# PSYC 3430 Lecture Notes - Lecture 4: Null Hypothesis, Explained Variation, Repeated Measures Design

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**preview**shows pages 1-3. to view the full**16 pages of the document.**Instructor Notes - Chapter 13 - page 185

Chapter 13: Repeated-Measures ANOVA

Chapter Outline

13.1 Overview of Repeated-Measures Designs

13.2 The Repeated-Measures ANOVA

Hypotheses for the Repeated-Measures ANOVA

The F-ratio for Repeated-Measures ANOVA

The Logic of the Repeated Measures ANOVA

13.3 Hypothesis Testing and Effect Size with the Repeated-Measures ANOVA

Notation for the Repeated-Measures ANOVA

Stage 1 of the Repeated-Measures Analysis

Stage 2 of the Repeated-Measures Analysis

Calculation of the Variances (MS Values) and the F-Ratio

Measuring Effect Size for the Repeated-Measures ANOVA

In the Literature - Reporting the Results of a Repeated-Measures ANOVA

Post Hoc Tests with Repeated Measures ANOVA

Assumptions of the Repeated-Measures ANOVA

13.3 Advantages of the Repeated-Measures Design

Individual Differences and the Consistency of the Treatment Effects

13.5 Repeated-Measures ANOVA and Repeated-Measures t Test

Learning Objectives and Chapter Summary

1. Students should understand the logic underlying the analysis of variance for a repeated-

measures study.

The denominator of the F-ratio is intended to measure differences (or variance) that occur

simply by chance. These chance differences are the unsystematic, unpredictable

differences that are not caused by a treatment effect or some other systematic and

predictable source. In an independent-measures study where every score comes from a

different person, the naturally occurring differences from one person to another

(individual differences) are unpredictable and are included in the category of chance or

error variance. In a repeated-measures study, however, the differences from one person

to another are often systematic and predictable. For example, one individual may have

scores that are consistently higher than a second person. These consistent differences can

be measured and subtracted out of the variance in the denominator of the F-ratio. Thus,

the repeated-measures ANOVA introduces a second stage to the analysis where the

individual differences are measured and subtracted out of the variance.

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Instructor Notes - Chapter 13 - page 186

2. Students should be able to perform an analysis of variance to evaluate the mean differences

from a single-factor, repeated-measures research study.

The formulas and calculations for the repeated-measures ANOVA are almost identical to

those for the independent-measures analysis; in fact, the first stage of the repeated-

measures analysis is identical to the independent-measures analysis. The second stage of

the analysis involves computing and subtracting the SS and df values that measure the

individual differences between subjects. The calculation of SS and df between-subjects

in the second stage of the analysis follow exactly the same pattern as the calculation of

SS and df between-treatments in the first stage (see Box 13.1).

3. The calculation of Îˇ2 (the percentage of explained variance) to measure effect size is slightly

different for the repeated measures design. Instead of computing a percentage of the total

variability (like we did with the independent-measures ANOVA), we now compute a percentage

of the variability that is otherwise unexplained.

In a repeated-measures ANOVA, part of the variability is explained by the systematic

individual differences. This part can be calculated and subtracted out. We then compute

Îˇ2 as the percentage of the remaining variability that is explained by the treatment effects.

As a result,

SSbetween treatments

Îˇ2 = ââââââââââââââ

SStotal - SSbetween subjects

Other Lecture Suggestions

1. The repeated-measures ANOVA builds on the independent-measures analysis in Chapter 12.

The difference between the two methods focuses on removing individual differences. If students

understand the rationale for removing individual differences, then the repeated-measures

ANOVA makes more sense. The logic underlying the repeated-measures analysis is as follows:

The purpose for analysis of variance is to determine whether the data provide evidence

for a significant treatment effect. To accomplish this, the F-ratio is constructed so that the

numerator and the denominator are perfectly balanced if there is no treatment effect (if H0 is

true). Thus, if we obtain an unbalanced, exceptionally large, F-ratio, we have evidence for a

treatment effect. In a repeated-measures design, there are no individual differences between

treatments (the same individuals are in all the treatments), so there are no individual differences

in the numerator of the F-ratio. To keep the F-ratio balanced, we must also remove the

individual differences from the denominator. This is the second stage of the repeated-measures

ANOVA.

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Instructor Notes - Chapter 13 - page 187

2. A demonstration that manipulates the data from a repeated-measures ANOVA can help

emphasize two important points:

1. The repeated-measures ANOVA removes individual differences.

2. In situations where individual differences are large, a repeated-measures design can be

much more powerful than an independent-measures design. That is, the repeated-

measures design is much more likely to identify significant differences between

treatments.

Begin with data similar to the scores in end-of-chapter problem #9 and work through the analysis

of variance. Stop after the first stage of the analysis to demonstrate what would happen if the

scores were from an independent-measures design. Then, increase the individual differences by

adding 5 points to each score for person B and work through both the independent- and repeated-

measures analysis again. Note that the increased individual differences have a large effect on the

independent-measures ANOVA but have no effect at all on the repeated-measures analysis.

Caution: Adding 5 points to each score for person B will make G = 60 and ÎŁX2 = 447.

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