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--- r:factorial_anova [2026/04/14 23:34] – hkimscil
+++ r:factorial_anova [2026/04/28 13:32] (current) – [output interpretation] hkimscil
@@ Line 1: / Line 1: @@
 ====== Two-way ANOVA ======
 Factorial ANOVA 라고도 부른다.
+<tabbox rs.two.way.anova>
 <code>
 rm(list=ls(all=TRUE))
@@ Line 201: / Line 202: @@
      las = 2 # rotate x-axis ticks
 )
+m.a <- tapply(y, a, mean)
+m.b <- tapply(y, b, mean)
+with(dat, interaction.plot(a,b,y))
+points(x=1, y=m.a[1], col='black', pch=19)
+points(x=2, y=m.a[2], col='blue', pch=19)
+points(x=3, y=m.a[3], col='red', pch=19)
+text(x=1, y=m.a[1], pos=3, col='black', label=round(m.a[1],3))
+text(x=2, y=m.a[2], pos=3, col='blue', label=round(m.a[2],3))
+text(x=3, y=m.a[3], pos=3, col='red', label=round(m.a[3],3))
+with(dat, interaction.plot(b,a,y))
+points(x=1, y=m.b[1], col='black', pch=19)
+points(x=2, y=m.b[2], col='blue', pch=19)
+text(x=1, y=m.b[1], pos=3, col='black', label=round(m.b[1],3))
+text(x=2, y=m.b[2], pos=3, col='blue', label=round(m.b[2],3))
@@ Line 209: / Line 226: @@
 #
 #
 </code>
-====== Output, two-way ANOVA ======
+<tabbox ro.two.way.anova>
 <code>
 > rm(list=ls(all=TRUE))
@@ Line 668: / Line 684: @@
 >
 >
 </code>
+</tabbox>
 ====== output interpretation ======
@@ Line 675: / Line 694: @@
 {{:c:ms:2025:pasted:20250421-084815.png}}
 {{:c:ms:2025:pasted:20250430-125904.png}}
-{{:c:ms:2025:pasted:20250430-124435.png}}
+{{.:pasted:20260428-131628.png}}
 상호작용효과 포함 해석
   * drug1의 효과에 운동의 역할은 아주 중요한 것으로 밝혀졌다.
@@ Line 688: / Line 706: @@
   * 운동이 병행된 drg1과 drg3의  효과에는 차이가 없었다.
   * drg2의 운동유무, 그리고 drg3의 운동을 하지않음과 통계학적으로 유의미한 차이가 있었다.
+{{.:pasted:20260428-131558.png}}
-{{:c:ms:2025:pasted:20250430-130525.png}}
+<code>
+> m.lm <- (lm(y~a*b, data = dat))
+> summary(m.lm)
+Call:
+lm(formula = y ~ a * b, data = dat)
+Residuals:
+    Min      1Q  Median      3Q     Max
+-1.9469 -0.4908 -0.1742  0.5814  2.0851
+Coefficients:
+             Estimate Std. Error t value Pr(>|t|)
+(Intercept)    9.6868     0.4546  21.309  < 2e-16 ***
+adrg2          0.8050     0.6429   1.252   0.2226
+adrg3          0.6943     0.6429   1.080   0.2909
+bexerc         3.3284     0.6429   5.177 2.65e-05 ***
+adrg2:bexerc  -4.4910     0.9092  -4.940 4.84e-05 ***
+adrg3:bexerc  -1.6826     0.9092  -1.851   0.0766 .
+---
+Signif. codes:
+‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 1.016 on 24 degrees of freedom
+Multiple R-squared:  0.6703,	Adjusted R-squared:  0.6016
+F-statistic: 9.758 on 5 and 24 DF,  p-value: 3.474e-05
+> anova(m.lm)
+Analysis of Variance Table
+Response: y
+          Df Sum Sq Mean Sq F value    Pr(>F)
+a          2 12.566  6.2832  6.0811 0.0073026 **
+b          1 12.107 12.1069 11.7176 0.0022274 **
+a:b        2 25.740 12.8699 12.4561 0.0001948 ***
+Residuals 24 24.797  1.0332
+---
+Signif. codes:
+‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+>
+> ss.tot <- sum(anova(m.lm)[2])
+> ss.a <- anova(m.lm)[[2]][1]
+> ss.b <- anova(m.lm)[[2]][2]
+> ss.ab <- anova(m.lm)[[2]][3]
+> ss.bet <- ss.a + ss.b + ss.ab
+> ss.bet
+[1] 50.41308
+> ss.tot
+[1] 75.21048
+> ss.bet / ss.tot
+[1] 0.6702933
+>
+</code>