Statistics are persuasive.
统计数据的说服力很高。
So much so that people, organizations,and whole countries base some of their most important decisions on organized data.
以至于很多个人、机构甚至整个国家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 somethinglurking inside it, something that can turn the resultscompletely upside down.
任何一系列的统计数据都也许有一些隐藏的因素，可以颠覆整个结果。
For example, imagine you need to choosebetween two hospitals for an elderly relative's surgery.
例如，想象你现在需要在两家医院中选择一家为家里的老人做手术。
Out of each hospital's last 1000 patient's, 900 survived at Hospital A, while only 800 survived at Hospital B.
在每个医院最近收治的1000例患者中，A医院有900例患者存活，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, remember that not all patientsarrive at the hospital with the same level of health.
但是在你做出决定前，要记得这两家医院收治的患者入院时，健康状态并不一致。
And if we divide each hospital'slast 1000 patients into those who arrived in good healthand those who arrived in poor health,
如果我们将1000例患者分为两组，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 patientswho arrived in poor health, of which 30 survived.
A医院只有100例入院时健康状况不好，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 for patients who arrive at hospital in poor health, with a survival rate of 52.5%.
对于重症患者来说，去B医院的生存率为52.5%，所以，B医院是更好的选择。
And what if your relative's healthis 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 stillthe better choice, with a survival rate of over 98%.
出人意料，轻症患者在B医院的生存率超过98%，B医院依旧是更好的选择。
So how can Hospital A have a betteroverall survival rate if Hospital B has better survival ratesfor patients in each of the two groups?
既然B医院两组病人的生存率都更高，为什么A医院的总体生存率会更高呢？
What we've stumbled upon is a caseof 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 appearto show opposite trends depending on how it's grouped.
即同一批数据仅因为分组不同，得出的结果完全相悖。

This often occurs when aggregated datahides 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, which is a hidden additional factorthat significantly influences results.
条件变量有时被称为潜伏变量，这个隐藏的额外变量会显著影响结果。
Here, the hidden factor is the relativeproportion of patients who arrive in good or poor health.
这里，隐藏变量是患者到达医院时健康状况的构成比。
Simpson's paradox isn't justa hypothetical scenario.
“辛普森悖论”并非只是假说。
It pops up from time to time in the real world, sometimes in important contexts.
它时不时出现在现实生活中，有时是很重要的背景下。
One study in the UK appeared to show that smokers had a higher survival ratethan nonsmokers over a twenty-year time period.
英国一项研究显示，在20年里，吸烟者生存率高于不吸烟者。
That is, until dividing the participantsby age group showed that the nonsmokers were significantly older on average,
但根据参与者的年龄分组后，发现不吸烟组人群的平均年龄显著较高，
and thus, more likelyto die during the trial period, precisely because they were living longerin general.
所以，不吸烟组在随访过程中更容易死亡，恰巧是因为不吸烟者通常更长寿。
Here, the age groups are the lurking variable, and are vital to correctly interpret the data.
在这个例子中，年龄就是潜伏变量，而且它对于正确解释数据至关重要。
In another example, an analysis of Florida's death penalty cases
另外一个例子中，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 between black and white defendantsconvicted of murder.
在黑人和白人在被指控谋杀的时候，判刑轻重没有种族差别。
But dividing the cases by the raceof 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, black defendants were more likelyto be sentenced to death.
无论在何种情况下，黑人都更容易被判处死刑。
The slightly higher overall sentencing rate for white defendants was due to the fact
白人之所以总体被判刑的比例高，是因为当受害者是白人的时候，
that cases with white victims were more likely to elicit a death sentence than cases where the victim was black,
相比于受害者是黑人而言，更容易导致死刑的判决；
and most murders occurred betweenpeople 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 dividedin any number of ways,
数据可以有无数种分组方法，
and overall numbers may sometimesgive a more accurate picture than data divided into misleadingor arbitrary categories.
相对于将数据分成具有误导性的、主观性的类别而言，总体数字有时能更给出更加精准的图景。
All we can do is carefully study theactual situations the statistics describe and consider whether lurking variablesmay be present.
我们能做的就是仔细地研究这些数据所描述的实际情况，并且考虑是否有潜伏变量。
Otherwise, we leave ourselvesvulnerable to those who would use data to manipulate othersand promote their own agendas.
否则，那些用数据去操纵别人同时推进自己的日程的人，可以轻松伤害我们。