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Forty practice flashcards covering key ideas, formulas, and examples related to repeated-measures ANOVA, multigroup designs, and post-hoc analyses from the lecture notes.
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What does a multigroup design allow researchers to do?
Compare three or more levels of an independent variable in a single study.
Give one advantage of including three or more levels of an independent variable.
It can reveal non-linear or curvilinear relationships that two-level designs miss.
Which statistical test is used for a between-subjects multigroup design with one IV?
A one-way ANOVA (between-subjects).
Which statistical test is used for a within-subjects multigroup design with one IV?
A repeated-measures one-way ANOVA.
The repeated-measures ANOVA is essentially an extension of what two-group test?
The paired-samples (dependent) t-test.
In a repeated-measures design, how many groups of participants are there?
Only one group; the same participants experience every level of the IV.
Name a common situation in which a repeated-measures ANOVA is appropriate that involves time.
When the same participants are measured at multiple time points to track change (e.g., pre-test, post-test).
Name a second situation when a repeated-measures ANOVA is appropriate that involves conditions.
When participants experience several experimental conditions and their responses to each are compared.
What does the omnibus F-test in a repeated-measures ANOVA tell you?
Whether any overall differences exist among the related means.
What type of test must follow a significant omnibus F to locate specific group differences?
Post hoc tests such as planned comparisons or Tukey HSD.
State the null hypothesis for a repeated-measures ANOVA with three levels.
H0: μ1 = μ2 = μ3 (all related population means are equal).
State the alternative hypothesis for a repeated-measures ANOVA with three levels.
HA: At least one related population mean differs from another.
How is the F statistic calculated in a repeated-measures ANOVA?
F = MSconditions ÷ MSerror.
Between-treatments variance reflects which two components?
The treatment effect plus random error not due to individual differences.
Within-treatments variance is further divided into which two parts in a repeated-measures ANOVA?
Between-subjects variability and unexplained (error) variability.
Which portion of variance becomes the numerator of the F-ratio in an RM ANOVA?
Between-treatments (between-conditions) variance.
Which portion of variance becomes the denominator of the F-ratio in an RM ANOVA?
Error variance after removing between-subjects variability.
Why does removing between-subjects variability increase statistical power in an RM ANOVA?
It reduces the error term, increasing the F value and the chance of detecting true effects.
Give the formula for total degrees of freedom (DFtotal) in RM ANOVA.
DFtotal = N − 1.
Provide the formula for degrees of freedom between treatments (DFbetween).
DFbetween = K − 1 (where K is the number of levels).
Provide the formula for degrees of freedom within treatments (DFwithin).
DFwithin = N − K.
Provide the formula for degrees of freedom between subjects (DFsubjects).
DFsubjects = n − 1 (n = number of participants).
Provide the formula for degrees of freedom for error (DFerror).
DFerror = (N − K) − (n − 1).
In the RM ANOVA summary table, what are the three main sources of variance?
Conditions (Between Treatments), Subjects, and Error.
What symbol (T) represents in RM ANOVA calculations?
The sum of scores in each treatment condition.
What does the symbol P represent in RM ANOVA calculations?
The sum of scores for each participant across all conditions.
What does the symbol G represent in RM ANOVA calculations?
The grand total of all scores in the experiment.
What effect size measure was taught for RM ANOVA in the lecture?
Eta-squared (η²).
Write the general formula for Eta-squared.
η² = SSbetween ÷ (SSbetween + SSerror).
Which specific post hoc test was demonstrated in the lecture slides?
The Tukey Honestly Significant Difference (HSD) test.
Write the formula for the Tukey q statistic used in HSD.
q = |M1 − M2| ÷ √(MSerror / n).
When looking up the critical q value, which two parameters are required?
The number of treatments (k) and the error degrees of freedom (DFerror).
In Dr. Ashe’s back-pain study, what was the obtained F value?
F = 21.04.
In that study, what were the numerator and denominator degrees of freedom?
df1 = 3 (conditions), df2 = 9 (error).
Was the null hypothesis rejected in Dr. Ashe’s back-pain study?
Yes; the F value exceeded the critical value, indicating significant differences over time.
According to the Tukey tests, which time point differed from all others in the pain study?
The "Before treatment" time point had significantly higher pain scores than 1-week, 1-month, and 6-month scores.
What did the large effect size (η² = .88) indicate about the treatment effect?
The treatment accounted for 88% of the variance, indicating a very strong effect.
In the professors’ exam difficulty example, was the repeated-measures ANOVA significant?
No; F(2,10) = 0.29, which was far below the critical value.
What alpha level was used in the professors’ exam difficulty example?
α = .01.
Why are ANOVA hypotheses always stated as non-directional?
Because the ANOVA tests only whether differences exist, not the direction of those differences.