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--- repeated_measure_anova [2017/05/10 09:12] – hkimscil
+++ repeated_measure_anova [2017/06/02 06:56] – created hkimscil
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-See also, [[ANOVA]], [[:Factorial Anova|Factorial ANOVA]]
+~~REDIRECT>repeated_measures_anova~~
-설명이 불충분하므로, [[:Repeated Measure Anova#s-3|아래 참고 사이트]](reference)를 숙지할 것.
-====== 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 SS<sub>within</sub>
-    * and solely use the latter as SS<sub>error</sub>
-    * 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 SS<sub>error</sub> will be **__smaller__**
-    * But, with this SS<sub>error</sub>, 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  |
-SS<sub>total</sub> = $\Sigma{(X-\overline{X})^2} $ = 3489.2 \\
-SS<sub>participants</sub> = $w\Sigma{(\overline{X}_{participants}-\overline{X})}$ = 833.6 \\
-SS<sub>weeks</sub> = $n\Sigma{(\overline{X}_{week} - \overline{X})}$ = 1934.5 \\
-SS<sub>residual</sub>  \\
-= SS<sub>error</sub> \\
-= SS<sub>total</sub> - SS<sub>participants</sub> - SS<sub>weeks</sub>  \\
-= 721.1 \\
-\\
-df<sub>total</sub> = N - 1 = 45 - 1 = 44 \\
-df<sub>week</sub> = 5 - 1 = 4 = df<sub>between</sub> \\
-df<sub>participants</sub> = 9 - 1 = 8 = df<sub>subjects</sub> \\
-df<sub>error</sub>= (n - 1)(k - 1) = 8 * 4 = 32 = 40 - 8 = 32 \\
-df<sub>within</sub> = 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 ======
-  * [[http://wwwstage.valpo.edu/other/dabook/ch12/c12-1.htm|Repeated measures one-way ANOVA]] by Akkelin
-    * {{:ezdata.sav|ezdata: SPSS Data file}}
-  * http://www.psych.utoronto.ca/courses/c1/chap14/chap14.html
-  * https://statistics.laerd.com/statistical-guides/repeated-measures-anova-statistical-guide.php