Differences

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--- anova [2020/05/20 15:13] – [Example] hkimscil
+++ anova [2020/05/20 15:51] – [Example 2] hkimscil
@@ Line 518: / Line 518: @@
 ====== Example ======
+가설. 단어맞히기 게임에서 첫글자를 힌트로 주거나, 마지막 글자를 힌트로 주거나, 힌트를 주지 않은 세 그룹 간에 틀린 단어의 숫자에 차이가 있을 것이다.
 |  |First Letter \\ Condition 1 \\ X<sub>1</sub>|Last Letter \\ Condition 2 \\ X<sub>2</sub>|No Letter \\ Condition 3 \\ X<sub>3</sub> |
 | | 15 | 21 | 28 |
@@ Line 536: / Line 538: @@
 | a = $\sum{(X_i)^2}$  | 3888  | 5868  | 7614  |
 | a-b = Var.within  | 648  | 108  | 324  | $f = $1080   |
 \begin{eqnarray*}
 a & = & \sum (X_i)^2 = 17370 \\
@@ Line 545: / Line 548: @@
 g & = & SS_{between} = e - f = 420
 \end{eqnarray*}
+| m.total = Mean.total  | $b = \; $ 23  |||
+| m.within = Mean.each.group  | 18  | 24  | 27  |
+| o = m.total - m.within  | 5   | -1  | -4  |
+| o%%^%%2  | 25  | 1  | 16  |
+| n  | 10  | 10  | 10  |
+| o%%^%%2 * n | 250  | 10  | 160  |
+| sum  | $g = \; $ 420  |||
 \begin{eqnarray*}
-k =  3 \\
+k & = & 3 \\
-n =  10 \\
+n & = & 10 \\
-N =  30 \\
+N & = & 30 \\
 \end{eqnarray*}
 \begin{eqnarray*}
-df_{between} =  \\
+e' & = & df_{between} =  \\
-df_{within} =  \\
+f' & = & df_{within} =   \\
-df_{total} =  \\
+g' & = & df_{total} =  \\
 \end{eqnarray*}
-<code>x1 <- c(15, 20, 14, 13, 18, 16, 13, 12, 18, 41)
+|          | SS   | df    | MS  | F   |
+| between  | $e = \;$ 420   | $e' = \;$ 2 | 210  |  210/40 = 5.25  |
+| within   | $f = \;$ 1080  | $f' = \;$ 27 | 40  |   |
+| total    | $g = \;$ 1500  | $g' = \;$ 29 |   |   |
+F<sub>crit</sub>(2, 27) =  3.35
+F<sub>cal</sub> = 5.25
+F<sub>cal</sub> > F<sub>crit</sub> 이므로 3집단 간의 평균은 통계학적으로 의미가 있는 차이를 가지고 있다.
+====== Example 2 ======
+<code>
+x1 <- c(15, 20, 14, 13, 18, 16, 13, 12, 18, 41)
 x2 <- c(21, 25, 29, 18, 26, 22, 26, 24, 28, 21)
 x3 <- c(28, 30, 32, 28, 26, 30, 25, 36, 20, 15)
 </code>
-<code>> data.frame(x1,x2,x3)
+<code>> xc <- data.frame(x1,x2,x3)
    x1 x2 x3
   15 21 28
@@ Line 612: / Line 635: @@
 <code>
-> colnames(xs[1]) <- "wrong"
+> colnames(xs)  <- c("wrong", "condition")
-> colnames(xs[2]) <- "cond"
 </code>
-<code># cf
+<code>
+# cf
 # lengthofelements <- length(x1)
 # varofvariable <- var(x1)</code>
 <code>
-df_x1
+df.total <- length(xs$wrong) - 1
-df_x2
+ss.total <- var(xs$wrong)*df_tot
-df_x3
+var.total <- ss.total/df.total
+var.total.r <- var(xs$wrong)
-ss_x1
+df.x1 <- length(x1)-1
-ss_x2
+df.x2 <- length(x2)-1
-ss_x3
+df.x3 <- length(x3)-1
+ss.x1 <- var(x1)*df.x1
+ss.x2 <- var(x2)*df.x2
+ss.x3 <- var(x3)*df.x3
-df_bet
+ss.within <- ss.x1 + ss.x2 + ss.x3
-ss_bet
+df.within <- df.x1 + df.x2 + df.x3
+ss.between <- ss.total - ss.within
+df.between <- df.total - df.within
-df_tot
+ms.between <- ss.between/df.between
-ss_tot
+ms.within <- ss.within/df.within
+f.value <- ms.between/ms.within
-df_with
+ss.between
-ss_with
+df.between
-df_bet
+ss.within
-ss_bet
+df.within
-</code>
+ms.between
+ms.within
+f.value
-<code>
-df_tot <- length(xs$ind) - 1
-ss_tot <- var(xs$values)*df_tot
-var_tot <- var(xs$values)
-df_x1 <- length(x1)-1
-df_x2 <- length(x2)-1
-df_x3 <- length(x3)-1
-ss_x1 <- var(x1)*df_x1
-ss_x2 <- var(x2)*df_x2
-ss_x3 <- var(x3)*df_x3
 </code>
 ====== E.G. 1 (R) ======