Question 1

What assumption is NOT required in a repeated-measures ANOVA?
A) Continuous-level measurement
B) Homoscedasticity
C) Independence
D) Normality

Accepted Answer

The assumption of independence is not required in a repeated-measures ANOVA. This is because the study design involves matching participants on some characteristics and measuring them multiple times, resulting in correlated data. As a result, the assumption of independence is not necessary for this type of analysis. However, the assumptions of continuous-level measurement, homoscedasticity, and normality still apply.

Question 2

What unique assumption is required in repeated-measures ANOVA?
A) Continuous-level measurement
B) Homoscedasticity
C) Independence
D) Sphericity

Accepted Answer

Repeated-measures ANOVA assumes sphericity, which means that the variances of the differences between all possible pairs of related groups are equal. This assumption is unique to repeated-measures ANOVA and not necessary in regular ANOVA.

Question 3

Which of the following would result in the FEWEST potential Type I errors in a repeated-measures ANOVA?
A) Application of the Greenhouse-Geisser adjustment
B) Application of the Huynh-Feldt adjustment
C) Application of the Kruskal-Wallis adjustment
D) Using no adjustment technique

Accepted Answer

The Greenhouse-Geisser adjustment is known for being more conservative compared to other methods like the Huynh-Feldt adjustment. It tends to lower the chances of committing Type I errors (falsely rejecting the null hypothesis) in repeated-measures ANOVA by adjusting the degrees of freedom downward, which makes it harder to reach statistical significance. This is particularly useful in dealing with violations of the sphericity assumption in ANOVA. The Kruskal-Wallis adjustment is not applicable here as it is a non-parametric test used for different purposes, and using no adjustment technique would not specifically address the potential for increased Type I errors due to violations of assumptions in repeated-measures ANOVA.

Question 4

Which statistic is used to adjust the degrees of freedom when sphericity is violated?
A) Alpha
B) Beta
C) Epsilon
D) Gamma

Accepted Answer

When sphericity is violated, the Greenhouse-Geisser or Huynh-Feldt correction is applied, which adjusts the degrees of freedom using the epsilon statistic. Therefore, the correct choice is C, Epsilon.

Question 5

In a one-way repeated-measures ANOVA, a researcher measured 15 subjects under six different conditions. What number of degrees of freedom is correct for the F-ratio for testing the conditions effect?
A) 6, 90
B) 5, 90
C) 6, 70
D) 5, 70

Accepted Answer

In a repeated-measures ANOVA, the degrees of freedom for the conditions effect is calculated as (k-1), where k is the number of conditions. Here, k=6, so df for conditions = 6-1 = 5. The error degrees of freedom is calculated as (n-1)(k-1), where n is the number of subjects. Here, n=15, so df for error = (15-1)(6-1) = 70. Therefore, the correct degrees of freedom for the F-ratio is 5, 70.

Question 6

If the SS total, SS columns, SS rows, and SS error in a one-way repeated-measures ANOVA are 100, 50, 15, and 35, respectively, what is the explained sum of squares?
A) 50
B) 65
C) 85
D) 100

Accepted Answer

The explained sum of squares is equal to the sum of squares between (SS columns) in a repeated-measures ANOVA. Therefore, it is 50.

Question 7

Which two issues can we resolve by using an intraclass correlation technique rather than an interclass correlation technique?
A) Small-n problems and mean differences
B) More than two trials and small-n problems
C) Differing variances and more than two trials
D) Mean differences and more than two trials

Accepted Answer

Intraclass correlation is used when there are more than two trials and the focus is on mean differences within a group rather than between groups. Therefore, intraclass correlation technique can resolve the issues of mean differences and more than two trials.

Question 8

Which statistical procedure can we use to obtain an intraclass correlation coefficient?
A) A repeated-measures ANOVA
B) A Pearson product- moment correlation
C) A between-groups ANOVA
D) A fixed design

Accepted Answer

A repeated-measures ANOVA can be used to obtain an intraclass correlation coefficient, as it allows for the examination of variance within and between groups, which is necessary for calculating the ICC.

Question 9

A tennis teacher administers six trials of a wall volley test. What is the proper coefficient to use to estimate the reliability of this test?
A) Interclass correlation
B) Pearson product-moment correlation
C) Spearman-Brown formula
D) Kuder-Richardson coefficient
E) Intraclass correlation

Accepted Answer

Since the teacher administered the same test to the same individuals multiple times, the best option for estimating reliability is the intraclass correlation coefficient.

Question 10

An F ratio with 1 and 20 degrees of freedom is equivalent to which of the following? A) A (t-ratio)² with df = 20 B) A t-ratio with df = 20 C) A PPM with infinite df D) A PPM with 20 df

Accepted Answer

An F ratio with 1 and 20 degrees of freedom is equivalent to a t-ratio squared with 20 degrees of freedom. This is because the F distribution with 1 numerator degree of freedom is the square of the t distribution.

Question 11

For which terms in the ANOVA model are sphericity adjustments potentially important?
A) Between-groups factors
B) Within-groups factors
C) Neither A nor B
D) Both A and B

Accepted Answer

Sphericity adjustments are important for within-groups factors in ANOVA models because these adjustments correct for violations of the sphericity assumption, which is crucial when comparing means across three or more related groups.

Question 12

When is sphericity a concern with the within-groups model?
A) When sample size is large
B) When the repeated factor has more than two levels
C) When using a dependent t-test
D) None of the above is correct.

Accepted Answer

Sphericity is a concern with the within-groups model when the repeated factor has more than two levels. Sphericity refers to the assumption that the variances of the differences between all possible pairs of conditions are equal. When this assumption is violated, the F-ratio obtained from an ANOVA using the within-groups model may be biased, leading to incorrect conclusions. One way to address this is by using a correction factor, such as the Greenhouse-Geisser or Huynh-Feldt correction.

Question 13

What is reported when a repeated-measures ANOVA is used to estimate an intraclass reliability?
A) Pearson product-moment correlation coefficient
B) Interclass reliability
C) Intraclass reliability
D) Sphericity

Accepted Answer

A repeated-measures ANOVA is used to estimate intraclass reliability, which measures the consistency of measurements taken by the same rater or instrument on the same subjects over time. Therefore, the reported output should be related to intraclass reliability, which is represented by the intraclass correlation coefficient (ICC).

Quiz 10: One-Way Within-Groups Anova

What assumption is NOT required in a repeated-measures ANOVA?

What unique assumption is required in repeated-measures ANOVA?

Which of the following would result in the FEWEST potential Type I errors in a repeated-measures ANOVA?

Which statistic is used to adjust the degrees of freedom when sphericity is violated?

In a one-way repeated-measures ANOVA, a researcher measured 15 subjects under six different conditions. What number of degrees of freedom is correct for the F-ratio for testing the conditions effect?

If the SS total, SS columns, SS rows, and SS error in a one-way repeated-measures ANOVA are 100, 50, 15, and 35, respectively, what is the explained sum of squares?

Which two issues can we resolve by using an intraclass correlation technique rather than an interclass correlation technique?

Which statistical procedure can we use to obtain an intraclass correlation coefficient?

A tennis teacher administers six trials of a wall volley test. What is the proper coefficient to use to estimate the reliability of this test?

An F ratio with 1 and 20 degrees of freedom is equivalent to which of the following?

For which terms in the ANOVA model are sphericity adjustments potentially important?

When is sphericity a concern with the within-groups model?

What is reported when a repeated-measures ANOVA is used to estimate an intraclass reliability?