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# 異常點 (Outlier / 偏離值 / 離群值 ) - PowerPoint PPT Presentation

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### 異常點(Outlier / 偏離值 / 離群值)

• 票價調整幅度的方程式

• 0.5  綜合消費物價指數變動 + 0.5 工資指數變動－0.5 生產力增幅

• 統計處早前公布的2008/12「運輸服務業」名義工資指數為145.1，而正確數字實為150.5。根據更正的數據，2008年第二季至第四季的工資指數變動應為 1.311%，而不是 4.852%。

• 修正前

• 0.5  (-0.817%) + 0.5  (-4.852%) – 0.3%  8 / 12 = -3.03%

• 修正後

• 0.5  (-0.817%) + 0.5  (-1.311%) – 0.3%  8 / 12 = -1.26%

• 減價！不減價！可加不可減！名譽掃地！匪夷所思！名存實亡！形同虛設！

• 平均值(mean)

• 工資指數變動

• 修正前：0.377

• 修正後：0.673

Boxplot

• Mean ± 3SD

• Mean = 0.377, SD = 1.95

• Mean + 3SD = 6.23, Mean  3SD =  5.48

• Mean(i)±3SD(i)

• Mean(12)=0.853, SD(12)=1.10

• Mean(12) + 3SD(12) =4.14, Mean(12)  3SD(12) =  2.44

• 中位數絕對離差 (Median absolute deviation)

• 不具代表性，刪除。

• 具代表性，保留。

• 穩健方法（robust method）

• 中位數 (Median)

• 去頭尾平均數(Trimmed mean)

• k = [na] is the smallest integer ≥ na

• 5% trimmed mean

• 12  5% = 0.6

• 1個最大，1個最小值去掉

• 溫塞平均數(Winsorized mean)

• 最小中位數平方(Least median of squares)

• 最小消去平方(Least trimmed squares)

Cook, R.D. and Weisberg, S. (1982). Residuals and Influence in Regression. Chapman and Hall.

Rousseeuw, P.J. and Leroy, A.M. (2003). Robust Regression and Outlier Detection. Wiley.