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劉從葦,國立中正大學政治學系助理教授
陳光輝,加州大學聖塔芭芭拉分校政治學系博士候選人
Is Weighting a Routine or Something that Needs to be Justified? (in English)(抽樣調查資料之加權:正當的處理方法或是一種迷思?) 文章下載
* 本篇電子檔下載次數:21
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Survey research as a method of collecting sample data is supposed to produce sample statistics which can estimate the corresponding population parameters if the sampling design is appropriate. However, for reasons such as unit non-response, survey data is usually weighted by the institutes that collect the data or by researchers who analyse the data in order to correct or diminish the discrepancies between sample and population. Sample statistics based on weighted data are more representative of the population parameters than unweighted data in terms of some demographic characteristics.Therefore, to some extent, it seems legitimate to weight data and this manipulation has become a routine when dealing with survey data.

It is true that to weight data could be helpful, but this manipulation needs justifications. This paper therefore tries to argue that to weight data is no panacea and should not be taken for granted when considering the examples in Taiwan’s Election and Democratization Studies (TEDS) surveys. The first section discusses why weighted data is not necessarily representative of the population. As the TEDS surveys show, the turnout, the vote shares of parties, and marital status become more deviant from the population parameters after weighting the data.

If the focus is the relationships between variables, the correlations may be changed by weighting the data in bivariate or multivariate analysis. However, it is not clear whether we manufacture relationships which do not exist or if weighting the data actually helps us approximate the relationships that already exist in the population. Besides, it should be noted that to weight data set as a whole only deals with the problem of unit non-response, but does not solve the problem of item non-response.

The third section discusses why most efforts should be devoted to examining and improving questionnaires, sampling designs, and interviewerm straining and supervision, instead of simply appealing to post-weighting. If everything necessary has been tried, weighting data may be the last resort to improve the estimates. But the justifications for the selection of auxiliary variables and the methods of calculating weight factors should be provided rather than doing it without any explicit considerations. It is also important to consider whether the consequence of weighting is positive or negative.

經由抽樣設計恰當的調查研究所收集到的樣本資料應該能夠準確估計母體參數。但是因為單位無反應的問題,執行調查的單位或分析資料的學者通常會以加權的方式來 減少樣本統計量與母體參數之間的差距。加權後的資料在人口學變項上比未加權資料較為接近母體參數,因此加權似乎是一個合理處理樣本資料的做法。

然而,即使加權是可行的解決方法,也絕非萬靈丹。在加權前也必需提出事後操弄資料的理由,而不是將加權視為理所當然。本文以台灣選舉與民主化調查為例,首 先說明加權後的資料不必然較接近母體參數的原因。投票率、各政黨得票率、與婚姻狀況在加權後反而和母體參數有較大的差距。

除了單一變數分析之外,當討論的主題是變數間的關係時,加權可能增加也可能減少相關性的強度。雖然加權似乎會影響相關性,但其影響究竟是更接近真實的關 係,抑或是扭曲真正的相關性則不得而知。此外,通常對整筆資料作加權只處理了單元無反應的問題,但仍然沒有解決多變量分析一定會遇到的項目無反應問題。

不論是單一變數分析或是多變量分析,在加權之前應該先嘗試其他增加樣本代表性與提高資料品質的方法。如果沒有先投入更多時間與心力在問卷設計、抽樣設計、 訪員訓練與監督上,加權只是低成本的取巧做法。最後,假使一定要加權,必須說明與討論為什麼要加權、以哪些變數加權、如何加權、以及加權所產生的影響,而 非不加思考地將加權當作例行公事。
黃紀,國立中正大學政治學系教授。
張佑宗,國立台灣大學政治學系助理教授。
樣本代表性檢定與最小差異加權:以2001年台灣選舉與民主化調查為例 文章下載
* 本篇電子檔下載次數:24
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樣本代表性檢定的目的,在發覺樣本是否被過度扭曲,而影響對母群特質的推估。大多數的民意調查計畫,包括電訪與面訪,如果發現樣本結構與母群不符,所採取的補救措施,不外乎「事後分層加權」或是「反覆多重加權」這兩種方式。然而,調查研究需要檢定的變數,通常超過一個以上,而「事後分層加權」所需之母群多變數聯合分佈值,往往為未知。因此,目前最常採用的是「反覆多重加權」的方式,但「反覆多重加權」實際執行時,最大的問題在於其檢定方式是透過卡方檢定,通常只要其檢定P值大於0.5,就認定樣本與母群一致,而未考慮一個最佳化的加權值。

本文旨在提出第三種事後加權的處理方式,也就是「最小差異加權」的方法,它能同時考慮數個變項,而找出最佳的加權值。我們以「2001年台灣選舉與民主化調查(TEDS 2001)資料為例,分別進行「反覆多重加權」與「最小差異加權」,並與2000年戶口普查之母群資料比較,發現就性別、年齡、教育與地理區堿四個變數的聯合分佈估計值,整體而言,最小差異加權的估計值,有將近七成比「反覆多重加權」的估計值更接近母群的聯合分佈值,應值得後續研究進一步探討。