Q-Eng

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　代表頁に戻る

平均値の罠 「シンプソンのパラドックス」 に注意。 　統計をうのみにしてはいけない。
Simpson's paradox： 英国の統計学者.E. H. シンプソンが1951年に提示。
　　　　　　　　　　　　　 「全体で見たときの相関」 と 「分割して見たときの相関」 が逆に
　　　　　　　　　　　　　 なることがある。　（背景や条件 ← 「潜伏変数」 に注意が要る）

易　04分・・150wpm　 　2016/3/12 新出

字幕：上の動画は開始後 で字幕On/Off､ で言語選択。文字ｻｲｽﾞはｵﾌﾟｼｮﾝから｡
　　　　動画を見るとき、パソコンで画面全体を拡大するときれい。

★下記英文は ブラウザ クロムのマウスオーバー辞書が使えます｡

Statistics are persuasive（説得のある）. So much so that people, organizations, and whole countries base some of their most important decisions on organized data. But there's a problem with that. Any set of statistics might have something lurking inside it, something that can turn the results completely upside down.
　　注意：statistics　「統計学」は単数扱い、 「統計データ」は複数扱い。

For example, imagine you need to choose between two hospitals for an elderly relative's surgery. Out of each hospital's last 1000 patient's, 900 survived at Hospital A, while only 800 survived at Hospital B. So it looks like Hospital A is the better choice. But before you make your decision, remember that not all patients arrive at the hospital with the same level of health. And if we divide each hospital's last 1000 patients into those who arrived in good health and those who arrived in poor health, the picture starts to look very different.

Hospital A had only 100 patients who arrived in poor health, of which 30 survived. But Hospital B had 400, and they were able to save 210. So Hospital B is the better choice for patients who arrive at hospital in poor health, with a survival rate of 52.5%. And what if your relative's health is good when she arrives at the hospital? Strangely enough, Hospital B is still the better choice, with a survival rate of over 98%. So how can Hospital A have a better overall survival rate if Hospital B has better survival rates for patients in each of the two groups?

What we've stumbled（つまずく） upon is a case of Simpson's paradox, where the same set of data can appear to show opposite trends depending on how it's grouped. This often occurs when aggregated data hides a conditional variable, sometimes known as a lurking variable（潜伏変数）, which is a hidden additional factor that significantly influences results.

Here, the hidden factor is the relative proportion of patients who arrive in good or poor health. Simpson's paradox isn't just a hypothetical scenario. It pops up from time to time in the real world, sometimes in important contexts. One study in the UK appeared to show that smokers had a higher survival rate than nonsmokers over a twenty-year time period. That is, until dividing the participants by age group showed that the nonsmokers were significantly older on average, and thus, more likely to die during the trial period, precisely because they were living longer in general. Here, the age groups are the lurking variable, and are vital to correctly interpret the data.

In another example, an analysis of Florida's death penalty cases seemed to reveal no racial disparity（不均衡） in sentencing between black and white defendants convicted of murder. But dividing the cases by the race of the victim told a different story. In either situation, black defendants were more likely to be sentenced to death. The slightly higher overall sentencing rate for white defendants was due to the fact that cases with white victims were more likely to elicit（引き出す） a death sentence than cases where the victim was black, and most murders occurred between people of the same race.

So how do we avoid falling for the paradox? Unfortunately, there's no one-size-fits-all answer. Data can be grouped and divided in any number of ways, and overall numbers may sometimes give a more accurate picture than data divided into misleading or arbitrary categories. All we can do is carefully study the actual situations the statistics describe and consider whether lurking variables may be present. Otherwise, we leave ourselves vulnerable to those who would use data to manipulate others and promote their own agendas.
　one-size-fits-all ： フリーサイズの、万能の、汎用の、画一的な
-