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We often evaluate the success of medical treatments or social programs by how much of the population they help.
我们常常根据医疗或社会项目对人口的帮助程度来评估其成功与否。
But this can be a problem. Like, suppose we're treating a disease that afflicts both people and cats,
但这可能存在问题。比如，假设我们要治疗的疾病困扰着人类和猫类，
and among 1 cat and 4 people we treat, the cat and 1 person recover and 3 people die.
我们所治疗的1只猫和4个人中，这只猫和1人康复，3人死亡。
And of 4 cats and 1 person we don't treat, three of the cats recover while 1 cat and the person and die.
在没有接受治疗的4只猫和1个人中，3只猫痊愈，1只猫和这个人死亡。
In the real world, these numbers might be more like 300 and 100, or whatever,
在现实生活中，这些数字更有可能是300和100之类的，
but we'll keep them small so they're easier to keep track of.
我们是用小数字是为了方便记录。
So, in our sample, 100% of treated cats survive while only 75% of untreated cats do,
因此在我们的样本中，所有接受治疗的猫都痊愈了，但只有75%未接受治疗的猫活了下来，
and 25% of treated humans survive while 0% of untreated humans do.
并且25%的接受治疗的人类存活，而没有接受治疗的人都死亡了。
Which makes it seem like the treatment improves chances of recovery.
看起来似乎治疗提高了治愈的机会。
Except that if we aggregate the data, among all people and cats treated, only 40% survive,
但如果我们汇总这些数据，在所有接受治疗的人和猫中，只有40%存活了下来，
while among all people and cats left on their own, 60% recover.
而在所有未接受治疗的人和猫中，60%都康复了。
Which makes it seem like the treatment reduces chances of recovery. So which is it?
这样看来，治疗似乎降低了康复率。到底是哪一个呢？
This is an illustration of Simpson's paradox, a statistical paradox
以上是对辛普森悖论的举例
where it's possible to draw two opposite conclusions from the same data depending on how you divide things up,
这是一个统计悖论，即从相同的数据中得出两个相反的结论是可能的，这取决于你如何划分事物，
and statistics alone cannot help us solve it – we have to go outside statistics and understand the causality involved in the situation at hand.
单靠数据本身无法帮助我们解决问题—我们需要借助外部数据并了解当前情况所涉及的因果关系。
For example, if we know that humans get the disease more seriously and are therefore more likely to be prescribed treatment,
例如，如果我们知道人类的病情更严重，因此更有可能接受处方治疗，
then it can make sense that fewer individuals that get treated survive, even if the treatment increases the chances of recovery,
这样一来，即使治疗增加了康复的机会，接受治疗的个体存活下来的几率也会减少，
since the individuals that got treated were more likely to die in the first place.
因为接受治疗的个体首先更有可能死亡。
On the other hand, if we know that humans, regardless of how sick they are, are more likely to get treated than cats
另一方面，如果我们知道，不论病得有多严重，人类都比猫更有可能得到治疗
because no one wants to pay for kitty healthcare, then the fact that 4 out of 5 humans died while only 1 in 5 cats died suggests that, indeed,
因为没人愿意为猫咪的医疗保健买单，因此五分之四的人死亡，而仅有五分之一的猫死亡，这一事实表明
the treatment may be a bad choice. So if you're doing a controlled experiment,
治疗可能是一个糟糕的选择。所以如果你在做一个对照实验，
you need to make sure to not let anything causally related to the experiment influence who you apply your treatments to,
你需要确保不要让任何与实验相关的事情影响到你的治疗对象，
and if you have an uncontrolled experiment, you have to be able to take those outside biases into account.
如果你做的不是对照实验，你需要能够考虑到这些外部偏见。
As a more tangible example, Wisconsin has repeatedly had higher overall 8th grade standardized test scores than Texas,
举个更具体的例子，威斯康辛州8年级的标准化考试总分数再一次高于德克萨斯州，
so you might think Wisconsin is doing a better job. However, when broken down by race –
所以你会认为威斯康辛州表现更好。但当按种族划分时—
which, via entrenched socioeconomic differences is a major factor in standardized-test scores–
根深蒂固的社会经济差异是标准化考试分数的主要因素—
Texas students performed better than Wisconsin students on all fronts:
德克萨斯州的学生在所有方面的表现都好于威斯康星州的学生：
black Texas students scored higher than black Wisconsin students, and likewise with hispanic and white students.
德州黑人学生得分比威斯康辛州黑人学生高，西班牙裔和白人学生也是如此。
The difference in the overall ranking is because Wisconsin has proportionally far fewer black
整体排名的差异是因为威斯康辛州的黑人学生和西班牙裔学生所占比例很少
and hispanic students and proportionally more white students than Texas –
而白人学生所占比例比德州多—
so the takeaway certainly should not be that Wisconsin has better education than Texas!
所以结论当然不应该是威斯康辛州的教育比德州更好！
Just that it has proportionally more socioeconomically advantaged students.
只是在比例上，它有更多社会经济地位优越的学生。
So understanding the underlying cause of the context of statistics can have huge public implications.
因此，理解统计背景下的潜在原因可能会产生巨大的公共影响。
In some situations there's also a nice graphical way to picture Simpson's paradox:
在一些情况中，还有一种很好的画图方式来描述辛普森悖论：
as two separate trends that each go one way, but the overall trend between the populations goes the other way.
作为两种不同的趋势，每一种都走向一个方向，但人口之间的总体趋势是走向另一个方向的。
Like, maybe more money makes people sadder, and more money makes cats sadder,
比如，也许更多的钱会让人更悲伤，更多的钱会让猫更悲伤，
but if cats are both much happier and richer than people to start with, the overall trend appears, incorrectly, to be that more money makes you happier.
但如果猫咪一开始就比人类更快乐更有钱，总的趋势似乎是，更多的钱让你更快乐，这是不正确的。
In this case, being a cat makes you happier but also happened to have more money.
在这种情况下，当一只猫让你更快乐也碰巧更有钱。
And you can also misinterpret this graph to show that, overall, more money makes you a cat,
你也可以错误地解读这幅图来表明，总的来说，更多的钱让你成为一只猫，
which I think helps illustrate very well the ability to lie or reach incorrect conclusions by blindly using statistics without context!
我认为这有助于很好地说明，盲目地使用没有背景的统计数据来撒谎或得出错误结论的能力！
Of course, this is not to say that statistics are always going to be paradoxical or confusing–
当然，这并不是说统计数据总是自相矛盾或令人困惑的—
it's quite possible that everything will just make sense from the get-go,
很有可能从一开始一切都是有意义的，
like if people and cats both get sadder when you give them more money,
比如，当你给人和猫更多钱的时候，他们都会变得更悲伤，
and cats are both poorer and happier than people, then the overall trend is no longer paradoxical: more money equals more sadness.
并且猫比人更穷但更快乐，那么整体趋势就不再是矛盾的了：更多的钱等于更多的悲伤。
But it's important to be aware that paradoxes like Simpson's paradox are possible,
但重要的是要意识到，像辛普森这样的悖论是可能的，
and we often need more context to understand what a statistic actually means.
并且通常我们都更多的背景才能理解数据的真实意义。
