STATS Ch. 13 Quiz 13 (NWACC)

In the first stage of a repeated-measures ANOVA, total degrees of freedom is partitioned into

between treatments df and within treatments df

A repeated-measures ANOVA produced an F-ration of F = 4.00 with df = 1, 14. If the same data were analyzed with a repeated-measures t test, what would be the df value for the t statistic?

14

The following table shows the results of a repeated-measures analysis of variance comparing two 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? Source; SS; df; MS; Between; xx; xx; 12; F = 4.00; Within; xx; xx; Bet. Sub.; 35; xx; Error; xx; xx; xx; Total; xx; xx

80

A repeated-measures study has n = 8 participants and k = 3 treatments. For this study, dferror= 21.

False

Because the repeated-measures ANOVA removes variance caused by individual differences, it usually is more likely to detect a treatment effect than the independent-measures ANOVA is.

True

If the F-ratios for factor A has df = 1, 36 and the F-ratio for the interaction has df = 2, 36, then the F-ratio for factor B will also have df = 2, 36.

True

In the second stage of the repeated-measures ANOVA, individual differences are removed from the denominator of the F-ratio.

True

The F-ratio for a repeated-measures ANOVA has df = 2, 16. The research study compared 3 treatments with a sample of n = 8 participants.

True

For the following data, what are the df values for the repeated-measures F-ratio? Treatments; Subject; I; II; III; P-totals; A; 3; 4; 5; 12; G = 27; B; 1; 1; 4; 6; SX2 = 109; C; 2; 1; 6; 9; T = 6; T = 6; T = 15; SS = 2; SS = 6; SS = 2

2,4

A new laundry detergent is supposed to be equally superior to the leading brand in both hot and cold water. If the new detergent works as predicted, then there should be an interaction between the brand of detergent and the temperature of the water.

False

Obtaining a significant interaction means that both factors A and B have significant main effects.

False

The result of a repeated-measures ANOVA stated that F(3, 21) = 4.57, p < .05. The study used a sample of n = 7 participants.

False

If the mean and variance are computed for each sample in an independent-measures, two-factor experiment, which of the following types of sample data will tend to produce large F-ratios for the two-factor ANOVA?

Large differences between sample means and small sample variances

What is the correct denominator for the repeated-measures F-ratio?

MSerror

For the following data, what is SStotal? Treatments Subject I II III P-totals A 3 4 5 12 G = 27 B 1 1 4 6 SX2 = 109 C 2 1 6 9 T = 6 T = 6 T = 15 SS = 2 SS = 6 SS = 2

NOT 10

In a two-factor ANOVA, which of the following is not computed directly but rather is found by subtraction?

SSAxB

In a repeated-measures analysis of variance, how does the magnitude of the mean differences from one treatment to another contribute to the F-ratio?

The mean differences add to the numerator of the F-ratio.

If a two-factor analysis of variance produces a statistically significant interaction, what can you conclude about the main effects?

The significance of the main effects is not related to the significance of the interaction

What is the relationship among the separate F-rations in a two-factor ANOVA?

They may have different df values, but they all have the same denominator

A repeated-measures study uses a sample of n = 8 participants to evaluate the mean differences between two treatment conditions. The analysis of variance for this study will have dferror = 7.

True

A two-factor study compares 2 levels of factor A and 2 levels of factor B with a sample of n = 20 participants in each treatment condition. If the results are evaluated with a two-factor ANOVA, all the F-ratios will have df = 1, 76.

True

For a repeated-measures study, dfbetween treatments= 3 and dftotal = 27. This means that there were n = 7 participants in the study.

True

For a two-factor analysis of variance, the significance of any specific F-ratio is completely independent of the significance of the other F-ratios.

True

For an independent-measures two-factor analysis of variance, all of the F-ratios use the same denominator.

True

If a two-factor study has 2 levels of factor A and 3 levels of factor B, then dfbet. treatments = 5.

True

A repeated-measures t test produces a t statistic of t = 4.00 with df = 12. If the same data were evaluated with a repeated-measures ANOVA, the F-ratio would have df = 2, 12.

False

A two-factor analysis of variance produces an F-ratio for factor A that has df = 3, 36. This analysis is comparing three different levels of factor A.

False

A two-factor analysis of variance with 2 levels of factor A and 3 levels of factor B involves six separate hypothesis tests.

False

A two-factor study compares 2 levels of factor A and 3 levels of factor B with a sample of n = 5 participants in each treatment condition. This study uses a total of 25 participants.

False

For an independent-measures two-factor experiment, the bigger the values for the sample variances, the more likely it is that at least one of the F-ratios will be significant.

False

If the F-ratio for factor A has df = 1, 40 and the F-ratio for factor B has df = 3, 40, then the F-ratio for the interaction must have df = 2, 40.

False

A two-factor, independent-measures research study with 2 levels of factor A and 3 levels of factor B with n = 10 participants in each treatment condition would require a total of 60 participants.

True

The analysis of total variability into between-treatments and within-treatments variability is the same for a repeated-measures ANOVA and an independent-measures ANOVA.

True

Whenever a two-factor experiment results in a significant interaction, you should be cautious about interpreting the main effects because an interaction can distort, conceal, or exaggerate the main effects of the individual factors.

True

For the following data, what is the value of SSB? B1; B2; A1; n = 5; M = 1; SS = 10; n = 5; M = 2; SS = 20; A2; n = 5; M = 1; SS = 10; n = 5; M = 4; SS = 20

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 A´B interaction? B1; B2; A1; 20; 30; A2; 10; ?

20

A repeated-measures experiment compares three treatment conditions with a sample of n = 10 participants. If the data are analyzed with ANOVA, the analysis would have dftotal =

29

For an experiment involving 3 levels of factor A and 3 levels of factor B, with a sample of n = 8 in each treatment condition, what are the df values for the F-ratio for the AxB interaction?

4, 63

The F-ratio for a repeated-measures ANOVA has df = 1, 15. The research study used a total of n = 16 participants.

True

For a research study with 2 levels of factor A, 3 levels of factor B, and n = 5 in each treatment condition, what are the df values for the F-ratio evaluating the main effect for factor A?

1, 24

A repeated-measures study uses a sample of n = 15 participants to evaluate the mean differences among four treatment conditions. In the analysis of variance for this study, what is the value for dfbetween treatments?

3

The results of a two-factor analysis of variance produce df = 1, 30 for the F-ratio for factor A, and df = 2, 30 for the F-ratio for the AxB interaction. Based on this information, how many levels of factor B were compared in the study?

3

The results of a two-factor analysis of variance produce df = 2, 36 for the F-ratio for factor A and df = 2, 36 for the F-ratio for factor B. How many participants are in each of the treatment conditions?

5

A researcher obtains an F-ratio with df = 2, 12 in a repeated - measures study ANOVA. How many subjects participated in the study?

7

A repeated-measures ANOVA with n = 5 subjects has df within-treatment equal to 12. What is the value for dferror for this analysis?

8

A repeated-measures study uses a sample of n = 10 participants to evaluate the mean differences among three treatment conditions. For this study, dfbetween subjects = 18.

False

A repeated-measures analysis of variance for a study comparing three treatment conditions with a sample of n = 10 participants, produces an F-ratio of F = 5.40. For this result, which of the following is the correct statistical decision?

Reject the null hypothesis with a = .05 but not with a = .01

A researcher reports an F-ratio with df = 2, 40 from a repeated-measures ANOVA. How many treatment conditions were compared in this experiment?

3

A researcher reports an F-ratio with df = 2, 40 from a repeated-measures ANOVA. How many subjects participated in this experiment?

44

For the repeated-measures analysis, the F-ratio, on average, is expected to be zero when H0 is true.

False

When using the Scheffé post hoc test for a repeated-measures ANOVA, the denominator for the F ratio should be _____.

MS Error