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--- r:repeated_measure_anova [2025/05/12 08:23] – [E.g. 2] hkimscil
+++ r:repeated_measure_anova [2025/05/12 08:25] (current) – [E.g.2 by hand] hkimscil
@@ Line 298: / Line 298: @@
 +              + Error(reviewer),
 +              data = movrev)
+> m2.aov <- aov(score ~ movie
++               + Error(reviewer/movie),
++               data = movrev)
+>
 > #view model summary
 > summary(m.aov)
@@ Line 310: / Line 314: @@
 Residuals  8  142.7   17.83
 ---
-Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Signif. codes:
+‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+> summary(m2.aov)
+Error: reviewer
+          Df Sum Sq Mean Sq F value Pr(>F)
+Residuals  4  173.7   43.43
+Error: reviewer:movie
+          Df Sum Sq Mean Sq F value  Pr(>F)
+movie      2  363.3  181.67   10.19 0.00632 **
+Residuals  8  142.7   17.83
+---
+Signif. codes:
+‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
 >
 > # pairwise.t.test(movrev$score, movrev$movie, paired = T, p.adjust.method = "bonf")
 > attach(movrev)
-The following objects are masked from movrev (pos = 5):
+The following objects are masked from movrev (pos = 12):
+    movie, reviewer, score
+The following objects are masked from movrev (pos = 14):
     movie, reviewer, score
@@ Line 329: / Line 351: @@
 P value adjustment method: bonferroni
+> detach(movrev)
 > # or
 > with(movrev,
@@ Line 344: / Line 367: @@
 P value adjustment method: bonferroni
+>
+>
+</code>
+====== E.g.2 by hand ======
+<code>
+####
+# by hand
+####
+movrev
+tapply(movrev$score, list(reviewer, movie), mean) # 각 셀의 평균값
+m.tot <- mean(movrev$score)
+m.by.movie <- tapply(movrev$score, list(movie), mean)
+m.by.er <- tapply(movrev$score, list(reviewer), mean)
+ss.bet <- sum(5*(m.tot-m.by.movie)^2)
+df.bet <- 3-1 # 영화 가짓수 - 1
+ms.bet <- ss.bet / df.bet
+var.by.movie <- tapply(movrev$score, list(movie), var)
+ss.with <- sum(var.by.movie*4)
+df.with <- 4 + 4 + 4
+ms.with <- ss.with / df.with
+ms.bet
+ms.with
+ss.sub <- sum(3 * (m.tot-m.by.er)^2) # 3 treatments (movies)
+df.sub <- 5 - 1 # 5 persons - 1
+ms.sub <- ss.sub/df.sub
+ms.sub
+ss.res <- ss.with - ss.sub
+ss.res
+df.res <- 4 * 2 # (N-1)*(k-1)
+ms.res <- ss.res/df.res
+ms.res
+f.cal <- ms.bet/ms.res
+f.cal
+pf(f.cal, 2, 8, lower.tail = F)
+ss.bet
+ss.with
+ss.sub
+ss.res
+df.bet
+df.with
+df.sub
+df.res
+ms.bet
+ms.with
+ms.sub
+ms.res
+# check
+ss.with == ss.sub + ss.res
+df.with == df.sub + df.res
+summary(m.aov)
+#
+# no embedded
+# understand the meaning of embedded
+m0.aov <- aov(score ~ movie, data = movrev)
+summary(m0.aov)
+summary(m.aov)
+</code>
+<code>
+> ####
+> # by hand
+> ####
+> movrev
+   reviewer movie score
+         1     1    88
+         1     2    84
+         1     3    92
+         2     1    76
+         2     2    78
+         2     3    90
+         3     1    78
+         3     2    94
+         3     3    95
+        4     1    80
+        4     2    83
+        4     3    88
+        5     1    82
+        5     2    90
+        5     3    99
+> tapply(movrev$score, list(reviewer, movie), mean) # 각 셀의 평균값
+  2  3
+88 84 92
+76 78 90
+78 94 95
+80 83 88
+82 90 99
+> m.tot <- mean(movrev$score)
+>
+>
+> m.by.movie <- tapply(movrev$score, list(movie), mean)
+> m.by.er <- tapply(movrev$score, list(reviewer), mean)
+>
+> ss.bet <- sum(5*(m.tot-m.by.movie)^2)
+> df.bet <- 3-1 # 영화 가짓수 - 1
+> ms.bet <- ss.bet / df.bet
+>
+> var.by.movie <- tapply(movrev$score, list(movie), var)
+> ss.with <- sum(var.by.movie*4)
+> df.with <- 4 + 4 + 4
+> ms.with <- ss.with / df.with
+> ms.bet
+[1] 181.6667
+> ms.with
+[1] 26.36667
+>
+> ss.sub <- sum(3 * (m.tot-m.by.er)^2) # 3 treatments (movies)
+> df.sub <- 5 - 1 # 5 persons - 1
+> ms.sub <- ss.sub/df.sub
+> ms.sub
+[1] 43.43333
+>
+> ss.res <- ss.with - ss.sub
+> ss.res
+[1] 142.6667
+> df.res <- 4 * 2 # (N-1)*(k-1)
+> ms.res <- ss.res/df.res
+> ms.res
+[1] 17.83333
+>
+> f.cal <- ms.bet/ms.res
+> f.cal
+[1] 10.18692
+> pf(f.cal, 2, 8, lower.tail = F)
+[1] 0.006319577
+>
+> ss.bet
+[1] 363.3333
+> ss.with
+[1] 316.4
+> ss.sub
+[1] 173.7333
+> ss.res
+[1] 142.6667
+> df.bet
+[1] 2
+> df.with
+[1] 12
+> df.sub
+[1] 4
+> df.res
+[1] 8
+> ms.bet
+[1] 181.6667
+> ms.with
+[1] 26.36667
+> ms.sub
+[1] 43.43333
+> ms.res
+[1] 17.83333
+>
+> # check
+> ss.with == ss.sub + ss.res
+[1] TRUE
+> df.with == df.sub + df.res
+[1] TRUE
+> summary(m.aov)
+Error: reviewer
+          Df Sum Sq Mean Sq F value Pr(>F)
+Residuals  4  173.7   43.43
+Error: Within
+          Df Sum Sq Mean Sq F value  Pr(>F)
+movie      2  363.3  181.67   10.19 0.00632 **
+Residuals  8  142.7   17.83
+---
+Signif. codes:
+‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+> #
+> # no embedded
+> # understand the meaning of embedded
+> m0.aov <- aov(score ~ movie, data = movrev)
+> summary(m0.aov)
+            Df Sum Sq Mean Sq F value Pr(>F)
+movie        2  363.3  181.67    6.89 0.0102 *
+Residuals   12  316.4   26.37
+---
+Signif. codes:
+‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+> summary(m.aov)
+Error: reviewer
+          Df Sum Sq Mean Sq F value Pr(>F)
+Residuals  4  173.7   43.43
+Error: Within
+          Df Sum Sq Mean Sq F value  Pr(>F)
+movie      2  363.3  181.67   10.19 0.00632 **
+Residuals  8  142.7   17.83
+---
+Signif. codes:
+‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+>
+>
 >
 </code>