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A common misconception in statistics is to think that correlation implies causation-like,
统计学中一个常见的误解是，认为相关性意味着因果关系,
if more tall people have cats, you might think that means being tall makes people more likely to get a cat.
如果更多的高个子人养猫，你可能会认为这意味着个子高的人更有可能养猫。
![Q)[S~7{OLTZ~3P]ODEP9QZH.png](http://upload.kekenet.com/2021/1105/4281636099667.png "4281636099667.png")
However, simply knowing a correlation between height and cat ownership can't tell us which way the causality goes
然而，仅仅知道身高和养猫之间的关系并不能告诉我们因果关系的走向
-it may instead be that having a cat causes people to grow taller
-可能是养猫会让人长得更高
-or perhaps the real cause is something else altogether, like that the people and cats live on two separate islands,
-或者可能真正的原因是完全不同的，比如人和猫生活在两个独立的岛屿上，
one a lush paradise with enough food for growing tall and feeding pet cats, and the other a wasteland that limits both height and cat ownership.
一个是郁郁葱葱的天堂，有足够的食物促进长高，有足够的食物来喂养宠物猫，另一个是限制身高和养猫的荒原。
The point of examples like this is that noticing a correlation between two things doesn't imply that one of those things causes the other.
这类例子的要点是，注意到两件事之间的关联并不意味着这两件事中的一件导致了另一件事。
Hence the common refrain: correlation doesn't imply causation.
因此有一种常见的说法：相关性并不意味着因果关系。
And it's true-it doesn't !
这是真的--不是的！
But this oft-repeated mantra leads to another common misconception-the idea that you can't infer any causality from statistics.
但这句经常重复的口头禅导致了另一个常见的误解--认为你不能从统计数据中推断出任何因果关系。
You can! I mean, it's quite reasonable to think that, if two things are correlated, there's likely some reason, even if a single correlation can't tell you.
你可以的! 我的意思是，我们有理由认为，如果两件事是相关的，可能会有某种原因，即使单一的相关性不能告诉你。
Sometimes you can infer the causality from additional information-like knowing that one thing happened before the other
有时你可以从额外的信息中推断因果关系-比如知道一件事情发生在另一件事情之前-
-but you can also infer causality directly from correlations you just need more than one, together with something called causal networks.
但你也可以直接从你只需要一个以上的相关性以及一些称为因果网络的东西来推断因果关系。
Like, in our cat-height-island example, we know that cat ownership and height are correlated, but we don't know what the cause of that correlation is.
例如，在我们的猫高岛的例子中，我们知道猫的所有权和身高是相关的，但我们不知道这种相关性的原因是什么。
If we don't know anything else, then there are 19.
如果我们什么都不知道，那就有19个因果关系。
-yes 19 different causal relationships that could explain the situation.
-是的，19个不同的因果关系可以解释这种情况。
20 if you think the correlation is just an accident, so correlation certainly doesn't imply causation yet.
如果你认为这种关联只是一场意外，那就是20组因果关系。相关性当然还不意味着因果关系。
However, perhaps we know two other things: first, suppose people born on a particular island stay there,
然而，也许我们知道另外两件事：首先，假设出生在某个岛屿上的人留在那里，
so their height doesn't influence what island they live on,
这样他们的身高就不会影响他们生活在哪个岛屿上，
and we can rule out the relationships where height influences island.
我们可以排除身高影响岛屿的关系。
Second, suppose that on either island, taken by itself, there isn't any correlation between height and cat ownership;
其次，假设在任何一个岛上，单独考虑，身高和养猫之间没有任何关联；
then we can rule out all the options where height and cats influence each other directly .
那么我们可以排除身高和猫相互直接影响的所有选择。
This leaves us with just two options: either the islands are the causal explanation for both height and cat ownership
这给我们留下了两个选择：要么岛屿是身高和养猫的因果解释
(maybe, as before, one island is a lush, healthy paradise for both people and cats),
(也许像以前一样，一个岛屿对人和猫来说都是郁郁葱葱、健康的天堂)，
or else cat ownership is the causal explanation for the islands which are the causal explanation for height,
要么养猫是岛屿的因果解释，而岛屿是身高的因果解释
(like, maybe an abundance of cats turned the island into a paradise, thereby influencing the height of future cat owners).
(比如，也许大量的猫把岛屿变成了天堂，从而影响了未来猫主人的身高)。
So, starting with 19 possible causal relationships,
因此，从19个可能的因果关系开始，
we used correlations to narrow things down to just 2 options-not bad!
我们使用相关性将事情缩小到只有2个选项--还不错！
And we knew something about the timeline of one cat and people arrived the island,we might be narrow down to just one option.
如果我们知道一只猫和人类到达岛上的时间，我们可能会把范围缩小到只有一个选择。
Of course, this is just a simple example, but for any group of things,
当然，这只是一个简单的例子，但是对于任何一组事物，
you can use the various correlations between them (or lack of correlations) to eliminate some of the possible cause-and-effect relationships.
你都可以使用它们之间的各种相关性(或缺乏相关性)来消除一些可能的因果关系。
And that's how correlations CAN imply causation.
这就是相关性可以暗示因果关系的原因。
There is one problem, though… some experiments in quantum mechanics have correlations that rule out ALL possible cause and effect relationships.
但有一个问题，尽管…量子力学中的一些实验具有相关性，可以排除所有可能的因果关系。
We’ll have to save the details for a later video, but until then, may I suggest a new version of the famous refrain?
我们得把细节留到以后的视频里再说，但在那之前，我可以推荐这首著名叠唱的新版本吗？
“Correlation doesn't necessarily imply causation, but it can if you use it to evaluate causal models.
“相关性并不一定意味着因果关系，但如果你用它来评估因果模型，还是可以的。
…Except in quantum mechanics.”
…除了量子力学。”
I’ve got a little more about statistics and causality after this, but first I’m excited to introduce the very relevant sponsor for this video: Brilliant.Org.
在此之后，我对统计数据和因果关系有了更多的了解，但首先，我很兴奋地介绍本视频的相关赞助商:Brilliant.Org。
Brilliant is a problem solving website designed to help you practice and learn math and science via guided problems, puzzles and quizzes:
Brilliant是一个问题解决网站，旨在通过指导性问题、测试游戏和测验来帮助你练习和学习数学和科学：
I know that sounds kind of nerdy, but the truth is that the only way to truly learn and understand much of math and physics is to actively work through the material yourself – videos only get you so far.
我知道这听起来有点书呆子，但事实是，真正学习和理解大部分数学和物理的唯一方法是自己积极学习-视频只能带你走到这一步。
And Brilliant does a brilliant job of making that easy, sneakily enticing you into doing math and physics problems by means of intriguing questions structured for all ability and knowledge levels.
而Brilliant在这方面做得非常出色，通过针对为所有能力和知识水平的人构建有趣的问题，偷偷地诱使你做数学和物理问题。
I say this from experience, because if you haven't done a problem for a few days, Brilliant will send you an attention-grabbing puzzle , and I’ve been sucked in by quite a few of them.
我这么说是出于经验，因为如果你已经几天没有做一道题了，Brilliant会给你发送一个吸引眼球的谜题，而我已经被相当多问题迷住了。
If you want to try out Brilliant (which I recommend), heading to brilliant. Org/
如果您想尝试我推荐的Brilliant，请前往brilliant. Org/
minutephysics will let them know you came from here, and you can check out their courses on Probability, the Physics of the Everyday, Classical Mechanics, Gravitational Physics and so on.
请告诉他们你是从minutephysics 来的，你可以查看关于概率、日常物理、经典力学、引力物理等相关的课程。
Hey, glad you're still here-in case you're interested, there's a footnotes video
嘿，很高兴你还在这里-如果你感兴趣的话，这里有一个脚注视频，
covering a few things that got cut out of this one, like feedback loops and correlations that arise just by chance.
涵盖了这个视频中的一些内容，比如偶然出现的反馈循环和相关性。
The link's on screen and in the video description.
链接在屏幕上和视频描述中。
