Test 2: Repeated Measures ANOVA Flashcards
Independent t test
Independent Variable is a between-subject factor (different groups)
Dependent/Paired t test
Independent Variable is a within-subjects factor; same participants measured twice (pre-test/post-test), matched or correlated samples
When we have more than two groups, what do we use?
ANOVAs
Simple one-way ANOVA
Independent Variable is a between-subjects factor
One-way repeated-measures ANOVA
Independent Variable is a within-subjects factor; three or more tests are given (pre-, mid- and post-test)
Repeated-Measures
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
For a simple one-way ANOVA, what does the test assume?
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
Error variance
Comprised of intraindividual variability (variability within a person’s scores), interindividual variability (variability between people in different groups), and unexplained sources (error)
When only one group of subjects is measured more than once,
the data sets are dependent.
What is the total variability for a single group of subjects measured more than once expected to be?
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.
What does the less variability tend to do the mean square error term?
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.
One-way Repeated-Measures ANOVA partitions the total variance into 3 sources:
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
What does Variance due to participants (intraindividual variability) allow us to do?
Allows to estimate how much variance is due to different abilities of different participants because each participant is measured for each level
The assumptions of the simple one-way ANOVA (between-subjects designs) also apply to the repeated-measures ANOVA except for…
the independence of samples assumption and that the repeated-measures ANOVA must also meet an additional assumption of sphericity.
Sphericity
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.
Example of Sphericity
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.
Sphericity requires that the variance of the difference scores are…
equal.
What happens when the assumption of sphericity is violated?
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. )
What are the methods used to correct for violations of the assumption of sphericity?
The Greenhouse-Geisser adjustment and Huynh-Feldt adjustment. (Both corrections modify the degrees of freedom)
What does the application of the Greenhouse-Geisser adjustment assume?
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
Type II error
Accepting/retaining the null hypothesis when it is actually false
What does the Huynh-Feldt adjustment attempt to correct?
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
Although F may still be significant, these adjustments reduce the…
confidence we can place in our conclusion that the differences among the means are statistically significant
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?
we must accept the null hypothesis
Epsilon values are more conservative for what method?
Greenhouse-Geisser method provides better protection against making Type I errors but increasing the risk of making Type II errors
A strategy for determining the significance of F is discussed in the Vincent text:
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
As an alternative to the methods listed above, you could get around a severe violation using a…
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. )
The results of the F test only tell us what? (Post Hoc Tests)
That there is at least one difference among the means; it does not tell us where these differences lie.
Familywise Alpha (Post Hoc Tests)
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
What are the texts recommendations when the assumption of sphericity has not been violated? (Post Hoc Tests)
Tukey’s HSD; since it keeps the Type I error rate at the nominal value and results in the most statistical power
What are the texts recommendations if the assumption of sphericity has been violated? (Post Hoc Tests)
the best compromise is to use dependent/paired t tests with a Bonferroni correction.
What can an F value be evaluated to determine?
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)
In contrast to the simple ANOVA, the repeated-measures ANOVA must meet the additional assumption of…
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
