Repeated-Measures ANOVA & Multigroup Designs

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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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40 Terms

1
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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.

2
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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.

3
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Which statistical test is used for a between-subjects multigroup design with one IV?

A one-way ANOVA (between-subjects).

4
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Which statistical test is used for a within-subjects multigroup design with one IV?

A repeated-measures one-way ANOVA.

5
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The repeated-measures ANOVA is essentially an extension of what two-group test?

The paired-samples (dependent) t-test.

6
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In a repeated-measures design, how many groups of participants are there?

Only one group; the same participants experience every level of the IV.

7
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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).

8
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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.

9
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What does the omnibus F-test in a repeated-measures ANOVA tell you?

Whether any overall differences exist among the related means.

10
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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.

11
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State the null hypothesis for a repeated-measures ANOVA with three levels.

H0: μ1 = μ2 = μ3 (all related population means are equal).

12
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State the alternative hypothesis for a repeated-measures ANOVA with three levels.

HA: At least one related population mean differs from another.

13
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How is the F statistic calculated in a repeated-measures ANOVA?

F = MSconditions ÷ MSerror.

14
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Between-treatments variance reflects which two components?

The treatment effect plus random error not due to individual differences.

15
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Within-treatments variance is further divided into which two parts in a repeated-measures ANOVA?

Between-subjects variability and unexplained (error) variability.

16
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Which portion of variance becomes the numerator of the F-ratio in an RM ANOVA?

Between-treatments (between-conditions) variance.

17
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Which portion of variance becomes the denominator of the F-ratio in an RM ANOVA?

Error variance after removing between-subjects variability.

18
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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.

19
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Give the formula for total degrees of freedom (DFtotal) in RM ANOVA.

DFtotal = N − 1.

20
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Provide the formula for degrees of freedom between treatments (DFbetween).

DFbetween = K − 1 (where K is the number of levels).

21
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Provide the formula for degrees of freedom within treatments (DFwithin).

DFwithin = N − K.

22
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Provide the formula for degrees of freedom between subjects (DFsubjects).

DFsubjects = n − 1 (n = number of participants).

23
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Provide the formula for degrees of freedom for error (DFerror).

DFerror = (N − K) − (n − 1).

24
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In the RM ANOVA summary table, what are the three main sources of variance?

Conditions (Between Treatments), Subjects, and Error.

25
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What symbol (T) represents in RM ANOVA calculations?

The sum of scores in each treatment condition.

26
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What does the symbol P represent in RM ANOVA calculations?

The sum of scores for each participant across all conditions.

27
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What does the symbol G represent in RM ANOVA calculations?

The grand total of all scores in the experiment.

28
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What effect size measure was taught for RM ANOVA in the lecture?

Eta-squared (η²).

29
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Write the general formula for Eta-squared.

η² = SSbetween ÷ (SSbetween + SSerror).

30
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Which specific post hoc test was demonstrated in the lecture slides?

The Tukey Honestly Significant Difference (HSD) test.

31
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Write the formula for the Tukey q statistic used in HSD.

q = |M1 − M2| ÷ √(MSerror / n).

32
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When looking up the critical q value, which two parameters are required?

The number of treatments (k) and the error degrees of freedom (DFerror).

33
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In Dr. Ashe’s back-pain study, what was the obtained F value?

F = 21.04.

34
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In that study, what were the numerator and denominator degrees of freedom?

df1 = 3 (conditions), df2 = 9 (error).

35
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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.

36
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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.

37
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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.

38
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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.

39
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What alpha level was used in the professors’ exam difficulty example?

α = .01.

40
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Why are ANOVA hypotheses always stated as non-directional?

Because the ANOVA tests only whether differences exist, not the direction of those differences.