repeated_measure_anova
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Table of Contents
See also, ANOVA, Factorial ANOVA
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Repeated Measures ANOVA
Introduction
- one-way ANOVA for related, not-independent groups
- extension of the dependent t-test (one group t-test, repeated measure t-test)
- also, within-subjects ANOVA or ANOVA for correlated samples
- the simplest one is one-way repeated measures ANOVA
- which requires one independent and one dependent variable
- the independent variable is categorical (either nominal or ordinal)
- the dependent variable is continuous (interval or ratio)
Test Circumstances
- one subject with repeated measures across a time period (differences of mean scores across three or more time periods)
- one subject with repeated measures in different situation (treatments; differences of mean scores under three or more different conditions)
LOGICS
- $\text{independent ANOVA: } F = \displaystyle \frac{MS_{between}}{MS_{within}} = \frac{MS_{between}}{MS_{error}}$
- $\text{rep measures ANOVA: } F = \displaystyle \frac{MS_{between}}{MS_{within}} = \displaystyle \frac{MS_{conditions}}{MS_{error}}$
- but, $\text{SS}_\text{{within}}$ can be partitioned as
- $\text{SS}_{\text{ subjects}}$ and $\text{SS}_{\text{ error}}$
- Among the two, we can exclude the first from SSwithin
- and solely use the latter as SSerror
- This is to say:
- in $\text{independent ANOVA: } \text{SS}_\text{{within}} = \text{SS}_{\text{error}} $
- in $\text{rep measures ANOVA: } \text{SS}_\text{{within}} = \text{SS}_{\text{subjects}} + \text{SS}_{\text{error}}$
- This means that the term SSerror will be smaller
- But, with this SSerror, the df is going to be (n-1)(k-1)
| Headache Analysis | ||||||
|---|---|---|---|---|---|---|
| base treatment | average per case (subject, participant) |
|||||
| ser | w1 | w2 | w3 | w4 | w5 | $\overline{X}_{part}$ = average per case (subject, participant) |
| 1 | 21 | 22 | 8 | 6 | 6 | 12.6 |
| 2 | 20 | 19 | 10 | 4 | 9 | 12.4 |
| 3 | 7 | 5 | 5 | 4 | 5 | 5.2 |
| 4 | 25 | 30 | 13 | 12 | 4 | 16.8 |
| 5 | 30 | 33 | 10 | 8 | 6 | 17.4 |
| 6 | 19 | 27 | 8 | 7 | 4 | 13 |
| 7 | 26 | 16 | 5 | 2 | 5 | 10.8 |
| 8 | 13 | 4 | 8 | 1 | 5 | 6.2 |
| 9 | 26 | 24 | 14 | 8 | 17 | 17.8 |
| average per week | 20.78 | 20.00 | 9.00 | 5.78 | 6.78 | $\overline{X}$ = 12.47 |
| Stats | |
|---|---|
| Mean Total | 12.47 |
| $\Sigma{X_i}$ | 561 |
| $\Sigma{{X_i}^2}$ | 10483 |
| # of week | 5 |
| # of case (n) | 9 |
SStotal = $\Sigma{(X-\overline{X})^2} $ = 3489.2
SSparticipants = $w\Sigma{(\overline{X}_{participants}-\overline{X})}$ = 833.6
SSweeks = $n\Sigma{(\overline{X}_{week} - \overline{X})}$ = 1934.5
SSresidual
= SSerror
= SStotal - SSparticipants - SSweeks
= 721.1
dftotal = N - 1 = 45 - 1 = 44
dfweek = 5 - 1 = 4 = dfbetween
dfparticipants = 9 - 1 = 8 = dfsubjects
dferror= (n - 1)(k - 1) = 8 * 4 = 32 = 40 - 8 = 32
dfwithin = N - k = 45 - 5 = 40
ie
| 시각적 인지점수 | |||
|---|---|---|---|
| 참가자 | No visual distraction | Visual distraction | Sound Distraction |
| A | 47 | 22 | 41 |
| B | 57 | 31 | 52 |
| C | 38 | 18 | 40 |
| D | 45 | 32 | 43 |
reference
repeated_measure_anova.1496355879.txt.gz · Last modified: 2017/06/02 06:54 by hkimscil