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January 16
2017 年 1 月 16 日

誤用統計

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這是個講究數據的時代。可惜誤用統計數字,以訛傳訛的情景,舉目皆是,以下就舉幾個隨手撿拾的例子。

誤用統計 一
根據網絡流傳的說法,印度人罹患癡呆症的比例,比許多國家的人民低。由於印度人嗜吃含有薑黃素的咖哩,而據說薑黃素的功效可以預防、治療阿茲海默症,方便抑制 β 類澱粉蛋白的聚合顆粒沉積在腦神經的間隙,從而避免傳導訊息的能力受阻,所以就有人斷定,多吃咖哩可以避免老年癡呆症的發生。

認知障礙癡呆症狀與年齡(老化)息息相關,印度人壽命較短(平均約68歲),並不容易達到通稱的老年,當然就少有老年癡呆症的患者。除非經過嚴謹的分析,「多吃咖哩可以避免患老年癡呆症」的說法站不住腳。

誤用統計 二
香港男女的平均壽命之長在世界上排第一。長壽的原因,眾說紛紜,有說港式飲食清淡、蒸魚特佳、煲湯養生,有說香港醫療制度完備,有說港人國際化先進、西化教育早,也有說香港吸菸率低、交通便利、風水寶地,...;以上說法也許都有道理,但是這些優點只能說對生活品質的提昇有幫助,卻未必是長壽的根本原因。

嚴格講,香港人有優良的基因,但是此說從來沒有人提起過。回顧百年以來,香港的居民絕大部分都是大陸移民,移民成功者或用「財」打通關節,或靠「才」經過歷練選拔入港,大部分則憑藉著堅毅不撓克服千山萬水的阻絕而成功抵港,甚至還有經過嚴格挑選來港當警察、守衛的。雖然香港人口密度高、壓力大、核放射性強,這些成功移民香港的外人,都不是泛泛之輩,今天香港人的家庭背景並非常態分佈,乃是個經過大環境篩選、優勝劣敗的特別例子;他們身體好,智力也好,他們的後代命長、IQ 高,並不偶然!

誤用統計 三
40年前在美國讀書,老美非常驚訝於港、台留學生成績特優,就以為華人都是智慧出眾的天才;近幾年,統計結果顯示了印度裔的美國人是美國收入最高的族裔,所以有印度人富甲天下的說法;...。以上這些現象都是基於取自偏差的(biased)樣本,讀書、移民美國工作的不是常態的華人、印度人、...,他們成就突出,不足為奇!當然更不可一概而論,誤以為華人、印度人、... 全都出類拔萃。

誤用統計 四
最近新聞報告台灣警察人員酒後駕駛的比例在各行業中最高,因此有人主張對知法犯法的警察加倍處罰。

表面上,如此看法似乎頗有道理。但是仔細了解數據背景的前因後果之後,卻又發現並非如此。酒後駕駛的警察人員,被抓到後要向上報告,而其他類別的人酒後駕駛則未必須要報告,蘋果跟橘子擺放在同一個籃子裏分析,這哪是哪啊?通用的比較方法沒有意義。

結論
若無經過分析了解數字背後所代表的意義,而僅僅靠著表面文章,容易做出誤導的結論,而這些錯誤的結論,簡直濫竽充數、所在多有。

 


Misuse of statistics

Although we live in an era that emphasises data, the misuse of statistics is rampant, which can lead to the communication of erroneous messages. Here are some random examples.

Case one
There is a widely circulated online assertion that Indians have a lower rate of dementia than people from many other countries because curry contains curcumin. The theory is that curcumin decreases the accumulation of beta-amyloid plaque between nerve cells (neurons) in the brain, thus preventing the blocking of cell-to-cell signalling and reducing memory loss. This process can help to prevent and treat Alzheimer's disease (AD), the theory claims. However, the cognitive deficit in dementia is actually closely linked to age (or ageing). Indians have a comparatively short life expectancy (an average of 68 years compared to 84 years in Hong Kong). Thus, it is not surprising that there are fewer cases of dementia in India. Unless confirmed otherwise by more stringent research on the subject, the assertion that eating more curry helps prevent AD doesn't necessarily hold water.

Case two
People in Hong Kong, both men and women, have the longest average life expectancy in the world. But there is no consensus on the reasons for this. Some think it is because the Hong Kong diet is light and healthy. Hong Kong people tend to eat steamed fish, for example, which is healthier than fried fish. Others attribute it to Hong Kong's sound medical system and the habit of brewing herbal soups. Still others claim it is due to advanced internationalisation, the introduction of a Western education system, decreasing smoking rates, convenient transportation, or even feng shui. There may be some value to some or all of these claims in terms of quality of life and longevity, but they can hardly be considered as the fundamental reasons for the longevity of Hong Kong people.

In fact, the reason is more likely that Hong Kong people have superb genes for longevity, but somehow this is never mentioned. Looking back, we find that the majority of Hong Kong residents were originally immigrants who came from mainland China within the last hundred years. Successful immigrants either "bought" or "fought" their way in through talent and determination. Some had to overcome a multitude of difficulties, climbing mountains and swimming long distances to get to Hong Kong. Others managed to work their way into the Hong Kong police force or security guard field after passing scrupulous screening tests. These successful immigrants were not everyday people – they are perfect examples of "survival of the fittest". Therefore, it is not entirely coincidental that the survivors were healthier and more intelligent than average, and that their descendants have a longer life expectancy and higher IQ.

Case three
When I first went to study in the US, Americans were amazed at the intelligence, and grades, of Chinese students. Similarly, we read statistics demonstrating how Indian Americans, or Indo-Americans, are among the highest-paid Americans and therefore among the richest people in the world. But these phenomena are the result of comparisons based on biased samples. The Chinese studying in the US and the Indians immigrating to the US are not average citizens from those countries. Their excellence, therefore, is not surprising! We cannot claim that all Chinese or Indians are the smartest.

Case four
Another example of the misuse of statistics can be found in a recent news report revealing that Taiwan policemen seem to have the highest record of driving under the influence of alcohol among all professions. This has led to demands that these law-breaking policemen, who are supposed to uphold the law, should face a heavy double penalty.

This demand might sound reasonable at first glance. But careful examination of the data reveals a different picture. It turns out that policemen caught driving under the influence are obliged to report the incident, while people in other fields caught under the same circumstances are not. Therefore, the widely used comparison is completely invalid, like comparing apples with oranges.

Conclusion
Conclusions deduced from statistics without proper analysis are often misleading. Such fallacious conclusions can be found everywhere.

 

16 January, 2017

 

 

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