratio, you need to use the model and residual degrees of freedom (see Section 11.7.1).

Exercise

FieldStat4 11.MC.007.

The student welfare office was interested in trying to enhance students’ exam performance by investigating the effects of various interventions. They took five groups of students before their statistics exams and gave them one of five interventions: (1) a control group just sat in a room contemplating the task ahead (Control); (2) the second group had a yoga class to relax them (Yoga); (3) the third group were told they would get monetary rewards contingent upon the grade they received in the exam (Bribes); (4) the fourth group were given beta-blockers to calm their nerves (Beta-Blockers); and (5) the fifth group were encouraged to sit around winding each other up about how much revision they had/hadn’t done (You’re all going to fail). The student welfare office made four predictions: (1) all interventions should be different from the control; (2) yoga, bribery and beta-blockers should lead to higher exam scores than panic; (3) yoga and bribery should have different effects than the beta-blocker drugs; and (4) yoga and bribery should also differ. Which of the following planned contrasts (with the appropriate group codings) are correct to test these hypotheses?

Author’s Notes

Multiple Choice Options (correct choice comes first)

Feedback (rejoinder) for this choice Yes, this is correct (see Section 11.4).

Contrast Coefficients Condition Contras t 1 2 3 4

Control -4 0 0 0

Yoga 1 1 1 -1

Beta-Blockers 1 1 -2 0

Bribes 1 1 1 1

You're all going to fail 1 -3 0 0

Contrast Coefficients Condition Contras t 1 2 3 4

Control -4 0 0 3

Yoga 0 1 1 -1

Beta-Blockers 0 1 -2 0

Bribes 0 1 1 1

You're all going to fail 0 -3 0 0

Contrast Coefficients Condition Contras t 1 2 3 4

Control -4 1 1 1

Yoga 1 1 1 -1

Beta-Blockers 1 1 -2 1

Bribes 1 1 1 1

You're all going to fail 1 -3 1 1

This is incorrect. The sum of weights for all comparisons should be zero. If you add up the weights for a given contrast the result should be zero (see Section 11.4).

This is incorrect. The sum of weights for all comparisons should be zero. If you add up the weights for a given contrast the result should be zero (see Section 11.4).

Contrast Coefficients Condition Contras t 1 2 3 4

Control -4 1 1 1

Yoga 1 1 1 -4

Beta-Blockers 1 1 -4 1

Bribes 1 1 1 1

You're all going to fail 1 -4 1 1

This is incorrect. Remember that you want to compare only two chunks of variation at a time and that if a group is singled out in one comparison, that group should be excluded from any subsequent contrasts by being assigned a weight of zero (see Section 11.4).

Exercise

FieldStat4 11.MC.008.

Imagine you compare the effectiveness of four different types of stimulant to keep you awake while revising statistics using a one-way ANOVA. The null hypothesis would be that all four treatments have the same effect on the mean time kept awake. How would you interpret the alternative hypothesis?

Author’s Notes

Multiple Choice Options (correct choice comes first)

Feedback (rejoinder) for this choice

At least two of the stimulants will have different effects on the mean time spent awake.

Yes, this is correct. If the F-ratio is large enough to be statistically significant, then we know only that one or more of the differences between means are statistically significant (see Section 11.4).

All four stimulants have different effects on the mean time spent awake.

This is incorrect. If the F-ratio is large enough to be statistically significant, then we know only that one or more of the differences between means are statistically significant (see Section 11.4).

Two of the four stimulants have the same effect on the mean time spent awake.

This is incorrect. If the F-ratio is large enough to be statistically significant, then we know only that one or more of the differences between means are statistically significant (see Section 11.4).

None of the above

This is incorrect. If the F-ratio is large enough to be statistically significant, then we know only that one or more of the differences between means are statistically significant (see Section 11.4)

Exercise

FieldStat4 11.MC.009.

Of the tests below, which tests that the group means are a better fit of the data than the grand mean?

Author’s Notes

Multiple Choice Options (correct choice comes first)

Feedback (rejoinder) for this choice

Both the repeated-measures and independent ANOVA

Yes, this is correct (see Chapters 11 and 14).

The independent ANOVA only

This is incorrect. The repeated-measures ANOVA also tests that the group means are a better fit of the data than the grand mean (see Chapters 11 and 14).

The dependent ANOVA only

This is incorrect. The independent ANOVA also tests that the group means are a better fit of the data than the grand mean (see Chapters 11 and 14).

Friedman’s ANOVA

This is incorrect. This test is the nonparametric version of the repeatedmeasures ANOVA that is based on ranking the data (see Chapter 5).

Exercise

FieldStat4 11.MC.010.

The table below contains the length of time (minutes) for which different groups of students were able to stay awake to revise statistics after consuming 500 ml of one of three different types of stimulants. What is the variation in scores from groups A to B to C known as?

A

B

C

20

15

40

15

12

33

120

7

50

57

18

135

Author’s Notes

Multiple Choice Options (correct choice comes first)

Feedback (rejoinder) for this choice

The between-groups variance

Yes, this is correct (see Section 11.2).

The within-groups variance

This is incorrect. This is the variance within groups (see Section 11.2).

Homogeneity of variance

This is incorrect. This refers to the null hypothesis that the variances of the groups are equal (see Section 11.3.1).

The grand variance

This is incorrect. The grand variance is the variation between all scores, regardless of the experimental condition from which the scores come (see Section 11.2.3).

Exercise

FieldStat4 11.MC.011.

When the between-groups variance is a lot larger than the within-groups variance, the F-value is ____ and the likelihood of such a result occurring because of sampling error is _____ Author’s Notes

Multiple Choice Options (correct choice comes first)

Feedback (rejoinder) for this choice

large; low

Yes, this is correct. If the differences between group means are large enough, then the resulting model will be a better fit of the data than the grand mean (see Section 11.2.2).

large; high

This is incorrect. If the differences between group means are large enough, then the resulting model will be a better fit of the data than the grand mean (see Section 11.2.2).

small; low

This is incorrect. If the differences between group means are large enough, then the resulting model will be a better fit of the data than the grand mean (see Section 11.2.2).

small; high

This is incorrect. If the differences between group means are large enough, then the resulting model will be a better fit of the data than the grand mean (see Section 11.2.2).

Exercise

FieldStat4 11.MC.012.

Subsequent to obtaining a significant result from an exploratory one-way independent ANOVA, a researcher decided to conduct three t-tests to investigate where the differences between groups lie.

Which of the following statements is correct?

Author’s Notes

Multiple Choice Options (correct choice comes first)

Feedback (rejoinder) for this choice

The researcher should accept as statistically significant tests with a probability value of less than 0.016 to avoid making a Type I error.

Yes, this is correct. Conducting multiple ttests increases the familywise error rate, so if you are going to do this, it is important to divide the accepted probability level (.05) by the number of ttests you conduct (in this case 3).

Alternatively, you could run post hoc tests, which control the familywise error rate (see Section 11.5).

The researcher should have conducted orthogonal contrasts instead of t-tests to avoid making a Type I error.

This is incorrect. Orthogonal contrasts should only be used when specific hypothesis about which groups will differ are made before running the experiment (see Section 11.5).

This is the correct method to use. The researcher did not make any predictions about which groups will differ before running the experiment, therefore contrasts and post hoc tests cannot be used.

This is incorrect. Post hoc tests can be run when no prior predictions have been made regarding which groups will differ (see Section 11.5).

None of these options are correct.

This is incorrect. Conducting multiple ttests increases the familywise error rate, so if you are going to do this, it is important to divide the accepted probability level (.05) by the number of ttests you conduct (in this case 3).

Alternatively, you could run post hoc tests, which control the familywise error rate (see Section 11.5).

Exercise

FieldStat4 11.MC.013.

When conducting a one-way independent ANOVA with three levels on the independent variable, an F-ratio that is large enough to be statistically significant tells us: Author’s Notes

Multiple Choice Options (correct choice comes first)

Feedback (rejoinder) for this choice

That one or more of the differences between means is statistically significant but not where the differences between groups lie.

Yes, this is correct. It is therefore necessary after conducting an ANOVA to carry out further analysis to find out which groups differ (see Section 11.4).

That all of the differences between means are statistically significant.

This is incorrect. The F-ratio tells us only whether the model fitted to the data accounts for more variation than extraneous factors, it doesn’t tell us where the differences between groups lie (see Section 11.4).

That there is a significant three-way interaction.

This is incorrect. The F-ratio tells us only whether the model fitted to the data accounts for more variation than extraneous factors, it doesn’t tell us where the differences between groups lie (see Section 11.4).

That the model fitted to the data accounts for less variation than extraneous factors, but it doesn’t tell us where the differences between groups lie.

This is incorrect. An F-ratio that is large enough to be statistically significant actually tells us that the model fitted to the data accounts for more variation than extraneous factors (see Section 11.4).

Exercise

FieldStat4 11.MC.014.

What is the overall effect of an independent variable on a dependent variable known as?

Author’s Notes

Multiple Choice Options (correct choice comes first)

Feedback (rejoinder) for this choice

The main effect

Yes, this is correct (see Section 11.8).

The direct effect

This is incorrect (see Section 11.8).

The indirect effect

This is incorrect. The indirect effect is the effect of an independent variable on the dependent variable via a mediator variable (see Chapter 10).

The interaction effect

This is incorrect. A different effect across different groups or conditions is known as an interaction (see Section 6.5.4).

Exercise

FieldStat4 11.MC.015.

Increasing the number of independent variables in your study increases the likelihood of making a Type I error: true or false?

Author’s Notes

Multiple Choice Options (correct choice comes first)

Feedback (rejoinder) for this choice

True

Yes, this is correct due to the increase in the familywise error rate (see Section 11.3.2).

False

This is incorrect. Increasing the number of independent variables increases the familywise error rate (see Section 11.3.2).

Exercise

FieldStat4 11.MC.016.

If the differences between group means are large enough, then: Author’s Notes

Multiple Choice Options (correct choice comes first)

Feedback (rejoinder) for this choice

The resulting model will be a better fit of the data than the grand mean.

Yes, this is correct (See Section 11.2.2).

The resulting model will be a poorer fit of the data than the grand mean.

This is incorrect (see Section 11.2.2).

It is likely that the assumption of sphericity will have been violated.

This is incorrect (see Section 11.2.2).

The assumption of homogeneity of variances is likely to have been violated.

This is incorrect (see Section 11.2.2).

Exercise

FieldStat4 11.MC.017.

Which of the following is not a rule for conducting orthogonal contrasts?

Author’s Notes

Multiple Choice Options (correct choice comes first)

Feedback (rejoinder) for this choice

The sum of weights for a comparison should not be zero.

Yes, this is correct, because it is not a rule for conducting orthogonal contrasts.

The sum of weights for a comparison should equal zero. If you add up the weights for a given contrast the result should be zero (see Section 11.4.2).

The group that is singled out in one comparison should be excluded from any subsequent contrasts.

This is incorrect, because it is a rule for conducting orthogonal contrasts. You must compare only two chunks of variation at a time, and once a group has been singled out in a contrast it can’t be used in another contrast (see Section 11.4.2).

For a given contrast, the weights assigned to the group(s) in one chunk of variation should be equal to the number of groups in the opposite chunk of variation.

This is incorrect, because it is a rule for conducting orthogonal contrasts (see Section 11.4.2).

If we give a group a weight of zero then this eliminates that group from all calculations.

This is incorrect, because it is a rule for conducting orthogonal contrasts (see Section 11.4.2).

Exercise

FieldStat4 11.MC.018.

After an ANOVA you need more analysis to find out which groups differ. When you did not generate specific hypotheses before the experiment use: Author’s Notes (Hint: We need a way to contrast the different groups without inflating the Type I error rate.)

Multiple Choice Options (correct choice comes first)

Feedback (rejoinder) for this choice

Post hoc tests

Yes, this is correct. Post hoc tests compare every group (as if conducting several t-tests) but use a stricter acceptance criterion such that the familywise error rate does not rise above .05 (see Section 11.4).

Planned contrasts

This is incorrect. Planned comparisons are done when you have specific hypotheses that you want to test that were made before the experiment was conducted (see Section 11.4).

t-tests

This is incorrect. Conducting multiple ttests would inflate the familywise error rate. If we were to do this, we would have to use a stricter acceptance criterion such that the familywise error rate does not rise above .05 (see Section 11.4).

Bootstrapping

This is incorrect. Bootstrapping is a robust method of estimating standard errors and confidence intervals (see Section 11.4).

Exercise

FieldStat4 11.MC.019.

Imagine we conduct a one-way independent ANOVA with four levels on our independent variable and obtain a significant result. Given that we had equal sample sizes, we did not make any predictions about which groups would differ before the experiment and we want guaranteed control over the Type I error rate, which would be the best test to investigate which groups differ?

Author’s Notes (Hint: Post hoc tests do not require specific a priori predictions about which groups will differ.)

Multiple Choice Options (correct choice comes first)

Feedback (rejoinder) for this choice

Bonferroni

Yes, this is correct. If you want guaranteed control over the Type I error rate then use Bonferroni (see Section 11.5).

Hochberg’s GT2

This is incorrect. If sample sizes are very different use Hochberg’s GT2, but another test is better if you want to guarantee control over the Type I error rate (see Section 11.5).

Helmert

This is incorrect. Helmert is a structured contrast that is used when prior predictions about which groups will differ are made before the experiment (see Section 11.5).

Orthogonal contrasts

This is incorrect. You can use orthogonal contrasts only if you have made specific predictions before running your experiment (see Section 11.5).