How statistics can be misleading - Mark Liddell

翻译人员: Zihan Zhao-Holland 校对人员: Mingyu Cui

Statistics are persuasive.

统计数据的说服力很高，

So much so that people, organizations, and whole countries

以至于很多个人、机构甚至整个国家

base some of their most important decisions on organized data.

在做最重要的决定时都会参考统计数据。

But there's a problem with that.

但其实这样做有一个问题。

Any set of statistics might have something lurking inside it,

任何一系列的统计数据都也许有一些隐藏的因素，

something that can turn the results completely upside down.

可以颠覆整个结果。

For example, imagine you need to choose between two hospitals

例如，想象你现在需要在两家医院中选择一家

for an elderly relative's surgery.

为家里的老人做手术。

Out of each hospital's last 1000 patient's,

在每个医院最近收治的1000例患者中，

900 survived at Hospital A,

A医院有900例患者存活。

while only 800 survived at Hospital B.

然而，B医院只有800例患者存活。

So it looks like Hospital A is the better choice.

这样看来，A医院是更好的选择。

But before you make your decision,

但是，在你做出决定前，

remember that not all patients arrive at the hospital

要记得，这两家医院收治的患者入院时，

with the same level of health.

健康状态并不一致。

And if we divide each hospital's last 1000 patients

如果我们将1000例患者分为两组，

into those who arrived in good health and those who arrived in poor health,

入院时健康状态好的 和入院时健康状态不好的，

the picture starts to look very different.

结果就截然不同。

Hospital A had only 100 patients who arrived in poor health,

A医院只有100例入院时健康状况不好，

of which 30 survived.

其中30例存活。

But Hospital B had 400, and they were able to save 210.

B医院有400例入院时健康状况不好， 210例被救活了。

So Hospital B is the better choice

对于重症患者来说，

for patients who arrive at hospital in poor health,

去B医院的生存率为52.5%。

with a survival rate of 52.5%.

所以，B医院是更好的选择。

And what if your relative's health is good when she arrives at the hospital?

那如果您的亲人入院时健康状态好呢？

Strangely enough, Hospital B is still the better choice,

出人意料，轻症患者在B医院的生存率超过98%，

with a survival rate of over 98%.

B医院依旧是更好的选择。

So how can Hospital A have a better overall survival rate

既然B医院两组病人的生存率都更高，

if Hospital B has better survival rates for patients in each of the two groups?

为什么A医院的总体生存率会更高呢？

What we've stumbled upon is a case of Simpson's paradox,

我们遇到的这种现象被称为“辛普森悖论”——

where the same set of data can appear to show opposite trends

同一批数据仅因为分组不同，

depending on how it's grouped.

得出的结果完全相悖。

This often occurs when aggregated data hides a conditional variable,

“辛普森悖论”常常发生在总体数据隐藏了条件变量时，

sometimes known as a lurking variable,

条件变量有时被称为潜伏变量。

which is a hidden additional factor that significantly influences results.

这个隐藏的额外变量会显著影响结果。

Here, the hidden factor is the relative proportion of patients

这里，隐藏变量是患者到达医院时

who arrive in good or poor health.

健康状况的构成比。

Simpson's paradox isn't just a hypothetical scenario.

“辛普森悖论”并非只是假说，

It pops up from time to time in the real world,

它时不时出现在现实生活中，

sometimes in important contexts.

有时，是很重要的背景下。

One study in the UK appeared to show

英国一项看起来展示出，

that smokers had a higher survival rate than nonsmokers

在20年里，

over a twenty-year time period.

吸烟者生存率高于不吸烟者。

That is, until dividing the participants by age group

但根据参与者的年龄分组后，

showed that the nonsmokers were significantly older on average,

发现不吸烟组人群的平均年龄显著较高，

and thus, more likely to die during the trial period,

所以，不吸烟组在随访过程中更容易死亡，

precisely because they were living longer in general.

恰巧是因为不吸烟者通常更长寿。

Here, the age groups are the lurking variable,

在这个例子中，年龄就是潜伏变量，

and are vital to correctly interpret the data.

而且它对于正确解释数据至关重要。

In another example,

另外一个例子中，

an analysis of Florida's death penalty cases

佛罗里达州一项在死刑犯中所进行的分析显示，

seemed to reveal no racial disparity in sentencing

在黑人和白人在被指控谋杀的时候，

between black and white defendants convicted of murder.

判刑轻重没有种族差别，

But dividing the cases by the race of the victim told a different story.

但根据受害者的种族分组后，结果大不相同。

In either situation,

无论在何种情况下，

black defendants were more likely to be sentenced to death.

黑人都更容易被判处死刑。

The slightly higher overall sentencing rate for white defendants

白人之所以总体被判刑的比例高，

was due to the fact that cases with white victims

是因为当受害者是白人的时候，

were more likely to elicit a death sentence

相比于受害者是黑人而言，

than cases where the victim was black,

更容易导致死刑的判决；

and most murders occurred between people of the same race.

而且，大部分的谋杀都发生在同一个种族内的。

So how do we avoid falling for the paradox?

我们怎样才能不被“辛普森悖论”所误导呢？

Unfortunately, there's no one-size-fits-all answer.

不幸的是，并没有统一的答案。

Data can be grouped and divided in any number of ways,

数据可以有无数种分组方法，

and overall numbers may sometimes give a more accurate picture

相对于将数据分成具有误导性的，主观性的类别而言，

than data divided into misleading or arbitrary categories.

总体数字有时能更给出更加精准的图景。

All we can do is carefully study the actual situations the statistics describe

我们能做的就是仔细地研究这些数据所描述的实际情况，

and consider whether lurking variables may be present.

并且考虑是否有潜伏变量。

Otherwise, we leave ourselves vulnerable to those who would use data

否则，那些用数据去操纵别人，同时推进自己的日程的人，

to manipulate others and promote their own agendas.

可以轻松伤害我们。