Chapter 12- ANOVA

1. An analysis of variances produces dfbetween treatments 5 2 and dfwithin treatments 5 24. For this analysis, what is dftotal? a. 26 b. 27 c. 28 d. Cannot be determined without additional information

a

A researcher uses an ANOVA to evaluate the mean difference between two treatment conditions and obtains F = 4.00 with df = 1, 16. If an independent- measures t statistic had been used instead of the ANOVA, then what t value would be obtained and what is the df value for t? a.t = 2.00 with df = 16 b. t = 2.00 with df = 17 c. t = 16 with df = 16 d. t = 16 with df = 17

a

For an analysis of variance, the differences between the sample means contrib- ute to the _________ and appears in the _________ of the F-ratio. a. variance between treatments, numerator b. variance between treatments, denominator c. variance within treatments, numerator d. variance within treatments, denominator

a

If an analysis of variance is used for the following data, what would be the effect of changing the value of M_2 to 30? M_1 = 15 SS_1 = 90 M_2 = 25 SS_2 = 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 SSbetween and increase the size of the F-ratio d. Decrease SSbetween and decrease the size of the F-ratio

a

What is suggested by a large value for the F-ratio in an ANOVA? a. There is a treatment effect and the null hypothesis should be rejected. b. There is no treatment effect and the null hypothesis should be rejected. c. There is a treatment effect and you should fail to reject the null hypothesis. d. There is no treatment effect and you should fail to reject the null hypothesis.

a

An analysis of variance produces SStotal = 40 and SSwithin = 10. For this analysis, what is SSbetween? a. 30 b. 50 c. 400 d. Cannot be determined without additional information.

a. 30

Imagine that you add a treatment effect that increases one of the population means by 10 points. No other changes occur. What should happen to the F-ratio (as compared to what it was before the treatment effect? a. The numerator would get larger, but the denominator would not be affected. b. The denominator would get larger but the numerator would not be affected. c. Both the numerator and denominator would get larger. d. Impossible to say without more information.

a. The numerator would get larger, but the denominator would not be affected.

1. How many levels are there in a single-factor independent-measures design comparing depression scores of participants with and without treatment? a. 1 b. 2 c. 3 d. 4

b

A research report concludes that there are significant differences among treatments, with "F(2, 27)= 8.62, p < .01, n^2 = 0.46." How many treatment conditions were compared in this study? a.2 b. 3 c. 29 d. 30

b

An ANOVA finds significant treatment effects for a study comparing three treatments with means of M1 = 8, M2 = 4, M3 = 2. If Tukey's HSD is computed to be HSD 5 2.50, then which of the treatments are significantly different? a. 1 vs. 2 and 2 vs. 3 b. 1 vs. 2 and 1 vs. 3 c. 1 vs. 3 and 2 vs. 3 d. 1 vs. 2 and 1 vs. 3 and 2 vs. 3

b

Which combination of factors is most likely to produce a large value for the F-ratio and a large value for h2? a. Large mean differences and large sample variances b. Large mean differences and small sample variances c. Small mean differences and large sample variances d. Small mean differences and small sample variances

b

Which of the following accurately describes the F-ratio in an analysis of variance? a. The F-ratio is a ratio of two (or more) sample means. b. The F-ratio is a ratio of two variances. c. The F-ratio is a ratio of sample means divided by sample variances. d. None of the above.

b

If the null hypothesis is true and there is no treatment effect, what value is expected on average for the F-ratio? a. 0 b. 1.00 c. k - 1 d. N - k

b. 1.00

A researcher reports an F-ratio with df = 2, 36 for an independent-measures experiment. How many treatment conditions were compared in this experiment? a. 2 b. 3 c. 36 d. 38

b. 3

Under what circumstances are post tests necessary? a. When you reject the null hypothesis with exactly 2 treatment conditions b. When you reject the null hypothesis with more than 2 treatment conditions c. When you fail to reject the null hypothesis with exactly 2 treatment conditions d. When you fail to reject the null hypothesis with more than 2 treatment conditions

b. When you reject the null hypothesis with more than 2 treatment conditions

Which combination of factors is most likely to produce a large value for the F-ratio? a. large mean differences and large sample variances b. large mean differences and small sample variances c. small mean differences and large sample variances d. small mean differences and small sample variances

b. large mean differences and small sample variances

In general the distribution of F-ratios is _____. a. symmetrical with a mean of zero 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 equal to dfbetween

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

1. Under what circumstances are post hoc tests necessary after an ANOVA? a. When H0 is rejected b. When there are more than two treatments c. When H0 is rejected and there are more than two treatments d. You always should do post hoc tests after an ANOVA.

c

A research study compares three treatments with n 5 5 in each treatment. If the SS values for the three treatments are 25, 20, and 15, then the analysis of variance would produce SSwithin equal to ______. a. 12 b. 20 c. 60 d. Cannot be determined from the information given

c

A researcher uses analysis of variance to test for mean differences among four treatments with a sample of n 5 6 in each treatment. The F-ratio for this analy- sis would have what df values? a. df =3, 5 b. df = 3, 15 c. df = 3, 20 d. df = 4, 24

c

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

c

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. 18 b. 19 c. 1, 18 d. 1, 19

c. 1,18

A researcher reports an F-ratio with df = 1, 24 for an independent-measures experiment. How many individual subjects participated in the experiment? a. 24 b. 25 c. 26 d. 27

c. 26

For ANOVA, we assume that all of the populations have the same variance. The denominator is a good estimate of that variance number _______________, and the numerator is a good estimate of that number___________. a. If the null is true; if the null is false b. If the null is true; if the null is true c. Whether the null is true or false; if the null is true. d. Whether the null is true or false; if the null is false.

c. Whether the null is true or false; if the null is true.

For an experiment comparing more than two treatment conditions you should use analysis of variance rather than separate t tests because _____. a. separate t tests would require substantially more computations b. a test based on variances is more sensitive than a test based on means c. conducting several t tests would inflate the risk of a Type I error d. There is no difference between the two tests, you can use either one.

c. conducting several t tests would inflate the risk of a Type I error

In analysis of variance, the F-ratio is a ratio of _____. a. sample means b. sample means divided by variances c. two variances d. sample variances divided by sample means

c. two variances

An analysis of variance is used to evaluate the mean differences among three treat- ment conditions. The analysis produces SSwithin treatments 5 20, SSbetween treatments 5 40, and SStotal 5 60. For this analysis, what is MSbetween treatments? a. 20/3 b. 20/2 c. 40/3 d. 40/2

d

Identify the true statement about the Tukey HSD test. a. The formula for the Tukey HSD returns the critical value of F that you must exceed in order to say that a mean difference is significantly different. b. The test procedure allows you to make all possible contrasts (pairwise plus other linear combinations and functions) for the entire set of k treatments. c. The test procedure requires you to calculate a new F ratio for each comparison of means. d. The HSD test can be appropriate with all types of ANOVA we've covered (one way between subjects, one-way repeated measures, two-way between subjects ANOVA). e. All of the above

d. The HSD test can be appropriate with all types of ANOVA we've covered (one way between subjects, one-way repeated measures, two-way between subjects ANOVA).