異常值

異常值（英文：outlier），中文又叫離群值，係統計學上嘅概念，指某個數據點同第啲數據比起嚟「唔尋常」，通常係講緊佢嘅數值距離平均水平或者常見分佈好遠。異常值出現嘅成因有好多，可能源自量度錯誤、入數據嗰陣入錯、樣本特性，亦有可能代表真實但稀有嘅現象^[1]^[2]。

基本概論

異常值嘅幾個例子：

想像而家測量成年人身高，大部分數據集中喺 160 至 190 厘米之間，但搵到有個數值係 250 厘米。
某城市嘅氣溫通常介乎喺攝氏 10 至 35 度之間，但某日紀錄到攝氏零下 15 度嘅氣溫。
某次考試，啲學生嘅成績分佈大多喺 50 - 70 分之間，但有個學生考到 100 分。

喺統計工作上，某啲情況下可能需要對異常值做特別處理。

應對方法

統計學中有幾種方法嚟識別異常值。統計師齋靠留意敘述統計指標，已經可以留意到異常值嘅存在。最簡單嘅可以係留意吓數據數值嘅全距同埋四分位距，睇吓呢啲值會唔會離咗群。而且離群值亦往往會令到標準差數值異常咁大^[3]；離群值仲會令到平均值扭曲，假如研究者憑經驗知道該變數嘅平均值合理水平喺邊，亦有可能透過平均值嚟判斷係咪有離群值。

喺實際應用上，研究者好多時都想排除異常值先至做分析。噉係因為諸如結構方程模型同聚類分析等嘅統計分析方法，都容易受到異常值影響而結果出現扭曲。假如研究緊嗰個變數呈常態分佈，研究者可以用所謂嘅三 σ 法則^{[註 1]}，意思即係話數值同平均值相差超過三個標準差嘅^[4]，就一律當係異常值，研究者會將佢哋排除，或者做數值轉換將佢哋變做等同離平均三個標準差咁遠嘅值，排除或轉換過後先郁手做分析^[5]。

不過，排除異常值嘅做法都有一定爭議性，例如喺某啲情況下異常值可能反映緊真實但少有嘅現象，攞走呢啲數值會對分析結果嘅有效度造成負面影響。因此，假若某個數值唔係明顯填錯或者入錯數，研究者都有誘因 kip1 住。明顯填錯嘅例子：問卷調查問受訪者嘅年齡，大部份答 20 至 70 歲之間，但有一份紀錄係 250 歲，呢個好大機會係入錯或填錯。可能係極端但真實嘅例子：假想長跑比賽嘅完賽時間，大部分參加者用咗 3 至 6 個鐘跑完，但有某位運動員只需要 2 小時 10 分，呢個數值係極端，但有可能係真實值，未必可以隨便刪除^[6]。

參見

引咗

↑ Grubbs, F. E. (February 1969). "Procedures for detecting outlying observations in samples". Technometrics. 11 (1): 1–21. doi:10.1080/00401706.1969.10490657. An outlying observation, or "outlier," is one that appears to deviate markedly from other members of the sample in which it occurs.
↑ Maddala, G. S. (1992). "Outliers". Introduction to Econometrics (第2版). New York: MacMillan. pp. 89. ISBN 978-0-02-374545-4. An outlier is an observation that is far removed from the rest of the observations.
↑ Tukey, John W (1977). Exploratory Data Analysis. Addison-Wesley. ISBN 978-0-201-07616-5. OCLC 3058187.
↑ Brydges, C.R., Ozolnieks, K.L. and Roberts, G., 2017. Working memory–not processing speed–mediates fluid intelligence deficits associated with attention deficit/hyperactivity disorder symptoms. Journal of neuropsychology, 11(3), pp.362-377，佢哋 p. 367 嗰度有講："Specifically, a test score was considered a univariate outlier if it was >3 SDs from the between-subjects variable mean, and was replaced with a value that was 3 SDs from the mean."
↑ Removing Outliers. Understanding How and What behind the Magic. Medium.
↑ Outliers: To Drop or Not to Drop

註釋

↑ 當中 σ 讀音近似粵拼：sik1 maa4，係標準差嘅數學符號。

外拎

[1] Grubbs, F. E. (February 1969). "Procedures for detecting outlying observations in samples". Technometrics. 11 (1): 1–21. doi:10.1080/00401706.1969.10490657. An outlying observation, or "outlier," is one that appears to deviate markedly from other members of the sample in which it occurs.

[2] Maddala, G. S. (1992). "Outliers". Introduction to Econometrics (第2版). New York: MacMillan. pp. 89. ISBN 978-0-02-374545-4. An outlier is an observation that is far removed from the rest of the observations.

[3] Tukey, John W (1977). Exploratory Data Analysis. Addison-Wesley. ISBN 978-0-201-07616-5. OCLC 3058187.

[5] Brydges, C.R., Ozolnieks, K.L. and Roberts, G., 2017. Working memory–not processing speed–mediates fluid intelligence deficits associated with attention deficit/hyperactivity disorder symptoms. Journal of neuropsychology, 11(3), pp.362-377，佢哋 p. 367 嗰度有講："Specifically, a test score was considered a univariate outlier if it was >3 SDs from the between-subjects variable mean, and was replaced with a value that was 3 SDs from the mean."

[6] Removing Outliers. Understanding How and What behind the Magic. Medium.

[7] Outliers: To Drop or Not to Drop

[4] 當中 σ 讀音近似粵拼：sik1 maa4，係標準差嘅數學符號。

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