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 repeated_measure_anova [2017/06/02 06:54]hkimscil removed repeated_measure_anova [2017/06/02 06:56] (current)hkimscil created Both sides previous revision Previous revision 2017/06/02 06:56 hkimscil created2017/06/02 06:54 hkimscil removed2017/05/10 09:12 hkimscil 2017/05/10 09:08 hkimscil 2016/06/23 19:05 hkimscil 2016/06/23 19:04 hkimscil 2015/10/13 11:46 hkimscil 2015/10/13 10:03 hkimscil 2015/10/13 09:21 hkimscil 2015/10/13 08:57 hkimscil 2015/10/13 08:55 hkimscil 2015/10/13 08:43 hkimscil created 2017/06/02 06:56 hkimscil created2017/06/02 06:54 hkimscil removed2017/05/10 09:12 hkimscil 2017/05/10 09:08 hkimscil 2016/06/23 19:05 hkimscil 2016/06/23 19:04 hkimscil 2015/10/13 11:46 hkimscil 2015/10/13 10:03 hkimscil 2015/10/13 09:21 hkimscil 2015/10/13 08:57 hkimscil 2015/10/13 08:55 hkimscil 2015/10/13 08:43 hkimscil created Line 1: Line 1: - 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 SSwithin​ + - * and solely use the latter as SS<​sub>​error​ + - * 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​ will be **__smaller__** + - * But, with this SS<​sub>​error,​ 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​ = $\Sigma{(X-\overline{X})^2}$ = 3489.2 \\ + - SS<​sub>​participants​ = $w\Sigma{(\overline{X}_{participants}-\overline{X})}$ = 833.6 \\ + - SS<​sub>​weeks​ = $n\Sigma{(\overline{X}_{week} - \overline{X})}$ = 1934.5 \\ + - SS<​sub>​residual ​ \\ + - = SS<​sub>​error​ \\ + - = SS<​sub>​total​ - SS<​sub>​participants​ - SS<​sub>​weeks ​ \\ + - = 721.1 \\ + - \\ + - df<​sub>​total​ = N - 1 = 45 - 1 = 44 \\ + - df<​sub>​week​ = 5 - 1 = 4 = df<​sub>​between​ \\ + - df<​sub>​participants​ = 9 - 1 = 8 = df<​sub>​subjects​ \\ + - df<​sub>​error​= (n - 1)(k - 1) = 8 * 4 = 32 = 40 - 8 = 32 \\ + - df<​sub>​within​ = 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 + 