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--- absolute_value_of_deviation_score [2016/06/23 06:34] – created hkimscil
+++ absolute_value_of_deviation_score [2020/11/05 08:54] (current) – hkimscil
@@ Line 1: / Line 1: @@
 ====== Using absolute value of deviation score as an alternative of standard deviation ======
+<WRAP box 450px><fs xx-large><fc #ff0000>**Q:**</fc></fs> 왜 차이값을 (deviation score) 제곱하여 더한 값의 평균 (즉, [[:Variance|분산 Variance]]) 을 사용하나요? 차이값의 절대값을 더한 값의 평균을 사용하는 것이 더 직관적이지 않나요? </WRAP>
+ $ \text{absolute value of deviation score} = \displaystyle \frac {\sum |(X_i-\mu)| }{N} $
+  - 우선, raw data에서 분산값을 계산하기가 쉽다. (See http://wiki.commres.org/ANOVA#s-2.2) $$
+\begin{eqnarray*}
+\text{SS} & = & \small{\sum} (X_i-\overline{X})^2  \\
+  & = & \text{. . . .}  \\
+  & = & {\sum} X_i^2 - \frac{({\sum} {X_i)^2}}{n}
+\end{eqnarray*}
+  - 실제로 Mean absolute deviation (MAD) 으로 사용되고 있기도 하다. see [[wp>Average_absolute_deviation|Average Absolute Deviation]]
+  - See [[http://stats.stackexchange.com/questions/118/why-square-the-difference-instead-of-taking-the-absolute-value-in-standard-devia|Cross Validated에서 나온 질문과 답]]