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给你一万个爱上统计学的理由 – 译学馆
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给你一万个爱上统计学的理由

Why you should love statistics | Alan Smith

追溯到2003年
Back in 2003,
英国政府进行了一项调查
the UK government carried out the survey.
这项调查旨在测量人口的计算能力
And it was a survey that measured levels of numeracy in the population.
然后他们震惊地发现
And they were shocked to find out that
英国每100个处于工作年龄段的成年人中
for every 100 working age adults in the country,
有47个缺乏一级计算能力
47 of them lacked level 1 numeracy skills.
就现在而言 一级计算能力是
Now level 1 numeracy skills–
英国普通中等教育证书的低端分数
that’s low-end GCSE score.
计算能力包括百分比 分数 小数的计算
It’s the ability to deal with fractions, percentages and decimals.
测试结果让英国政府很是绝望
So this figure prompted a lot of hand-wringing in Whitehall.
英国政府为此改变了政策
Policies were changed,
设立了投资
investments were made,
2011年他们又进行了一次该测试
and then they ran the survey again in 2011.
请你猜猜结果是多少?
So can you guess what happened to this number?
上升到了49
It went up to 49.
(笑声)
(Laughter)
事实上 当我在《金融时报》报道这个数字时
And in fact, when I reported this figure in the FT,
我们的一个读者还开玩笑说:
one of our readers joked and said,
“这个数字只能让51%的人口感到震惊”
“This figure is only shocking to 51% of the population.”
(笑声)
(Laughter)
其实我想告诉你们我在学校宣布这个数字时
But I preferred actually the reaction of a school child
学生们的反应
when I presented at a school this information,
他们举起手说:
who raised their hand and said,
“万一测试者本身就是那49%不达标人数中的一个呢?”
“How do we know that the person who made that number isn’t one of the 49% either?”
所以很明显
So clearly,
计算能力成了一个问题
there’s a numeracy issue,
因为它是重要的生活技能
because these are important skills for life,
我们现在更习惯于用数字来介绍
and a lot of the changes that we want to introduce
本世纪的社会变化了
in this century involve us becoming more comfortable with numbers.
现在不止英国有这个问题
Now it’s not just an English problem.
经合组织今年发布了一些有关年轻人计算能力的数据
OECD this year released some figures looking at numeracy in young people,
一马当先的是美国
and leading the way, the USA–
美国将近40%的年轻人计算能力偏低
nearly 40 percent of young people in the US have low numeracy.
英国也在榜单上
Now England is there too,
有7个经合组织国家的百分比超过20%
but so there’s seven OECD countries with figures above 20 percent.
这当然算是个问题
And that is a problem,
因为照理说不该这样
because it doesn’t have to be that way.
如果你看这张表的末尾
If you look at the far end of this graph,
你会发现荷兰和韩国的百分比还不到10%
you can see the Netherlands and Korea are in single figures.
所以我们当然要好好解决一下计算能力这个问题
So there’s definitely a numeracy problem that we want to address.
现在根据这些研究
Now as useful as studies like these are,
我想我们就那么把人分为了两个类别
I think they really we risk herding people inadvertently into one of two categories;
也就是存在两类人
that there are two kinds of people:
一种对数字应用自如 能处理有关数字的问题
those people that are comfortable with numbers, that can do numbers,
另一类则不能做到这一点
and the people who can’t.
今天我在此声明 我觉得这种二分法是错误的
And what I’m trying to talk about here today is to say that I believe that is a false dichotomy.
它并不是不变的配对
It’s not an immutable pairing.
被数字启发的你可以不必有很强的计算能力
I think you don’t have to have tremendously high levels of numeracy to be inspired by numbers,
计算能力只能算是个开始
and that should be the starting point to the journey ahead.
我觉得开始数字之旅的方法之一是
And one of the ways in which we can begin that journey,
关注统计学
for me is looking at statistics.
现在我先承认一点
Now I am the first to acknowledge that statistics
统计学有那么一点大众理解问题
has got somewhat of an image problem.
(笑声)
(Laughter)
作为数学的一部分 即便是数学家们对它也不是特别喜爱
It’s the part of mathematics that even mathematicians don’t particularly like,
因为除了统计学 数学都是精确和确定的
because whereas the rest of math is all about precision and certainty,
统计学几乎完全相反
statistics is almost the reverse of that.
但我本人是统计学转业者
But actually, you know, I was a late convert to the world of statistics myself.
如果你去问我的本科教授
If you’d asked my undergraduate professors
大学毕业后我最不擅长的两个领域可能是什么
what two subjects would I be least likely to excel in after university,
他们会告诉你 统计学和计算机编程
they’d have told you statistics and computer programming,
然而我现在却站在这里向你展示我编程的统计图
and yet here I am about to show you some statistical graphics that I programmed.
那么是什么导致了我的变化?
So what inspired that change in me?
是什么让我觉得统计学事实上很有趣?
What made me think that statistics is actually an interesting thing?
因为统计学与我们息息相关
It’s really because statistics are about us.
如果你看一下单词“统计”的词源
If you look at the etymology of the word statistics,
它是一门有关我们所处国家或社区的数据处理科学
it’s the science of dealing with data about the state or the community that we live in.
所以统计学关涉到我们整个群体
So statistics are about us as a group,
而非个人
not us as individuals.
我认为作为一种群居动物
And I think as social animals,
个人如何与群体、同类发生联系 这样的话题让人着迷
we share this fascination about how we as individuals relate to our groups, to our peers.
而统计学在这方面非常强大 让人惊讶
And statistics in this way are at their most powerful when they surprise us.
伊普索·莫利调查机构近年来进行了一些相当精彩的调查
And there’s been some really wonderful survey carried out recently by Ipsos MORI the last few years.
他们对英国的1,000多名成年人进行了调查
They did a survey of over 1,000 adults in the UK,
他们问 英格兰和威尔士每100个人中
and said, okay for every 100 people in England and Wales,
有多少是穆斯林呢?
how many of them are Muslim?
这次调查的平均答案是24
Now the average answer from this survey,
24这个数字在全体人民中非常具有代表性
which was supposed to be representative of the total population, was 24.
起码大家是这么认为的
That’s what people thought.
也就是英国人认为他们国家每100个人里有24个穆斯林
British people think 24 out of every 100 people in the country are Muslim.
但是官方数据显示穆斯林人数是5人
Now official figures reveal that figure to be about five.
所以我们的感知和统计数据呈现的现实之间
So there’s this big variation between what we think, our perception,
存在很大差异
and the reality as given by statistics.
我觉得很有意思 是什么导致了错误感知呢?
And I think that’s interesting. What could possibly be causing that misperception?
下面这个研究我很感兴趣
And I was so thrilled with the study,
我开始在许多演讲中提到这个问题
I started to take questions out in presentations. I was referring to it.
我曾在哈默史密斯的圣保罗女子学校做演讲
Now I did a presentation at St. Paul’s School for Girls in Hammersmith,
当时到场的人也像今天一样
and I had an audience rather like this,
只不过观众是清一色的6年级女生
except it was in comprised entirely of sixth-form girls.
我问:
And I said,
“姑娘们 你们觉得英国公众会认为每年有多少少女怀孕?”
“Girls how many teenage girls do you think the British public think get pregnant every year?”
当我说道英国公众认为
And the girls were apoplectic when I said
每年100个少女中会有15个怀孕时 大家很激动
the British public think of 15 out of every 100 teenage girls get pregnant in the year.
她们当然有权生气
And they had every right to be angry,
因为按官方数据显示的结果
because in fact I’d have to have closer to 200 dots before I could color one in,
画上差不多200个圈圈才能涂上一个
in terms of what the official figures tell us.
如同计算能力
And rather like numeracy,
这不只是英国才存在这方面的问题
this is not just an English problem.
伊普索·莫利机构近年来将这项调查推向全世界
Ipsos MORI expanded this survey in recent years to go across the world.
他们就问沙特阿拉伯人
And so they asked Saudi Arabians,
你们国家每100个成年人中
for every 100 adults in your country,
有多少超重或肥胖的?
how many of them are overweight or obese?
他们的平均答案是
And the average answer from the Saudis
比1/4多那么一点
was just over a quarter.
他们就是这么想的 超重或肥胖成年人仅有1/4
That’s what they thought. Just over a quarter of adults overweight or obese.
然而官方数据显示 实际上接近3/4
The official figures show, actually it’s nearer to three-quarters.
所以这又是个很大的差异
So again, a big variation.
我喜欢接下来这个例子:他们来到日本 问日本人
And I love this one: they asked in Japan, they asked the Japanese,
每100个日本人中
for every 100 Japanese people,
有多少住在农村?
how many of them live in rural areas?
平均答案是五五开 比对半儿多一点吧
The average again this is the average was about a 50-50 split, just over halfway.
也就是他们认为每100个日本人中 有56个住在农村
They thought 56 out of every 100 Japanese people lived in rural areas.
但官方数据显示是7个
The official figure is seven.
这么大的差异惊到了一些人
So extraordinary variations, and surprising to some,
但读过丹尼尔·卡纳曼的书的人很淡定
but not surprising to people who’ve read the work of Daniel Kahneman,
卡纳曼是诺贝尔经济学奖获得者
for example, the Nobel-winning economist.
他和同事阿莫斯·特沃斯基耗时多年
He and his colleague Amos Tversky, spent
来研究人们的感知和现实之间的脱节
years researching this disjoint between what people perceive and the reality,
事实上大家都是相当蹩脚的直观统计者
the fact that people are actually pretty poor intuitive statisticians.
造成这种现象的原因是多方面的
And there are many reasons for this.
当然个人经历会影响到我们的感知
Individual experiences, certainly, can influence our perceptions,
但是 媒体也可以故意引导
but so too, can things like the media reporting things by exception,
而非客观报道
rather than what’s normal.
对此卡纳曼有一句很漂亮的话
Kahneman had a nice way of referring to that.
“我们会对常识盲目”
He said, “we can be blind to the obvious”–
允许我们对数字不敏感
so we’ve got the numbers wrong–
“但我们甚至不知道自己的盲目”
“but we can be blind to our blindness about it.”
然后你做的决策就会带来很严重的后果
And then has enormous repercussions for decision making.
在统计局和数字打交道就是家常便饭
So at the statistics office while this is all going on,
我觉得这样很有趣
I thought this is really interesting.
我想说的是 统计学是全球性的问题
I said, you know, this is clearly a global problem,
但或许也有地域因素存在
but maybe geography is the issue here.
有这样的问题:你对你的国家了解多少?
You know these were questions that were all about, how well do you know your country?
也就是问:你对6,400万人口了解多少?
So in this case, it’s, okay, you know, how well do you know 64 million people?
答案是 我不太了解
Not very well, it turns out, you know, I can’t do that.
所以我有个想法
So I had an idea, which was
从当地人的角度去考虑同种方法
to think about the same sort of approach but to think about it in a very local sense.
这是当地的吗?
Is this a local?
如果我们重新架构这个问题:
If we reframe the questions and say,
你对你所在的地区了解多少?
how well do you know your local area,
这样你的答案会不会更准确?
would your answers be any more accurate?
所以我设计了一个小测验:
So I devised a quiz:
你对你的地区了解多少?
How well do you know your area?
这是个简单的网页应用程序
It’s a simple Web app.
输入邮政编码 程序就会根据你所在地区的普查数据提出问题
You put in a post code and then it will ask you questions based on census data for your local area.
我设计这个程序时就有了一个想法
And I was very conscious in designing this.
我想使其对更广泛的人口范围开放
I wanted to make it open to the widest possible range of people,
而不仅仅是那49%计算能力不达标的人
not just the 49% who can get the numbers.
我希望每个人都参与进来
I wanted everyone to engage with it.
所以这个小测验的设计灵感
So for the design of the quiz,
来自1920~1930年代奥图·纽拉特的同形象
I was inspired by the isotypes of Otto Neurath from the 1920s and 30s.
即用重复图标来表示数字的方法
Now these are methods for representing numbers using repeating icons.
数字就在那里 但它们作为背景而存在
And if you like the numbers are there, but they sit in the background.
在不使用百分比 分数 比率等术语的情况下
So it’s a great way of representing quantity without
它是一种很好的表示数量的方法
resorting to using terms like percentage, fractions and ratios.
这个测验是这样的
So here’s the quiz.
测试的布局是 你左手边是重复的图标
The layout of the quiz is, you have your repeating icons on the left-hand side there,
右手边的地图和我们要问你的问题有关
and a map showing you the area we’re asking you questions about on the right-hand side.
共有7个问题
There are seven questions.
每个问题的答案范围在0~100之间
Each question there’s a possible answer between 0 and 100,
测试结束后 你会得到一个在0~100之间的总分数
and at the end of the quiz, you get an overall score between 0 and 100.
因为这里是TEDx埃克塞特现场
And so because this is TEDxExeter,
所以我们快速看一下测验中关于埃克塞特的前几个问题
I thought we would have a quick look at the quiz for the first few questions of Exeter.
第一个问题是:每100个人中
So the first question is: for every 100 people,
16岁以下的人有多少?
how many are aged under 16?
现在我对埃克塞特不太了解 所以大致猜一下
Now I don’t know Exeter very well at all, so I had a guess at this,
就是为了给大家演示一下如何测验
but it gives you an idea of how this quiz works.
你拖动滑块点亮图标
You drag the slider to highlight your icons,
然后点击“提交”来完成作答
and then just click Submit to answer,
我们用动画的方式得出你的答案和现实之间的不同
and we animate away the difference between your answer and reality.
结果是我猜的很不妙:答案是5
And it turns out, I was a pretty terrible guess: 5.
下一个问题是什么呢?
How about the next question?
就是问你们的年龄的中位数
This is asking about what the average age is,
就是年轻人和老年人的年龄中位数
so the age at which half the population are younger and half the population are older.
我觉得35岁对我来说是中年
And I thought 35–that sounds middle-aged to me.
(笑声)
(Laughter)
事实上 在埃克塞特结果是惊人的年轻
Actually, in Exeter, is incredibly young,
是我低估了大学在本地区的影响
and I’d underestimated the impact of the university in this area.
接下来 问题就不简单了
The questions get harder as you go through.
所以问题是关于住房所有权:
So this one’s now asking about homeownership:
100个家庭中 有多少存在抵押或贷款?
For every 100 households, how many are owned with a mortgage or loan?
我先赌一把最大值 因为我希望答案超过50
And I hedged my bets here, because I didn’t want to be more than 50 out on the answer.
(笑声)
(Laughter)
事实上这些问题越来越难
And actually, these get harder, these questions,
因为当你位于某地 某社区
because when you’re in an area, when you’re in a community, things like age–
年龄大小总是有线索可查
there are clues to whether a population is old or young.
你往周围瞟一眼就能猜出大概
Just by looking around the area, you can see it.
但像住房所有权就肉眼难辨了
Something like homeownership is much more difficult to see,
于是我们就得回到个人推理来处理了
so we revert to our own heuristics,
也就是我们偏向于认为有多少人有自己的房子
our own biases about how many people we think own their own homes.
眼下的事实是
Now the truth is,
我们发布这个测验时
when we published this quiz,
所依据的普查数据已经好几年没更新了
the census data that it’s based on was already a few years old.
你在网页上输入邮政编码 然后获得几年前的数据反馈
We’ve had online applications that allow you to put in a post code and get statistics back for years.
所以某种意义上 这些数据落后了 不够新
So in some senses, this was all a little bit old and not necessarily new.
但我对结果很感兴趣
But I was interested to see
我想看看基于人类偏见这个事实
what reaction we might get by gamifying the data in the way that we have,
游戏化的数据 动画手段能给人带来什么反应
by using animation and playing on the fact that people have their own preconceptions.
结果证明
It turns out the reaction was…
反应超出了我的预期
was more than I could have hoped for.
为了满足公众需求 我需要恒心壮志来运行该统计网站
It was a long-held ambition of mine to bring down a statistics website due to public demand.
(笑声)
(Laughter)
这个网址包括“统计”“政府”“英国”等词
This URL contains the words statistics, gov, and UK,
这三个词是网址中最不招人待见的词
which are three of people’s least favourite words in a URL.
不可思议的是 晚上9:45时该网站瘫痪了
And the amazing thing about this was that the website came down at quarter to 10 at night,
因为大家都基于个人自由意愿
because people were actually engaging with this data of their own free will,
利用个人时间为我们提供数据
using their own personal time.
我很高兴看到25万人在测试发起的48小时内
I was very interested to see that we got something like a quarter of a million
完成了这个实验
people playing the quiz within the space of 48 hours of launching it.
该测验在网上 社交媒体上引发巨大讨论
And it sparked an enormous discussion online, on social media,
这些讨论基本上是由那些很开心发现了自己的认知误区的人所主导
which was largely dominated by people having fun with their misconceptions,
从某些方面来讲 这一点让我非常开心
which is something that I couldn’t have hoped for any better, in some respects.
我也乐见于人们把该测验发给政客们
I also liked the fact that people started sending it to politicians.
你对你声称所代表的地区了解多少?
How well do you know the area you claim to represent?
(笑声)
(Laughter)
演讲结束前
And then just to finish,
我们回到这两种人身上
going back to the two kinds of people,
我非常好奇那些擅长数字的人在本次测验中的成绩
I thought it would be really interesting to see how people who are good with numbers would do on this quiz.
英格兰和威尔士的国家统计学家约翰·普林格
The national statistician of England and Wales,
你想当然地认为他的得分很高
John Pillinger, you would expect he would be pretty good.
但他在自己的地区方面只得了44分
He got 44 for his own area.
(笑声)
(Laughter)
杰瑞米·帕克斯曼
Jeremy Paxman–
实话实说 他喝了一杯酒后
admittedly, after a glass of wine–
得了36分 分数更不理想了
36, even worse, okay.
这说明数字可以启发我们 也能让我们大吃一惊
It just shows you that the numbers can inspire us all. They can surprise us all.
所以当我们提起统计学 往往认为它是不确定的科学
So very often we talk about statistics as being the science of uncertainty.
而今天我要说的最终观点是:
My parting thought for today is:
事实上 统计学是关于我们的科学
actually, statistics is the science of us.
这就是我们应该对数字着迷的原因
And that’s why we should be fascinated by numbers.
非常感谢
Thank you very much.
(掌声)
(Applause)

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本视频为你介绍统计学对人类的重要性。

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