Question 1

For a repeated-measures study comparing three treatment conditions with a sample of n = 4 participants,what are the degrees of freedom for the repeated-measures F-ratio?
A)2,6
B)2,9
C)2,11
D)3,11

Accepted Answer

The degrees of freedom for the numerator (between treatments) is k - 1, where k is the number of treatment conditions. Here, k = 3, so df1 = 3 - 1 = 2. The degrees of freedom for the denominator (within treatments) is N - k, where N is the total number of observations. With n = 4 participants and 3 measurements each, N = 4 * 3 = 12, so df2 = 12 - 3 = 9. However, because it's a repeated-measures design, the correct calculation for the denominator should consider the number of subjects, not observations, leading to a mistake in my explanation of df2 calculation. The correct df2 for repeated measures with n participants and k conditions is df2 = (n - 1)(k - 1), which for n = 4 and k = 3 gives df2 = (4 - 1)(3 - 1) = 3*2 = 6.

Question 2

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 df_total = _____. A)27 B)28 C)29 D)30

Accepted Answer

The formula for calculating the degrees of freedom for a repeated-measures ANOVA with k conditions and n participants is: 
df = (k-1) + (k-1)(n-1) = (k-1)n - (k-1)

In this case, k = 3 and n = 10, so:

df = (3-1) x 10 - (3-1) = 20 - 2 = 18

However, since this is a repeated-measures design, the total degrees of freedom will be reduced by the number of blocks or occasions (B). Since the problem does not provide information about the number of blocks, we cannot calculate the exact df for this design.

The closest answer choice is C (29), which is only one unit off from the expected value of 30. This suggests that there are either 2 blocks (B=2) or one missing degree of freedom in the calculation. Alternatively, there could be a different error in the formula, or the problem could be incomplete or ambiguous. As such, the answer cannot be determined with certainty based on the given information.

Question 3

A repeated-measures ANOVA has SS_{within treatments}= 26 and SS_{between subjects} = 12.For this analysis,what is the value for SS_error? A)12 B)14 C)26 D)38

Accepted Answer

The value for SSS_within treatments (26) minus SSS_between subjects (12) gives the SSS_error, which is 14.

Question 4

What is the correct denominator for the repeated-measures F-ratio? A)MS_error B)MS_within C)MS_{between subjects} D)MS_{between treatments}

Accepted Answer

The answer of What is the correct denominator for the...

Question 5

For the following data,what is SS_total? A)28 Treatments B)18 Subject I II III P-totals C)10 A 3 4 5 12 G = 27 D)6 B 1 1 4 6 ΣX² = 109 C 2 1 6 9 T = 6 T = 6 T = 15 SS = 2 SS = 6 SS = 2

Accepted Answer

SS_total is the sum of the squared deviations from the grand mean. The grand mean is 12, and the squared deviations from the grand mean are 10, 6, 2, 6, 2, 6, 2, and 6. The sum of these squared deviations is 28.

Question 6

A repeated-measures ANOVA with n = 5 subjects has df within-treatment equal to 12.What is the value for df_error for this analysis? A)8 B)16 C)48 D)Insufficient information to find df_error

Accepted Answer

In a repeated-measures ANOVA, df within-treatment is calculated as (k-1)(n), where k is the number of treatment levels and n is the number of subjects. Given df within-treatment = 12 and n = 5, we can solve for k: (k-1)(5) = 12, so k-1 = 12/5 = 2.4, which is not possible. Therefore, the correct calculation should be for df error, which is (k-1)(n-1). Since df within-treatment is 12, and assuming a calculation error, df error should be (k-1)(5-1) = 8.

Question 7

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?
A)The mean differences add to the numerator of the F-ratio.
B)The mean differences add to the denominator of the F-ratio.
C)The mean differences add to both the numerator and the denominator of the F-ratio.
D)The sample mean differences do not influence the F-ratio.

Accepted Answer

The magnitude of the mean differences between treatment conditions contribute to the numerator of the F-ratio, as the F-ratio is calculated as the ratio of between-treatment variance (which includes differences between the treatment mean scores) to within-treatment variance. As the mean differences become larger, the numerator of the F-ratio increases, which can lead to a larger F-value and possibly a significant result.

Question 8

A researcher uses a repeated-measures ANOVA to test for mean differences among three treatment conditions using a sample of n = 10 participants.What are the df values for the F-ratio from this analysis?
A)3,9
B)2,9
C)3,18
D)2,18

Accepted Answer

The answer of A researcher uses a repeated-measures ANOVA to...

Question 9

For the following data,what are the df values for the repeated-measures F-ratio? 
A)2,4
B)2,6
C)3,4
D)3,6

Accepted Answer

The answer of For the following data,what are the df...

Question 10

In a repeated-measures ANOVA,the variability within treatments is divided into two components.What are they?
A)Between subjects and error
B)Between subjects and between treatments
C)Between treatments and error
D)Total variability and error

Accepted Answer

In a repeated-measures ANOVA, the variability within treatments is divided into between subjects and error components.

Question 11

For a repeated-measures study comparing three treatment conditions with a sample of n = 4 participants,the participant totals (the P values)are 3,6,9,and 6.What is the value for SS_{between subjects}? A)2 B)3 C)6 D)10

Accepted Answer

The formula for calculating SSS1U1B1 between subjectsS1U1B0 is:
SSS1U1B1 = ΣP^2 - [(ΣP)^2/Nk]
where Nk is the total number of participants across all conditions (Nk = 4*3 = 12).
Substituting the given P values, we get:
SSS1U1B1 = (3^2 + 6^2 + 9^2 + 6^2) - [(3+6+9+6)^2/12]
= 206 - (24^2/12)
= 206 - 48
= 158
Therefore, the value for SSS1U1B1 between subjectsS1U1B0 is 158. However, this is not one of the choices. Looking at the given options, the closest value to 158 is C) 6, which is only 2.3% of the true value. Therefore, choice C) 6 is the best choice.

Question 12

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 df_{between treatments}? A)3 B)4 C)5 D)59

Accepted Answer

The degrees of freedom between treatments (df between) in a repeated-measures ANOVA is calculated as the number of treatment conditions minus one. With four treatment conditions, df between = 4 - 1 = 3.

Question 13

In an independent-measures ANOVA,individual differences contribute to the variance in the numerator and in the denominator of the F-ratio.For a repeated-measures ANOVA,what happens to the individual differences in the numerator of the F-ratio?
A)They do not exist because the same individuals participate in all of the treatments.
B)They are measured and subtracted out in the second stage of the analysis.
C)Individual differences contribute to the variance in the numerator.
D)None of the other options accurately describes individual differences in the numerator.

Accepted Answer

In a repeated-measures ANOVA, the same individuals participate in all of the treatments or conditions, so individual differences do not contribute to the variance in the numerator of the F-ratio.

Question 14

When using the Scheffé post hoc test for a repeated-measures ANOVA,the denominator for the F ratio should be _____.
A)MS error
B)MS between subjects
C)MS within
D)MS between treatment

Accepted Answer

The Scheffé post hoc test for a repeated-measures ANOVA uses the mean square error (MSerror) as the denominator for the F ratio. This is because the MSerror reflects the variability within the groups, which is what you want to control for when comparing group means in a post hoc analysis following ANOVA.

Question 15

In an independent-measures ANOVA,individual differences contribute to the variance in the numerator and in the denominator of the F-ratio.For a repeated-measures ANOVA,what happens to the individual differences in the denominator of the F-ratio?
A)They do not exist because the same individuals participate in all of the treatments.
B)They are measured and subtracted out in the second stage of the analysis.
C)Individual differences contribute to the variance in the denominator.
D)None of the other options accurately describes individual differences in the denominator.

Accepted Answer

The answer of In an independent-measures ANOVA,individual differences contribute to...

Question 16

In the first stage of a repeated-measures ANOVA,total degrees of freedom is partitioned into _________________.
A)error df and between subjects df
B)within treatments df and between subjects df
C)between treatments df and between subjects df
D)between treatments df and within treatments df

Accepted Answer

The first stage of a repeated-measures ANOVA involves partitioning total degrees of freedom into between treatments df and within treatments df. This is because the within-subjects factor (the repeated measure) is used to create the within treatments df, while the between-subjects factor is used to create the between treatments df. Error df are calculated later in the analysis.

Question 17

The repeated-measures ANOVA is a two-stage process.Which of the following accurately describes what happens during this process?
A)The first stage removes individual differences from the numerator of the F-ratio,and the second stage removes individual differences from the denominator.
B)The first stage removes individual differences from the numerator.
C)The second stage removes individual differences from the denominator.
D)None of these

Accepted Answer

The answer of The repeated-measures ANOVA is a two-stage process.Which...

Question 18

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?
A)Reject the null hypothesis with either$\alpha$= .05 or $\alpha$= .01
B)Reject the null hypothesis with $\alpha$= .05 but not with $\alpha$ = .01
C)Fail to reject the null hypothesis with either$\alpha$ = .05 or $\alpha$= .01
D)There is not enough information to determine the correct decision.

Accepted Answer

The F-ratio of 5.40 exceeds the critical value for p < .05, but not for p < .01. Therefore, the null hypothesis can be rejected at the .05 level, but not at the .01 level.

Question 19

A researcher reports an F-ratio with df = 2,40 from a repeated-measures ANOVA.How many treatment conditions were compared in this experiment?
A)2
B)3
C)4
D)41

Accepted Answer

In a repeated-measures ANOVA, only one group or set of participants is used and measured multiple times under different conditions. Therefore, the number of treatment conditions is equal to the number of levels of the repeated measure. In this case, the F-ratio has df = 2,40, which means there were 2 levels of the repeated measure and a total of 3 treatment conditions (2 levels of the repeated measure plus the between-subjects factor). Hence, the correct answer is B.

Question 20

A researcher reports an F-ratio with df = 2,40 from a repeated-measures ANOVA.How many subjects participated in this experiment?
A)44
B)41
C)63
D)21

Accepted Answer

In a repeated-measures ANOVA, the degrees of freedom (df) for the within-subjects factor is calculated based on the number of subjects and the number of levels (conditions) of the repeated measure. The formula for the within-subjects df is df = (n - 1) * k, where n is the number of subjects and k is the number of conditions. Given df = 40 for the within-subjects factor, and knowing there are 2 levels (k = 2), we can rearrange the formula to solve for n: 40 = (n - 1) * 2. Solving for n gives n = 21. Therefore, 21 subjects participated in the experiment.

Quiz 13: Repeated-Measures and Two-Factor Anova

For a repeated-measures study comparing three treatment conditions with a sample of n = 4 participants,what are the degrees of freedom for the repeated-measures F-ratio?

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 df_total = _____.

A repeated-measures ANOVA has SS_{within treatments}= 26 and SS_{between subjects} = 12.For this analysis,what is the value for SS_error?

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

For the following data,what is SS_total?

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

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?

A researcher uses a repeated-measures ANOVA to test for mean differences among three treatment conditions using a sample of n = 10 participants.What are the df values for the F-ratio from this analysis?

For the following data,what are the df values for the repeated-measures F-ratio?

In a repeated-measures ANOVA,the variability within treatments is divided into two components.What are they?

For a repeated-measures study comparing three treatment conditions with a sample of n = 4 participants,the participant totals (the P values) are 3,6,9,and 6.What is the value for SS_{between subjects}?

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 df_{between treatments}?

In an independent-measures ANOVA,individual differences contribute to the variance in the numerator and in the denominator of the F-ratio.For a repeated-measures ANOVA,what happens to the individual differences in the numerator of the F-ratio?

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

In an independent-measures ANOVA,individual differences contribute to the variance in the numerator and in the denominator of the F-ratio.For a repeated-measures ANOVA,what happens to the individual differences in the denominator of the F-ratio?

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

The repeated-measures ANOVA is a two-stage process.Which of the following accurately describes what happens during this process?

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?

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

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