repeated_measure_anova
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====== Repeated Measures ANOVA ====== | ====== Repeated Measures ANOVA ====== | ||
+ | Introduction | ||
+ | * one-way ANOVA for // | ||
+ | * 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; | ||
+ | |||
+ | 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 SS< | ||
+ | * and solely use the latter as SS< | ||
+ | * This is to say: | ||
+ | * in $\text{independent ANOVA: } \text{SS}_\text{{within}} = \text{SS}_{\text{error}} $ | ||
+ | * in $\text{rep measures ANOVA: } \text{SS}_\text{{within}} = \text{SS}_{\text{subjects}} + \text{SS}_{\text{error}}$ | ||
+ | |||
+ | |||
^ Headache Analysis | ^ Headache Analysis | ||
- | | || | + | | | base treatment |
- | | ser | w1 | w2 | w3 | w4 | w5 | $\overline{X}_{part}$ \\ = average per case | | + | | ser | w1 | w2 | w3 | w4 | w5 | $\overline{X}_{part}$ \\ = average |
| 1 | 21 | 22 | 8 | 6 | 6 | 12.6 | | | 1 | 21 | 22 | 8 | 6 | 6 | 12.6 | | ||
| 2 | 20 | 19 | 10 | 4 | 9 | 12.4 | | | 2 | 20 | 19 | 10 | 4 | 9 | 12.4 | | ||
Line 15: | Line 43: | ||
| 8 | 13 | 4 | 8 | 1 | 5 | 6.2 | | | 8 | 13 | 4 | 8 | 1 | 5 | 6.2 | | ||
| 9 | 26 | 24 | 14 | 8 | 17 | 17.8 | | | 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 | | + | | average |
^ Stats ^^ | ^ Stats ^^ |
repeated_measure_anova.txt · Last modified: 2024/05/13 08:39 by hkimscil