Why you should love statistics | Alan Smith

譯者: 易帆 余 審譯者: Melody Tang

Back in 2003,

在2003年，

the UK government carried out a survey.

英國政府進行了一項調查。

And it was a survey that measured levels of numeracy

主要是調查

國民的算數能力。

in the population.

And they were shocked to find out

他們驚訝地發現，

that for every 100 working age adults in the country,

該國的成年就業者當中，

47 of them lacked Level 1 numeracy skills.

平均100個裡面有47個 缺乏等級一的算數能力。

Now, Level 1 numeracy skills -- that's low-end GCSE score.

等級一算數能力， 相當於低階的國中數學能力。

It's the ability to deal with fractions, percentages and decimals.

這個等級代表你會計算 分數、百分比、小數點。

So this figure prompted a lot of hand-wringing in Whitehall.

這個數據讓英國政府緊張地手心冒汗。

Policies were changed,

不但改變了政策、

investments were made,

也編訂了預算，

and then they ran the survey again in 2011.

然後，在2011年他們再調查一遍。

So can you guess what happened to this number?

各位猜猜，數字變到多少？

It went up to 49.

上升到49。

(Laughter)

（笑聲）

And in fact, when I reported this figure in the FT,

事實上，當我把這數據 刊登在金融時報後，

one of our readers joked and said,

我們其中一位讀者開玩笑地說，

"This figure is only shocking to 51 percent of the population."

「這個數據只嚇到 51% 的人。」

(Laughter)

（笑聲）

But I preferred, actually, the reaction of a schoolchild

但我實際上更喜歡一個小學生的反應，

when I presented at a school this information,

當我在他的學校演講提到這件事情時，

他舉手問說，

who raised their hand and said,

"How do we know that the person who made that number

「我們如何知道，算出這個數據的人

isn't one of the 49 percent either?"

會不會也是在 49% 裡面的人？」

(Laughter)

（笑聲）

So clearly, there's a numeracy issue,

所以很明顯的，算術能力不足問題相當嚴重，

because these are important skills for life,

因為在我們人生中， 這些都是很重要的技能，

and a lot of the changes that we want to introduce in this century

而且，我們想要介紹的這個世紀的許多變化

involve us becoming more comfortable with numbers.

需要我們能夠更自在地面對數字。

Now, it's not just an English problem.

這不僅是英國的問題。

OECD this year released some figures looking at numeracy in young people,

OECD（經濟合作與發展組織） 今年也發佈了一些年輕人的算數能力數據，

and leading the way, the USA --

美國第一名，

nearly 40 percent of young people in the US have low numeracy.

他們將近有40%的年輕人算數能力有問題。

Now, England is there too,

英國也差不多，

but there are seven OECD countries with figures above 20 percent.

總共有七個OECD的會員國， 他們的數據都高於 20% 。

That is a problem, because it doesn't have to be that way.

這問題很嚴重，因為不該如此。

如果你仔細看這張圖表的末端，

If you look at the far end of this graph,

你可以看到荷蘭跟韓國的數據只有個位數。

you can see the Netherlands and Korea are in single figures.

So there's definitely a numeracy problem that we want to address.

所以我們必須解決這個有關數學程度的問題。

Now, as useful as studies like these are,

然而，就算這些報告很有用，

I think we risk herding people inadvertently into one of two categories;

我認為我們把人類分成這兩類是有風險的；

that there are two kinds of people:

就只是這兩類：

those people that are comfortable with numbers, that can do numbers,

一類是能自在地面對數字的人，會算數的人，

and the people who can't.

另一類是不會算數的人。

And what I'm trying to talk about here today

而我今天要談的是，

is to say that I believe that is a false dichotomy.

我認為這樣的兩分法是錯誤的。

It's not an immutable pairing.

這兩類人不會永遠都如此。

I think you don't have to have tremendously high levels of numeracy

我認為你不需要懂高階數學，

to be inspired by numbers,

也能被數字所啟發，

and that should be the starting point to the journey ahead.

而且，這應該是未來旅程的起點。

And one of the ways in which we can begin that journey, for me,

開啟這趟旅程的其中一個方法， 對我而言，

is looking at statistics.

就是觀察統計數據。

Now, I am the first to acknowledge that statistics has got somewhat

我應該是第一個說

統計比較像是個圖像問題的人。

of an image problem.

(Laughter)

（笑聲）

It's the part of mathematics

它是數學的一部分，

that even mathematicians don't particularly like,

但是數學家並不特別喜歡統計，

because whereas the rest of maths is all about precision and certainty,

因為其它的數學講究的是 精準性及確定性，

statistics is almost the reverse of that.

而統計幾乎是相反的。

But actually, I was a late convert to the world of statistics myself.

但實際上，我自己是比較晚愛上統計的。

If you'd asked my undergraduate professors

如果你問我的大學教授

what two subjects would I be least likely to excel in after university,

我畢業後兩個最不可能會 成為我日後強項的科目，

they'd have told you statistics and computer programming,

他們會告訴你，是統計及電腦編程，

and yet here I am, about to show you some statistical graphics

但我今天來這邊，是要向各位展示一些

我編程的統計資料圖表。

that I programmed.

So what inspired that change in me?

那到底是什麼改變了我？

是什麼事讓我覺得統計真的很有趣？

What made me think that statistics was actually an interesting thing?

It's really because statistics are about us.

那是因為統計跟我們有關。

If you look at the etymology of the word statistics,

如果你有去查「統計」這個詞的詞源意義，

it's the science of dealing with data

它是一門有關

我們生活周遭的數據科學。

about the state or the community that we live in.

So statistics are about us as a group,

所以統計是有關我們群體，

not us as individuals.

而不是我們個人。

And I think as social animals,

我認為身為群居動物的我們，

we share this fascination about how we as individuals relate to our groups,

我們每個人都很想知道，

我們個人與團體、同儕之間 有什麼關聯性。

to our peers.

And statistics in this way are at their most powerful

而這也是統計在這些方面最有力，

when they surprise us.

那麼另人驚訝。

And there's been some really wonderful surveys carried out recently

最近有一些很棒的調查，

是由 Ipsos MORI（英國的市場調查公司） 近幾年所進行的調查。

by Ipsos MORI in the last few years.

They did a survey of over 1,000 adults in the UK,

他們對一千多位英國民眾進行了訪問，

and said, for every 100 people in England and Wales,

問他們說，「你認為住在英格蘭及威爾斯的

how many of them are Muslim?

每一百個人中，平均有多少人是穆斯林（回教徒）？」

Now the average answer from this survey,

在這次的調查中，

which was supposed to be representative of the total population, was 24.

這些可以代表大多數人的受訪民眾， 他們認為應該有 24% 。

That's what people thought.

這是人們的想法。

British people think 24 out of every 100 people in the country are Muslim.

英國人認為每一百個人當中 有 24 個是穆斯林。

Now, official figures reveal that figure to be about five.

但官方的統計數字大約只有 5 。

So there's this big variation between what we think, our perception,

所以我們認為的觀念與

and the reality as given by statistics.

實際上的統計有著很大的差距。

And I think that's interesting.

所以我認為這很有趣，

到底是什麼原因造成這樣的認知差距？

What could possibly be causing that misperception?

And I was so thrilled with this study,

我對這樣的研究相當感興趣。

I started to take questions out in presentations. I was referring to it.

我在每次的演講中， 都會提出類似的相關問題。

Now, I did a presentation

之前，我到阿姆斯特丹的聖保羅學校，

at St. Paul's School for Girls in Hammersmith,

向學校的女同學做了一次演講，

and I had an audience rather like this,

聽眾人數和在座的差不多，

except it was comprised entirely of sixth-form girls.

除了他們都是六年級的女學生。

And I said, "Girls,

我問她們，「女孩子們，

how many teenage girls do you think the British public think

你們猜一下，英國大眾認為

get pregnant every year?"

英國的未成年女生每年懷孕的人數有多少？」

And the girls were apoplectic when I said

那些女孩子們聽到我的回答，幾乎要中風了，

the British public think that 15 out of every 100 teenage girls

我說，「英國大眾認為你們平均每年

100 個人裡面有 15 個人會懷孕。」

get pregnant in the year.

And they had every right to be angry,

她們的確有權力表達她們的憤怒，

because in fact, I'd have to have closer to 200 dots

因為事實上，

根據官方的數據，

before I could color one in,

我必須有將近200個圓點

in terms of what the official figures tell us.

[官方數據：每一百人中有0.6人] 才能在其中一個上色。

And rather like numeracy, this is not just an English problem.

算術能力不是只有英國才有的問題。

Ipsos MORI expanded the survey in recent years to go across the world.

MORI市場調查公司，最近這幾年， 也到全世界進行其它調查。

And so, they asked Saudi Arabians,

他們去問沙烏地阿拉伯人：

for every 100 adults in your country,

在你們國家的成年人當中，

how many of them are overweight or obese?

平均每100人有多少人是 體重過重或肥胖的？

And the average answer from the Saudis was just over a quarter.

那些沙烏地阿拉伯人回答： 平均應該比四分之一多一點，

That's what they thought.

這是他們自己認為的數字，

Just over a quarter of adults are overweight or obese.

只有 28% 的人是有體重過重或肥胖的問題。

實際上，官方數據是將近四分之三，

The official figures show, actually, it's nearer to three-quarters.

(Laughter)

（笑聲）

So again, a big variation.

所以你看，差距很大。

And I love this one: they asked in Japan, they asked the Japanese,

我喜歡這一個，他們問日本人說：

for every 100 Japanese people,

「每100個日本人中，

how many of them live in rural areas?

有多少人住在農村地區？」

The average was about a 50-50 split, just over halfway.

他們說大概 50-50 ，差不多剛過半。

They thought 56 out of every 100 Japanese people lived in rural areas.

他們認為每 100 個人中， 有 56 個人住在農村地區。

The official figure is seven.

但官方數據只有 7 。

So extraordinary variations, and surprising to some,

如此大的差距，讓有些人很驚訝，

but not surprising to people who have read the work

但有些人看到這個數據時並會不感到驚訝，

of Daniel Kahneman, for example, the Nobel-winning economist.

像是，諾貝爾獎經濟得主，丹尼爾·卡尼曼。

He and his colleague, Amos Tversky, spent years researching this disjoint

他和他的同事，阿姆斯·特爾斯基，

花了好幾年的時間研究 人們的主觀與實際上的差距，

between what people perceive and the reality,

the fact that people are actually pretty poor intuitive statisticians.

他們發現， 人們在對統計方面的直覺度相當薄弱。

And there are many reasons for this.

這有很多原因。

Individual experiences, certainly, can influence our perceptions,

個人經歷，肯定會影響我們的觀念，

but so, too, can things like the media reporting things by exception,

同時，媒體對於例外事件的報導， 而不是平常的事，

rather than what's normal.

也會影響我們的觀念。

Kahneman had a nice way of referring to that.

關於這一點，卡尼曼有一個很好的比喻。

He said, "We can be blind to the obvious" --

他說，「我們經常無視於明顯的事情——

so we've got the numbers wrong --

所以，我們都猜錯了數字——

但我們若對我們的無知也一無所知， 那就真的太瞎了。」

"but we can be blind to our blindness about it."

And that has enormous repercussions for decision making.

而且這對你做決定，會有很大的影響。

So at the statistics office while this was all going on,

所以，我在統計辦公室 面對這樣的事情時，

I thought this was really interesting.

我心想，這真的很有趣。

I said, this is clearly a global problem,

我是說，這是個全球性的問題，

但也許只是因為地理性的問題。

but maybe geography is the issue here.

These were questions that were all about, how well do you know your country?

這些問題是不是 與你對國家的認知有關？

So in this case, it's how well do you know 64 million people?

像是測驗你對6400萬人口的認識？

Not very well, it turns out. I can't do that.

很難，其實，我也辦不到。

So I had an idea,

所以，我想到了一個辦法，

which was to think about this same sort of approach

跟這些問題的問法有點像，

but to think about it in a very local sense.

但會要你去思考比較當地的問題。

Is this a local?

會不會當地的問題就比較好回答？

If we reframe the questions and say,

如果我們把問題改成，比如說，

how well do you know your local area,

你對當地的認識有多深，

would your answers be any more accurate?

你會不會回答地比較精準？

So I devised a quiz:

所以，我設計了這樣的測試：

How well do you know your area?

你對你所在的區域認識有多深？

It's a simple Web app.

這是一個很簡單的網路 App 應用程式。

You put in a post code

你只要輸入郵遞區號，

and then it will ask you questions based on census data

然後程式就會問你一些

for your local area.

當地資料調查出來的問題。

And I was very conscious in designing this.

我很小心地設計這個應用程式。

I wanted to make it open to the widest possible range of people,

我希望對吸引絕大部分人，

not just the 49 percent who can get the numbers.

而不是只有 49% 的人會回答而已。

I wanted everyone to engage with it.

我希望每個人都能參與回答。

So for the design of the quiz,

所以，為了設計這個測試，

I was inspired by the isotypes

我被奧圖·紐拉特

在1920~1930年所用的圖像符號所啟發。

of Otto Neurath from the 1920s and '30s.

Now, these are methods for representing numbers

他的方法是利用重複的圖像

using repeating icons.

代表不同的數字。

And the numbers are there, but they sit in the background.

數字就隱藏在圖像的背後，

So it's a great way of representing quantity

所以用這樣的方式表達數量， 是一個很好的方式，

without resorting to using terms like "percentage,"

不須要用「百分比」、

"fractions" and "ratios."

「分數」、「比例」來表示。

So here's the quiz.

這裡是這個測試，

測試展現的方式是這樣的：

The layout of the quiz is,

you have your repeating icons on the left-hand side there,

你的左邊會有一些重複的圖像，

and a map showing you the area we're asking you questions about

題目中地區的地圖

on the right-hand side.

顯示在你的右手邊。

There are seven questions.

一共有七個問題。

Each question, there's a possible answer between zero and a hundred,

每一個問題的答案是零到100

回答完題目後，

and at the end of the quiz,

you get an overall score between zero and a hundred.

你會得到一個零到100的分數。

And so because this is TEDxExeter,

因為我們這一場在埃克塞特舉辦的 TEDx演講，

I thought we would have a quick look at the quiz

我想，我們可以很快的看一下

for the first few questions of Exeter.

有關埃克塞特的一些問題。

And so the first question is:

第一題：

每100人中，有多少人是未滿16歲的？

For every 100 people, how many are aged under 16?

Now, I don't know Exeter very well at all, so I had a guess at this,

我對埃克塞特也不是很了解， 所以我也只能用猜的，

but it gives you an idea of how this quiz works.

但你可以透過這個考試來了解。

You drag the slider to highlight your icons,

你可以拖曳這個滑標來標示圖像，

and then just click "Submit" to answer,

然後點選「提交」傳送答案，

and we animate away the difference between your answer and reality.

我們就會將你的答案與實際的差距 用動畫方式表示出來。

And it turns out, I was a pretty terrible guess: five.

結果，我猜的答案（24）差很多， 答案是5。

How about the next question?

下一問題呢？

這一題問平均年齡是多少，

This is asking about what the average age is,

so the age at which half the population are younger

哪一半的人口較年輕，

另一半較老。

and half the population are older.

And I thought 35 -- that sounds middle-aged to me.

我猜是35歲， 因為我覺得那是中年人的年紀。

(Laughter)

（笑聲）

Actually, in Exeter, it's incredibly young,

實際上，埃克塞特的人口相當年輕（20），

and I had underestimated the impact of the university in this area.

我低估了這個區域裡的大學的影響。

The questions get harder as you go through.

接下來的題目越來越難。

So this one's now asking about homeownership:

這一題是關於擁有房產的人口比例：

For every 100 households, how many are owned with a mortgage or loan?

每100人中，有多少人有設定或揹貸款？

And I hedged my bets here,

保險起見，我猜高一點，

because I didn't want to be more than 50 out on the answer.

因為我不想一半的答案都是錯的。

(Laughter)

（笑聲） [實際：25，你猜：50]

And actually, these get harder, these questions,

實際上，這些題目越來越難，

because when you're in an area, when you're in a community,

因為如果你是在地的，你身處當地的社區，

things like age -- there are clues to whether a population is old or young.

像年齡這種問題...人口的老、少 多少還有點線索可尋，

Just by looking around the area, you can see it.

只要稍微觀察一下你的生活周遭即可。

Something like homeownership is much more difficult to see,

但像是有多少人擁有房產， 這就很難看得出來，

so we revert to our own heuristics,

所以我們會採用我們個人的「啟發法」，

our own biases about how many people we think own their own homes.

也就是我們對「有多少人擁有房產」 這件事情上的個人偏見。

Now the truth is, when we published this quiz,

事實上，當我們公佈這些問題後，

the census data that it's based on was already a few years old.

調查的結果是基於幾年前的資料。

We've had online applications that allow you to put in a post code

我們的線上應用程式 讓你可以在輸入郵遞區號後，

and get statistics back for years.

取得數年之前的統計資料。

So in some senses,

所以在某些方面，

this was all a little bit old and not necessarily new.

有些資料已經有點老舊、還沒有更新。

But I was interested to see what reaction we might get

但我當時比較有興趣的是，

如果把這些問題變得比較遊戲化， 大家會有什麼樣的反應，

by gamifying the data in the way that we have,

by using animation

藉由動畫，

and playing on the fact that people have their own preconceptions.

和娛樂方式來看看大家對自己偏見的反應。

It turns out, the reaction was, um ...

結果，反應...相當...嗯...

was more than I could have hoped for.

比我想像的還熱烈。

長久以來的我的一個野心就是，

It was a long-held ambition of mine to bring down a statistics website

因應大眾的要求， 設立一個統計網站。

due to public demand.

(Laughter)

（笑聲）

This URL contains the words "statistics," "gov" and "UK,"

這個連結包括了「統計」、 「政府」、「英國」這些字眼，

which are three of people's least favorite words in a URL.

它在連結上有三個字是人們最不喜歡的。

And the amazing thing about this was that the website came down

令人驚訝的是，

網站在當天晚上9點50分上架後，

at quarter to 10 at night,

because people were actually engaging with this data

因為這個時段，人們比較會想要

of their own free will,

利用自己的時間，

using their own personal time.

自在地參與這項資料的問答。

I was very interested to see

我很驚訝，

that we got something like a quarter of a million people

差不多有將近25萬人

playing the quiz within the space of 48 hours of launching it.

在網站發佈後的48小時內， 玩了這些問題的遊戲。

And it sparked an enormous discussion online, on social media,

它在網路、社群媒體上 引起了熱烈的討論，

which was largely dominated

那些討論的人大多數

by people having fun with their misconceptions,

對自己的錯覺感到相當驚喜，

which is something that I couldn't have hoped for any better,

這個結果在某些方面，

遠遠超出我的意料之外。

in some respects.

I also liked the fact that people started sending it to politicians.

我也因為有人開始把這個遊戲寄給政治人物 覺得很開心。

How well do you know the area you claim to represent?

讓這些民意代表考考 他們對自己所代表的區域是否熟悉？

(Laughter)

（笑聲）

And then just to finish,

做為總結，

going back to the two kinds of people,

回到之前把人分成兩種的問題上，

I thought it would be really interesting to see

我在想，

如果可以請那些對數字很懂的人 來回答這些題目，應該會很有趣。

how people who are good with numbers would do on this quiz.

The national statistician of England and Wales, John Pullinger,

英格蘭威爾斯國家統計學者，約翰·普林爾，

你可能會認為他應該會表現不錯。

you would expect he would be pretty good.

He got 44 for his own area.

他在他自己的區域才得到44分。

(Laughter)

（笑聲）

Jeremy Paxman -- admittedly, after a glass of wine -- 36.

傑諾米·帕斯曼，他自己承認， 在小酌一杯酒後，得到了36分，

Even worse.

還更差。

It just shows you that the numbers can inspire us all.

這僅僅是告訴我們，數字可以啟發我們所有人。

They can surprise us all.

也可以讓我們所有人感到驚訝。

So very often, we talk about statistics

所以，每當我們提到統計，

as being the science of uncertainty.

想到的都是科學與不確定性。

My parting thought for today is:

我今天要告訴大家的是：

actually, statistics is the science of us.

實際上，統計是與我們生活 息息相關的科學，

And that's why we should be fascinated by numbers.

而這也是為什麼 我們應該要對數字感到有趣的原因。

Thank you very much.

非常感謝各位。

(Applause)

（掌聲）