Quiz 7 (Chapter 12)

Which of the following is expected if the null hypothesis is true for an analysis of variance? SS(between) should be about the same size as SS(total) MS(between) should be about the same size as MS(total) SS(between) should be about the same size as SS(within) MS(between) should be about the same size as MS(within)

MS(between) should be about the same size as MS(within)

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? 2,20 2,19 1,19 1,20

1, 20 (There are always two levels in a t-test, so the df(between) of the equivalent ANOVA will be 1. We als know from the t test that the total n was 22 (because df = 20 = (n1-1)+(n2-1) for an independent-measures t-test). The df(within) for the F-ratio is N-k, or 22 - 2, or 20.)

An independent-measures research study compares three treatment conditions using a sample of n=5 in each treatment. For this study, the three sample totals are T1 = 5, T2 = 10, and T3 = 15. What value would be obtained for SS(between)? 5 10 15 1

10 (From the equation SS(between) = sum of (T^2 / n) - (G^2 / N), we calculate 25/5 + 100/5 + 225/5 - 900/15 = 10. This equation is one of the four ways to find SS(between) that were discussed in a recent lecture.)

An analysis of variance comparing three treatment conditions produces df(total) = 24. For this ANOVA, what is the value of df(between)? 3 22 21 2

2 (df(between) = k-1 = 3-1 = 2. )

An analysis of variance produces df(between) = 3 and df(within) = 24. For this analysis, what is df(total)? 28 27 Cannot be determined without additional information. 26

27 (df(total) = df(between) + df(within), so 24+3 = 27.)

An analysis of variance produces SS(total) = 40 and SS(within) = 10. For this analysis, what is SS(between)? 30 400 50 Cannot be determined without additional information.

30 (SS(between) = SS(total) - SS(within), so 40 - 10 = 30.)

For an F-ratio with df=2,10, the critical value for a hypothesis test using alpha = 0.05 would be ________. 19.39 4.10 99.40 7.56

4.10

An independent-measures research study compares three treatment conditions using a sample of n=10 in each treatment. For this study, the three samples have SS1 = 10, SS2 = 20, and SS3 = 15. What value would be obtained for MS(within)? 45/27 = 1.67 45/29 = 1.55 45/3 = 15.0 45/30 = 1.5

45/27 = 1.67 (Specifically, MS(within) = (SS1+SS2+SS3) / (df1+df2+df3) = (10+20+15) / (9+9+9) = 45/27 = 1.67.)

In general, what factors will produce the largest F-ratio? Large mean differences and large variances Small mean differences and small variances Small mean differences and large variances Large mean differences and small variances

Large mean differences and small variances

An analysis of variance is used to evaluate the mean differences for a research study comparing three treatments with a separate sample of 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? There is not enough information to make a statistical decision. Fail to reject the null hypothesis with either alpha = 0.05 or alpha = 0.01. Reject the null hypothesis with alpha = 0.05, but not with alpha = 0.01. Reject the null hypothesis with either alpha = 0.05 or alpha = 0.01.

Reject the null hypothesis with alpha = 0.05, but not with alpha = 0.01. (Specifically, there are three treatments, so df(between) = 2, and each treatment has n=6, so df(within) = 5+5+5 = 15. From the table, F(crit) for 2, 12 degrees of freedom = 3.885 at alpha = 0.05, and 6.927 at alpha = 0.01. Our F statistic of 4.10 is greater than the former, but not greater than the latter.)

In an analysis of variance, which of the following is directly influenced by the size of the sample mean differences? SS(within) SS(between) All three SS values are directly influenced. SS(total)

SS(between) (The correct answer is that SS(between) is directly influenced by the size of the sample mean differences. )

In analysis of variance, the F-ratio is a ratio of _______. sample variances divided by sample means. sample means. variances. sample means divided by variances.

Variances (MS(within) and MS(between) are both variances.)

Under what circumstances are post hoc tests useful/necessary? When you reject H0 with exactly 2 treatment conditions. When you fail to reject H0 with more than two treatment conditions. When you fail to reject H0 with exactly 2 treatment conditions. When you reject H0 with more than 2 treatment conditions.

When you reject H0 with more than 2 treatment conditions.

Under what circumstances is the experimentwise alpha level a concern? Whenever an experiment compares exactly two treatments. Whenever you do analysis of variance. Whenever an experiment involves more than one hypothesis test. Whenever the alpha level is greater than 0.05.

Whenever an experiment involves more than one hypothesis test. (More than one hypothesis test creates a multiple comparisons problem, which, if not corrected, makes the alpha value for the experiment as a whole substantially higher than that for each individual test.)

In analysis of variance, the term "factor" refers to ________. a treatment mean. a treatment total. a dependent variable. an independent variable

an independent variable

A researcher uses an analysis of variance to test for mean differences among three treatment conditions using a sample of n=8 participants in each treatment. What degrees of freedom would the F ratio from this analysis have? df = 3, 21 df = 2, 23 df = 2, 21 df = 23

df = 2, 21 (Specifically, there are 8+8+8-1 = 23 total degrees of freedom, and k-1 = 2 degrees of freedom between groups, and 7+7+7 = 21 degrees of freedom within groups. So df = 2, 21 (i.e., between, within).)

In general, the distribution of F-ratios is ____________. positively skewed with all values greater than or equal to zero. symmetrical with a mean of zero. symmetrical with a mean equal to df(between). negatively skewed with all values greater than or equal to zero.

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

The null hypothesis for an ANOVA states that ____________. there are no differences between any of the population means. None of the other three choices are correct. all of the population means are different from one another. at least one of the population means is different from the others.

there are no differences between any of the population means.

The purpose of post hoc tests is _____________. to determine how much total difference exists between the treatments to determine which treatments are significantly different None of the above. to determine whether or not a Type I error occurred.

to determine which treatments are significantly different

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

1

An analysis of variance produces SS(between) = 20, SS(within) = 30, and an F-ratio with df = 2, 15. For this analysis, what is the F-ratio? 30/20 = 1.50 10/2 = 5.00 2/10 = 0.20 20/30 = 0.67

10/2 = 5.00 (Specifically, the numerator is SS(between)/df(between) = 20/2 = 10, and the denominator is SS(within)/df(within) = 30/15 = 2, and 10/2 = 5.00.)

An analysis of variance comparing three treatment conditions produces df(total) = 24. For this ANOVA, what is the value of df(within)? 21 22 2 3

22 (Correct; if k is the number of treatment conditions, then df(between) = k-1 = 2. Then, df(within) = df(total) - df(between) = 24-2 = 22. Alternatively, df(within) = N - k = 25 - 3 = 22.)

A researcher reports an F-ratio with df = 2, 36 from an independent-measures research study. Based on the df values, how many treatments were compared in the study, and what was the total number of subjects participating in the study? 2 treatments and 38 subjects 3 treatments and 39 subjects 2 treatments and 37 subjects 3 treatments and 38 subjects

3 treatments and 39 subjects (The number of treatments is one more than the numerator df, and the number of subjects is df(total)+1, which is df(within)+df(between)+1. )

An analysis of variance produces SS(within) = 40 and SS(total) = 70. In this analysis, what is the value of SS(between)? 110 30 Cannot be determined without additional information. 40

30 (SS(between) = 30, because SS(between) = SS(total) - SS(within) = 70 - 40 = 30.)

When comparing more than two treatment means, why should you use an analysis of variance instead of using several uncorrected t tests? Conducting several t tests would inflate the risk of a Type I error. There is no difference between the two tests; you can use either one. A test based on variances is more sensitive than a test based on means. Separate t tests would require substantially more computations.

Conducting several t tests would inflate the risk of a Type I error. (conducting several t tests would inflate the risk of a Type I error. Bonferroni correction would fix this problem, but multiple t tests still are not a particularly good solution.)