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--- r:oneway_anova [2020/10/12 15:53] – hkimscil
+++ r:oneway_anova [2020/10/12 16:36] – hkimscil
@@ Line 1: / Line 1: @@
 ====== Oneway ANOVA ======
+===== data =====
 | (온도조건)x1  | 50.5  | 52.1  | 51.9  | 52.4  | 50.6  | 51.4  | 51.2  | 52.2  | 51.5  | 50.8  |
 | (온도조건)x2  | 47.5  | 47.7  | 46.6  | 47.1  | 47.2  | 47.8  | 45.2  | 47.4  | 45.0  | 47.9  |
@@ Line 160: / Line 161: @@
   46.2   hi
 </code>
+===== ANOVA by hand =====
 <code>
 mean.by.group.xs <- tapply(xs$score, xs$temp, mean)
@@ Line 178: / Line 179: @@
 > n.by.group.xs <- tapply(xs$score, xs$temp, length)
 > df.by.group.xs <- n.xs-1
+> ss.within <- sum(var.by.group.xs * df.by.group.xs)
 >
 > mean.by.group.xs
@@ Line 194: / Line 196: @@
 </code>
+<code>
+mean.xs <- mean(xs$score)
+n.total <- length(xs$score)
+df.total <- n.total-1
+n.group.xs <- 3
+df.between <- n.group.xs -1
+df.within <- sum(df.by.group.xs)
+n.total
+df.total
+df.between
+df.within
+ss.total <- var(xs$score) * (length(xs$score)-1)
+ss.total <- var(xs$score) * df.total
+ss.between <- sum(n.by.group.xs * (mean.by.group.xs - mean.xs)^2)
+ss.within <- sum(var.by.group.xs * df.by.group.xs)
+ss.total
+ss.between
+ss.within
+ss.total
+ss.between + ss.within
+ms.between <- ss.between/df.between
+ms.within <- ss.within/df.within
+ms.total <- ss.total/df.total
+ms.total
+ms.between
+ms.within
+f.calculated <- ms.between/ms.within
+f.calculated
+var(xs$score)
+</code>
+<code>
+> mean.xs <- mean(xs$score)
+> n.total <- length(xs$score)
+> df.total <- n.total-1
+> n.group.xs <- 3
+> df.between <- n.group.xs -1
+> df.within <- sum(df.by.group.xs)
+> n.total
+[1] 30
+> df.total
+[1] 29
+> df.between
+[1] 2
+> df.within
+[1] 27
+>
+> ss.total <- var(xs$score) * (length(xs$score)-1)
+> ss.total <- var(xs$score) * df.total
+> ss.between <- sum(n.by.group.xs * (mean.by.group.xs - mean.xs)^2)
+> ss.within <- sum(var.by.group.xs * df.by.group.xs)
+> ss.total
+[1] 175.695
+> ss.between
+[1] 156.302
+> ss.within
+[1] 19.393
+> ss.total
+[1] 175.695
+> ss.between + ss.within
+[1] 175.695
+>
+> ms.between <- ss.between/df.between
+> ms.within <- ss.within/df.within
+> ms.total <- ss.total/df.total
+>
+> ms.total
+[1] 6.058448
+> ms.between
+[1] 78.151
+> ms.within
+[1] 0.7182593
+>
+> f.calculated <- ms.between/ms.within
+> f.calculated
+[1] 108.8061
+> var(xs$score)
+[1] 6.058448
+>
+</code>
+===== ANOVA function (aov) =====
+<code>
+x.mod <- aov(score~temp, data=xs)
+x.mod
+summary(x.mod)
+TukeyHSD(x.mod)
+</code>
 <code>
-> x.mod <- aov(values~ind,data=xs)
+> x.mod <- aov(score~temp, data=xs)
 > x.mod
 Call:
-   aov(formula = values ~ ind, data = xs)
+   aov(formula = score ~ temp, data = xs)
 Terms:
-                    ind Residuals
+                   temp Residuals
 Sum of Squares  156.302    19.393
 Deg. of Freedom       2        27
@@ Line 210: / Line 305: @@
 > summary(x.mod)
             Df Sum Sq Mean Sq F value  Pr(>F)
-ind          2 156.30   78.15   108.8 1.2e-13 ***
+temp         2 156.30   78.15   108.8 1.2e-13 ***
 Residuals   27  19.39    0.72
 ---
@@ Line 220: / Line 315: @@
 % family-wise confidence level
-Fit: aov(formula = values ~ ind, data = xs)
+Fit: aov(formula = score ~ temp, data = xs)
-$ind
+$temp
-       diff       lwr        upr     p adj
+         diff       lwr        upr     p adj
-x2-x1 -4.52 -5.459735 -3.5802652 0.0000000
+mid-low -4.52 -5.459735 -3.5802652 0.0000000
-x3-x1 -5.11 -6.049735 -4.1702652 0.0000000
+hi-low  -5.11 -6.049735 -4.1702652 0.0000000
-x3-x2 -0.59 -1.529735  0.3497348 0.2813795
+hi-mid  -0.59 -1.529735  0.3497348 0.2813795
-</code>
-<code>> tapply(xs$values, xs$ind, mean)
-   x1    x2    x3
-.46 46.94 46.35 </code>
-SS<sub>between</sub>
-<code>> meanxs <- mean(xs$values)
-> mx1 <- mean(x1)
-> mx2 <- mean(x2)
-> mx3 <- mean(x3)
-> x2ss <- 10*((meanxs - mx2)^2)
-> x3ss <- 10*((meanxs - mx3)^2)
-> x1ss <- 10*((meanxs - mx1)^2)
-> xss <- x1ss+x2ss+x3ss
-> xss
-[1] 156.302
-</code>
+> </code>
 ====== E.g. 1 ======