Differences

This shows you the differences between two versions of the page.

--- factorial_anova [2023/05/01 01:26] – hkimscil
+++ factorial_anova [2024/09/24 08:33] (current) – [예 1] hkimscil
@@ Line 324: / Line 324: @@
     1      2         9
     1      2         8
-    1      2        12
+    1      2        10
     2      2        13
     2      2        15
@@ Line 337: / Line 337: @@
     2      3        10
     2      3        13
->
 > de$type <- factor(de$type, level=c(1,2), label=c("super", "best"))
 > de$w.temp <- factor(de$w.temp, level=c(1,2,3), label=c("cold", "warm", "hot"))
@@ Line 353: / Line 352: @@
 super   warm         9
 super   warm         8
-super   warm        12
+super   warm        10
   best   warm        13
   best   warm        15
@@ Line 366: / Line 365: @@
   best    hot        10
   best    hot        13
->
 > de.anova <- aov(cleanness ~ type * w.temp, data=de)
 > summary(de.anova)
             Df Sum Sq Mean Sq F value   Pr(>F)
-type         1  20.17   20.17   9.811  0.00576 **
+type         1     24   24.00   15.43 0.000986 ***
-w.temp       2 200.33  100.17  48.730 5.44e-08 ***
+w.temp       2    193   96.50   62.04 8.41e-09 ***
-type:w.temp  2  16.33    8.17   3.973  0.03722 *
+type:w.temp  2     21   10.50    6.75 0.006496 **
-Residuals   18  37.00    2.06
+Residuals   18     28    1.56
 ---
 Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+>
+> with(de, interaction.plot(x.factor=type,
++                           trace.factor=w.temp, response=cleanness,
++                           fun=mean, type="b", legend=T,
++                           ylab="cleanness", main="Interaction Plot (type by temp)",
++                           pch=c(1,19)))
+>
 >
 </code>
+{{:pasted:20240429-083635.png}}
-{{:pasted:20200529-165842.png}}
 만약에 손으로 계산했다면 R에서
 <code>
-pf(9.810810811, 1, 18, lower.tail=F)
+de <- read.csv("http://commres.net/wiki/_media/detergent.csv", sep = ",", header=T)
-pf(48.72972973, 2, 18, lower.tail=F)
+de
-pf(3.972972973, 2, 18, lower.tail=F)
+de$type <- factor(de$type, level=c(1,2), label=c("super", "best"))
+de$w.temp <- factor(de$w.temp, level=c(1,2,3), label=c("cold", "warm", "hot"))
+de
+de.typenova <- aov(cleanness ~ type * w.temp, data=de)
+summary(de.typenova)
+with(de, interaction.plot(x.factor=type,
+                          trace.factor=w.temp, response=cleanness,
+                          fun=mean, type="b", legend=T,
+                          ylab="cleanness", main="Interaction Plot (type by temp)",
+                          pch=c(1,19)))
+attach(de)
+table(type, w.temp)
+n.sub <- length(cleanness)
+n.type.group <- 2
+n.w.temp.group <- 3
+tapply(cleanness, list(type, w.temp), mean) # 각 셀에서의 평균
+df.within.each <- tapply(cleanness, list(type, w.temp), length) -1  # 각 셀에서의 샘플숫자
+n.within.each <- df.within.each + 1
+df.within <- sum(df.within.each) # df within
+var.within <- tapply(cleanness, list(type, w.temp), var) # var.within
+ss.within.each <- tapply(cleanness, list(type, w.temp), var) * df.within.each
+ss.within.each
+ss.within <- sum(ss.within.each) # ss.within
+ss.within
+interaction.plot(type, w.temp, cleanness)
+mean.type <- tapply(cleanness, list(type), mean)
+mean.w.temp <- tapply(cleanness, list(w.temp), mean)
+mean.type
+mean.w.temp
+var.type <- tapply(cleanness, list(type), var)
+var.w.temp <- tapply(cleanness, list(w.temp), var)
+mean.tot <- mean(cleanness)
+var.tot <- var(cleanness)
+n.sub <- length(cleanness)
+df.tot <- n.sub - 1
+ss.tot <- var.tot * df.tot
+## between
+mean.each <- tapply(cleanness, list(type, w.temp), mean)
+mean.each
+mean.tot <- mean(cleanness)
+mean.tot
+n.each <- tapply(cleanness, list(type, w.temp), length)
+n.each
+n.type.each <- tapply(cleanness, list(type), length)
+n.w.temp.each <- tapply(cleanness, list(w.temp), length)
+ss.w.bet <- sum(n.each*(mean.each-mean.tot)^2)
+ss.w.bet
+ss.tot
+ss.within
+ss.w.bet
+ss.w.bet + ss.within
+ss.type <- sum(n.type.each * ((mean.tot - mean.type)^2))
+ss.w.temp <- sum(n.w.temp.each * ((mean.tot - mean.w.temp)^2))
+ss.type
+ss.w.temp
+ss.type.w.temp <- ss.w.bet - (ss.type + ss.w.temp)
+ss.type.w.temp
+ss.tot
+ss.w.bet
+ss.within
+ss.type
+ss.w.temp
+ss.type.w.temp
+df.tot <- n.sub - 1
+df.w.bet <- (n.type.group * n.w.temp.group) - 1
+df.type <- n.type.group - 1
+df.w.temp <- n.w.temp.group - 1
+df.type.w.temp <- df.w.bet - (df.type + df.w.temp)
+df.within <- sum(df.within.each)
+df.tot
+df.w.bet
+df.type
+df.w.temp
+df.type.w.temp
+df.within
+ms.type <- ss.type / df.type
+ms.w.temp <- ss.w.temp / df.w.temp
+ms.type.w.temp <- ss.type.w.temp / df.type.w.temp
+ms.within <- ss.within / df.within
+ms.type
+ms.w.temp
+ms.type.w.temp
+ms.within
+f.type <- ms.type / ms.within
+f.w.temp <- ms.w.temp / ms.within
+f.type.w.temp <- ms.type.w.temp / ms.within
+alpha <- .05
+# confidence interval
+ci <- 1 - alpha
+f.type
+# 봐야할 F분포표에서의 F-value
+# qt 처럼 qf 사용
+# qf(alpha, df.w.between, df.within, lower.tail=F) 처럼 사용
+qf(ci, df.type, df.within)
+# 혹은
+# qf(alpha, df.type, df.within, lower.tail = F)
+# 도 마찬가지
+pf(f.type, df.type, df.within, lower.tail = F)
+f.w.temp
+qf(ci, df.w.temp, df.within)
+pf(f.w.temp, df.w.temp, df.within, lower.tail = F)
+f.type.w.temp
+qf(ci, df.type.w.temp, df.within)
+pf(f.type.w.temp, df.type.w.temp, df.within, lower.tail = F)
+# aov result
+summary(de.typenova)
 </code>
-<code>
-> pf(9.810810811, 1, 18, lower.tail=F)
-[1] 0.00575844
-> pf(48.72972973, 2, 18, lower.tail=F)
-[1] 5.439849e-08
-> pf(3.972972973, 2, 18, lower.tail=F)
-[1] 0.03722434
->
-> </code>
 ===== 예 2.  cookie experiment =====
@@ Line 483: / Line 610: @@
 | a R Squared = .102 (Adjusted R Squared = .066)  ||||||
+데이터 파일
-{{http://commres.net/wiki/_media/cookies.csv|cookies.csv}} 데이터파일 위치
 {{:r:cookies.csv}}
+손으로 계산하기
 {{:r:cookies.xlsx}}
@@ Line 755: / Line 882: @@
 ====== Materials and links ======
   * {{:AnovaData.sav}}
-  * http://www.uwsp.edu/psych/stat/13/anova-2w.htm
-  * http://faculty.vassar.edu/lowry/ch16pt1.html
-  * http://faculty.vassar.edu/lowry/ch16pt2.html
-  * http://faculty.vassar.edu/lowry/ch16pt3.html
-  * http://faculty.vassar.edu/lowry/ch16pt4.html
-  * http://faculty.vassar.edu/lowry/ch16pt5.html
-{{tag>factorial anova, statistics, Two-Factor Analysis of Variance, 팩토리얼 아노바, 상호작용효과, 주효과}}
+{{tag>factorial_anova statistics Two-Factor_Analysis_of_Variance, 팩토리얼 아노바, 상호작용효과, 주효과}}