Test 2: Repeated Measures ANOVA

Question 1

Independent t test

Answer 1

Independent Variable is a between-subject factor (different groups)

Question 2

Dependent/Paired t test

Answer 2

Independent Variable is a within-subjects factor; same participants measured twice (pre-test/post-test), matched or correlated samples

Question 3

When we have more than two groups, what do we use?

Answer 3

ANOVAs

Question 4

Simple one-way ANOVA

Answer 4

Independent Variable is a between-subjects factor

Question 5

One-way repeated-measures ANOVA

Answer 5

Independent Variable is a within-subjects factor; three or more tests are given (pre-, mid- and post-test)

Question 6

Repeated-Measures

Answer 6

one of the most frequently used statistical tests in the health sciences; measures the significance of mean differences measured on the same subjects over repeated trials (time points); produces an F value

Question 7

For a simple one-way ANOVA, what does the test assume?

Answer 7

that the mean values are taken from independent groups that have no relationship; in this design, we partition the total variance (of our DV) into two sources: Between-group variance (treatment effects), Error

Question 8

Error variance

Answer 8

Comprised of intraindividual variability (variability within a person’s scores), interindividual variability (variability between people in different groups), and unexplained sources (error)

Question 9

When only one group of subjects is measured more than once,

Answer 9

the data sets are dependent.

Question 10

What is the total variability for a single group of subjects measured more than once expected to be?

Answer 10

less than if the scores came from different groups of people ( if the scores were independent) because interindividual variability has been eliminated by using a single group at multiple time points.

Question 11

What does the less variability tend to do the mean square error term?

Answer 11

This tends to reduce the mean square error term in the denominator of F in a manner similar to the correction made to the standard error of the difference in the dependent t test.

Question 12

One-way Repeated-Measures ANOVA partitions the total variance into 3 sources:

Answer 12

Variance due to treatment (or level of IV), Variance due to participants (intraindividual variability), Error (unexplained variability); Variability between subjects (interindividual variability) is no longer a factor

Question 13

What does Variance due to participants (intraindividual variability) allow us to do?

Answer 13

Allows to estimate how much variance is due to different abilities of different participants because each participant is measured for each level

Question 14

The assumptions of the simple one-way ANOVA (between-subjects designs) also apply to the repeated-measures ANOVA except for…

Answer 14

the independence of samples assumption and that the repeated-measures ANOVA must also meet an additional assumption of sphericity.

Question 15

Sphericity

Answer 15

refers to the condition where the variances of the differences btw all possible pairs of within-subject conditions (i.e. levels of the IV) are equal. The violation of sphericity occurs when this is not the case.

Question 16

Example of Sphericity

Answer 16

Consider a study in which subjects are measured at 3 time points: time1, time2, and time3. From this, we can calculate the diff scores btw each time period: time1 – time2, time2 – time3, and time3 – time1.

Question 17

Sphericity requires that the variance of the difference scores are…

Answer 17

equal.

Question 18

What happens when the assumption of sphericity is violated?

Answer 18

The Type I error rate will inflate; if alpha is set at 0.05, the true risk of committing Type I error will be higher than 0.05. (The assumption is not applicable in situations where only two repeated measures are used because only one set of differences can be calculated. )

Question 19

What are the methods used to correct for violations of the assumption of sphericity?

Answer 19

The Greenhouse-Geisser adjustment and Huynh-Feldt adjustment. (Both corrections modify the degrees of freedom)

Question 20

What does the application of the Greenhouse-Geisser adjustment assume?

Answer 20

Maximum violation of the assumption of sphericity; when the violation is minimal, this adjustment to the dof may be too severe, possibly resulting in a Type II error

Question 21

Type II error

Answer 21

Accepting/retaining the null hypothesis when it is actually false

Question 22

What does the Huynh-Feldt adjustment attempt to correct?

Answer 22

The amount of violation that has occurred only; in this adjustment the dof for error are multiplied by a value (epsilon, ε) that ranges from zero (maximum violation) to 1.0 (no violation); violation is considered insignificant if ε ≥ .75

Question 23

Although F may still be significant, these adjustments reduce the…

Answer 23

confidence we can place in our conclusion that the differences among the means are statistically significant

Question 24

If the obtained p value from the overall test is close to the rejection level of α = .05 (suppose we get a p =.04), and the adjustment increases it to p = .06 what must we do?

Answer 24

we must accept the null hypothesis

Question 25

Epsilon values are more conservative for what method?

Answer 25

Greenhouse-Geisser method provides better protection against making Type I errors but increasing the risk of making Type II errors

Question 26

A strategy for determining the significance of F is discussed in the Vincent text:

Answer 26

Evaluate F with the G-G adjustment first: If sig, reject the null (If not sig, evaluate F with no adjustment); If F with no adjustment is not sig (most liberal condition), accept the null hypothesis; If F with the G-G adjustment is not sig, but the F with no adjustment is sig, use the H-F adjustment (a moderate condition) to make your final determination

Question 27

As an alternative to the methods listed above, you could get around a severe violation using a…

Answer 27

multiple/multivariate analysis of variance (MANOVA) with the repeated measures designated as multiple dependent variables; with this, assumption of sphericity is not required (less powerful and provides better protection against Type I errors, but less against Type II errors. )

Question 28

The results of the F test only tell us what? (Post Hoc Tests)

Answer 28

That there is at least one difference among the means; it does not tell us where these differences lie.

Question 29

Familywise Alpha (Post Hoc Tests)

Answer 29

When we perform multiple statistical tests at a given alpha level (e.g. 0.05), the cumulative risk of committing at least one type I error across the family of tests will be greater than the original alpha of 0.05

Question 30

What are the texts recommendations when the assumption of sphericity has not been violated? (Post Hoc Tests)

Answer 30

Tukey’s HSD; since it keeps the Type I error rate at the nominal value and results in the most statistical power

Question 31

What are the texts recommendations if the assumption of sphericity has been violated? (Post Hoc Tests)

Answer 31

the best compromise is to use dependent/paired t tests with a Bonferroni correction.

Question 32

What can an F value be evaluated to determine?

Answer 32

If any significant differences exist among the means (when F is significant, a post hoc test must be applied to determine the specific means that differ from one another)

Question 33

In contrast to the simple ANOVA, the repeated-measures ANOVA must meet the additional assumption of…

Answer 33

Sphericity; when this assumption has been violated, adjustments to the dof and p values obtained must be made with either G-G or H-F correction techniques