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repeated_measure_anova [2017/06/02 06:54]
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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 +
repeated_measure_anova.txt · Last modified: 2017/06/02 06:56 by hkimscil