Peter Donnelly: How stats fool juries

As other speakers have said, it's a rather daunting experience --

Beste hizlariek esan duten moduan, nahiko esperientzia beldulgarria da -

a particularly daunting experience -- to be speaking in front of this audience.

esperientzia bereziki beldulgarria da - entzuleria honen aurrean hitz egitea.

But unlike the other speakers, I'm not going to tell you about

Baina besteek ez bezala, nik

the mysteries of the universe, or the wonders of evolution,

unibertsoko misterioei edo eboluzioaren edertasunari

or the really clever, innovative ways people are attacking

edo gure munduko desberdintasun handienei aurre egiteko

the major inequalities in our world.

erabiltzen ari diren modu berritzaileei buruz hitz egingo dizuet.

Or even the challenges of nation-states in the modern global economy.

Edo ekonomia global modernoan nazioek dituzten erronkei buruz.

My brief, as you've just heard, is to tell you about statistics --

Nire lana, estatistikaz hitz egitea da --

and, to be more precise, to tell you some exciting things about statistics.

hobe esanda, estatistikaren gauza liluragarriak kontatzea.

And that's --

Eta hori...

(Laughter)

(barreak)

-- that's rather more challenging

hori nire aurrekoek egindakoa, eta

than all the speakers before me and all the ones coming after me.

ondorendoek egingo dutena baino zailagoa da.

(Laughter)

(barreak)

One of my senior colleagues told me, when I was a youngster in this profession,

Lanbide honetan berria nintzenean, lankide batek esan zidan

rather proudly, that statisticians were people who liked figures

estatistikariak zenbakiak maite zituzten, baina kontable izateko

but didn't have the personality skills to become accountants.

pertsonalitaterik ez zuten pertsonak zirela.

(Laughter)

(barreak)

And there's another in-joke among statisticians, and that's,

Estatistikoen arteko beste txiste batek dio:

"How do you tell the introverted statistician from the extroverted statistician?"

"Nola ezberdindu estatistikari introbertitu bat

To which the answer is,

estatistikari extrobertitu batengandik?"

"The extroverted statistician's the one who looks at the other person's shoes."

"Estatistikari extrobertitua beste pertsonaren zapatetara begiratzen duena da"

(Laughter)

(barreak)

But I want to tell you something useful -- and here it is, so concentrate now.

Baina gauza bat esan nahi dizuet - eta orain doa, beraz adi.

This evening, there's a reception in the University's Museum of Natural History.

Gaur harrera bat dago Unibertsitateko Natur Zientzien Museoan.

And it's a wonderful setting, as I hope you'll find,

Ikusiko duzuen bezala, toki zoragarri bat da,

and a great icon to the best of the Victorian tradition.

tradizio victoriar hoberenaren ikono handi bat.

It's very unlikely -- in this special setting, and this collection of people --

Nekez gertatuko da, toki berezi horretan, hainbeste jende artean,

but you might just find yourself talking to someone you'd rather wish that you weren't.

baina gerta daiteke, nahi ez duzuen norbaitekin hitz egiten amaitzea.

So here's what you do.

Hau da egin behar duzuena.

When they say to you, "What do you do?" -- you say, "I'm a statistician."

"Zein da zure lanbidea?" galdetzean, "Estatistikaria naiz" erantzun.

(Laughter)

(barreak)

Well, except they've been pre-warned now, and they'll know you're making it up.

Beno, orain abisatuta zaudete, eta asmatzen ari zaretela jakingo du,

And then one of two things will happen.

baina bestela, bi gauza pasa daitezke.

They'll either discover their long-lost cousin in the other corner of the room

Gelaren beste puntan lehengusu bat aurkituko du,

and run over and talk to them.

eta harekin hitz egitera joango da,

Or they'll suddenly become parched and/or hungry -- and often both --

edo bapatean goseak eta egarriak ipiniko da -askotan biak-

and sprint off for a drink and some food.

eta edateko eta jateko zerbaiten bila joango da.

And you'll be left in peace to talk to the person you really want to talk to.

Eta zu lasai geratuko zara, benetan hitz egin nahi duzunarengana joateko.

It's one of the challenges in our profession to try and explain what we do.

Gure lanbidearen erronketako bat egiten duguna azaltzea da.

We're not top on people's lists for dinner party guests and conversations and so on.

Afari, hitzaldi eta horrelakoetara ez gaituzte gonbidatzen.

And it's something I've never really found a good way of doing.

Sekula ez dut asmatu hori nola lortu.

But my wife -- who was then my girlfriend --

Baina nire emazteak - orduan nire neskalagunak -

managed it much better than I've ever been able to.

nik sekula lortu ez dudana lortu zuen.

Many years ago, when we first started going out, she was working for the BBC in Britain,

Duela urte asko, elkarrekin hasi ginenean, berak BBCrako lan egiten zuen, Britainia Handian,

and I was, at that stage, working in America.

eta ni une horretan Estatu Batuetan nengoen lanean.

I was coming back to visit her.

Bera bisitatzera joan nintzen batean,

She told this to one of her colleagues, who said, "Well, what does your boyfriend do?"

bere laneko batek "eta zure mutil lagunak zer egiten du?" galdetu zion

Sarah thought quite hard about the things I'd explained --

Sarah-k nik azaldu nizkion gauzei buruz pentsatu,

and she concentrated, in those days, on listening.

egun haietan entzuten arreta jarri zuen,

(Laughter)

(barreak)

Don't tell her I said that.

Ez esan halakorik esan dudanik.

And she was thinking about the work I did developing mathematical models

eboluzioa eta genetika ulertzeko eredu matematikoak

for understanding evolution and modern genetics.

garatzen burutu nuen lanean pentsatu zuen

So when her colleague said, "What does he do?"

eta bere lankideak "zer egiten du?" galdetzean

She paused and said, "He models things."

Sarah-k etenaldi bat egin eta esan zion "gauzak modelatzen ditu".

(Laughter)

(barreak)

Well, her colleague suddenly got much more interested than I had any right to expect

Bere lankidea, bapatean, espero zitekeena baina gehiago interesatu zen

and went on and said, "What does he model?"

eta jarraitu zuen "zer modelatzen du?"

Well, Sarah thought a little bit more about my work and said, "Genes."

Sarh-k nire lanean pixka bat gehiago pentsatu eta "geneak" esan zion

(Laughter)

(barreak)

"He models genes."

"geneak modelatzen ditu".

That is my first love, and that's what I'll tell you a little bit about.

Hau da nire bizitzako amodioa, eta hortaz pixka bat hitz egingo dut.

What I want to do more generally is to get you thinking about

Gure munduan zoriak eta probabilitateak

the place of uncertainty and randomness and chance in our world,

duten lekuan pentsatzea nahi dut,

and how we react to that, and how well we do or don't think about it.

eta horren aurrean nola jokatzen dugun.

So you've had a pretty easy time up till now --

Orain arte nahiko erraza izan da,

a few laughs, and all that kind of thing -- in the talks to date.

orain arteko hitzaldietan barre batzuk egin dituzue.

You've got to think, and I'm going to ask you some questions.

Orain pentsatu egin behar duzue, galderak egingo dizkizuet.

So here's the scene for the first question I'm going to ask you.

Beraz, hau da lehen galderaren eszenatokia:

Can you imagine tossing a coin successively?

Imaginatu zaitezte txanpon bat behin eta berriz airera botatzen

And for some reason -- which shall remain rather vague --

eta arrazoi batengatik, ez dugu zehaztuko zergatik,

we're interested in a particular pattern.

patroi zehatz batetan interesa dugu.

Here's one -- a head, followed by a tail, followed by a tail.

Esaterako: aurpegia, gurutzea, gurutzea.

So suppose we toss a coin repeatedly.

Beraz txanpon bat behin eta berriz jaurtitzen dugu.

Then the pattern, head-tail-tail, that we've suddenly become fixated with happens here.

Eta... aurpegia-gurutzea-gurutzea, gure patroia agertzen da.

And you can count: one, two, three, four, five, six, seven, eight, nine, 10 --

Kontatu eta bat, bi, hiru, lau, bost, sei, zazpi, zortzi, bederatzi, hamar,

it happens after the 10th toss.

hamargarren jaurtiketaren ostean gertatu da.

So you might think there are more interesting things to do, but humor me for the moment.

Gauza interesgarriagoak egin daitezkeela pentsatuko duzue, baina jarrai iezaidazue une batez.

Imagine this half of the audience each get out coins, and they toss them

Imajinatu entzuleriaren alde honetako bakoitzak txanpon bat atera eta

until they first see the pattern head-tail-tail.

aurpegi-gurutze-gurutze patroia atera arte jaurtitzen duela.

The first time they do it, maybe it happens after the 10th toss, as here.

Egiten duten lehen aldian agian hamargarren jaurtiketan gertatzen da.

The second time, maybe it's after the fourth toss.

Bigarrenean agian laugarrenean.

The next time, after the 15th toss.

Eta ondoren hamabosgarrenean.

So you do that lots and lots of times, and you average those numbers.

Beraz txanpona askotan botatzen duzue, eta zenbaki horien bataz bestekoa kalkulatzen duzue.

That's what I want this side to think about.

Horretan pentsatzea nahi dut.

The other half of the audience doesn't like head-tail-tail --

Entzuleriaren beste aldeak ez du aurpegi-gurutze-gurutze nahi,

they think, for deep cultural reasons, that's boring --

arrazoi kulturalengatik aspergarria dela uste dute,

and they're much more interested in a different pattern -- head-tail-head.

eta gehiago gustatzen zaie aurpegi-gurutze-aurpegi patroia.

So, on this side, you get out your coins, and you toss and toss and toss.

Beraz hemen ere, txanponak atera eta jaurti eta jaurti hasten dira.

And you count the number of times until the pattern head-tail-head appears

Jaurtiketak kontatzen dituzte aurpegi-gurutze-aurpegi patroia atera arte.

and you average them. OK?

Eta bataz bestekoa ateratzen dute, ados?

So on this side, you've got a number --

Beraz alde honetan zenbaki bat dute,

you've done it lots of times, so you get it accurately --

askotan egin dute beraz zenbakia zehatza da,

which is the average number of tosses until head-tail-tail.

aurpegi-gurutze-gurutze lortu arte behar diren jaurtiketen bataz bestekoa da.

On this side, you've got a number -- the average number of tosses until head-tail-head.

Hemen beste zenbaki bat dute, aurpegi-gurutze-aurpegi lortu harteko bataz besteko jaurtiketa kopurua.

So here's a deep mathematical fact --

Hemen gauza matematiko sakon bat topatuko dugu,

if you've got two numbers, one of three things must be true.

bi zenbaki badituzu, hiru gauza gerta daitezke.

Either they're the same, or this one's bigger than this one,

Edo berdinak dira, bat bestea baino handiagoa da,

or this one's bigger than that one.

edo alderantziz.

So what's going on here?

Beraz, hemen zer gertatzen da?

So you've all got to think about this, and you've all got to vote --

Guztiok pentsatu behar duzue, eta guztiok erantzun behar duzue,

and we're not moving on.

bestela ez dugu jarraituko.

And I don't want to end up in the two-minute silence

Eta ez dut bi minutuko isilunearekin amaitu nahi

to give you more time to think about it, until everyone's expressed a view. OK.

guztioi erantzuteko denbora emateko.

So what you want to do is compare the average number of tosses until we first see

aurpegi-gurutze-aurpegi patroia lortu arte behar ditugun bataz besteko jaurtiketa kopurua

head-tail-head with the average number of tosses until we first see head-tail-tail.

aurpegi-gurutze-gurutze patroia lortu arte behar ditugunekin konparatu behar duzue.

Who thinks that A is true --

Zeintzuk uste dute A egia dela,

that, on average, it'll take longer to see head-tail-head than head-tail-tail?

bataz beste denbora gehiago beharko dela aurpegi-gurutze-aurpegi lortzeko aurpegi-gurutze-gurutze baino?

Who thinks that B is true -- that on average, they're the same?

Nork uste du B egia dela, batez bestekoa berdina dela?

Who thinks that C is true -- that, on average, it'll take less time

Nork uste du C egia dela, bataz beste denbora gutxiago beharko dela

to see head-tail-head than head-tail-tail?

aurpegi-gurutze-gurutze lortzeko aurpegi-gurutze-gurutze lortzeko baino?

OK, who hasn't voted yet? Because that's really naughty -- I said you had to.

Ados, nor falta da erantzuteko? Hori bihurrikeria bat da, erantzun egin behar zela esan dut.

(Laughter)

(barreak)

OK. So most people think B is true.

Ados, gehiengoak uste du B dela egia.

And you might be relieved to know even rather distinguished mathematicians think that.

Eta lasai, matematikari ezagun batzuek ere hori pentsatzen dute eta.

It's not. A is true here.

Baina ez, A da egia.

It takes longer, on average.

Bataz beste denbora gehiago behar du.

In fact, the average number of tosses till head-tail-head is 10

Izatez, aurpegi-gurutze-aurpegi lortzeko bataz besteko jaurtiketa kopurua 10 da

and the average number of tosses until head-tail-tail is eight.

eta aurpegi-gurutze-gurutze lortzeko 8.

How could that be?

Nola da posible hau?

Anything different about the two patterns?

Patroietan desberdintasunen bat dago?

There is. Head-tail-head overlaps itself.

Bai. aurpegi-gurutze-aurpegi gainjarri egiten da.

If you went head-tail-head-tail-head, you can cunningly get two occurrences

Aurpegi-gurutze-aurpegi bilatzen baduzu, zortearekin patroiaren

of the pattern in only five tosses.

bi sekuentzia lor ditzakezu bost jaurtiketatan.

You can't do that with head-tail-tail.

Hori ezin duzu aurpegi-gurutze-gurutze patroiarekin lortu.

That turns out to be important.

Eta hori garrantzitsua da.

There are two ways of thinking about this.

Bi modu daude honen inguruan pentsatzeko.

I'll give you one of them.

Bat erakutsiko dizuet.

So imagine -- let's suppose we're doing it.

Imajinatu, demagun egiten ari garela.

On this side -- remember, you're excited about head-tail-tail;

Alde honetan, gogoratu aurpegi-gurutze-gurutze

you're excited about head-tail-head.

eta zuek aurpegi-gurutze-aurpegi.

We start tossing a coin, and we get a head --

Txanpona jaurti eta aurpegia ateratzen da,

and you start sitting on the edge of your seat

zuen eserlekuaren iskinan zaudete, zerbait handia

because something great and wonderful, or awesome, might be about to happen.

ederra edo sinesgaitza gerta daitekeelako.

The next toss is a tail -- you get really excited.

Bigarren jaurtiketa gurutzea ateratzen da, benetan gustora zaudete.

The champagne's on ice just next to you; you've got the glasses chilled to celebrate.

Txanpaina izotzetan sartuta dago, eta kopak ospatzeko prest daude.

You're waiting with bated breath for the final toss.

Bihotza abiada bizian duzue azken jaurtiketan.

And if it comes down a head, that's great.

Aurpegia ateratzen bada izugarria izango da.

You're done, and you celebrate.

Lortu eta ospatu egingo duzue.

If it's a tail -- well, rather disappointedly, you put the glasses away

Gurutzea ateratzen bada, beno etsigarria da, kopak gorde

and put the champagne back.

eta txanpaina bere lekuan uzten duzue.

And you keep tossing, to wait for the next head, to get excited.

Eta jaurtitzen jarraitzen duzue, hurrengo aurpegiaren zain.

On this side, there's a different experience.

Alde honetan esperientzia ezberdina da.

It's the same for the first two parts of the sequence.

Berdina da sekuentziaren lehen bi zatitan.

You're a little bit excited with the first head --

Pixka bat gustora zaudete lehen aurpegiarekin,

you get rather more excited with the next tail.

eta oso gustura hurrengo gurutzearekin.

Then you toss the coin.

Orduan txanpona jaurtitzen duzue.

If it's a tail, you crack open the champagne.

Gurutzea bada txanpaina irekitzen duzue.

If it's a head you're disappointed,

Aurpegia bada, etsigarria da,

but you're still a third of the way to your pattern again.

baina zuen patroiaren herena badaukazue jada.

And that's an informal way of presenting it -- that's why there's a difference.

Eta hori aurkezteko modu ez formala litzateke, baina hori da desberdintasuna.

Another way of thinking about it --

Ikusteko beste modu bat,

if we tossed a coin eight million times,

txanpona 8 milioi aldiz botatzen badugu,

then we'd expect a million head-tail-heads

milioi bat aurpegi-gurutze-aurpegi esperoko genituzke

and a million head-tail-tails -- but the head-tail-heads could occur in clumps.

eta milioi bat aurpegi-gurutze-gurutze, baina aurpegi-gurutze-gurutzeak multzoka ager daitezke.

So if you want to put a million things down amongst eight million positions

Beraz, milioi bat gauza zortzi milioi posiziotan ipintzen badituzue

and you can have some of them overlapping, the clumps will be further apart.

eta gainjartze apur bat onartzen baduzue, multzoak elkarrengandik hurrunago egongo dira.

It's another way of getting the intuition.

Hau ulertzeko beste modu bat da.

What's the point I want to make?

Zer esan nahi dut?

It's a very, very simple example, an easily stated question in probability,

Oso adibide sinplea da, probabilitate galdera xume bat,

which every -- you're in good company -- everybody gets wrong.

eta guztiek, eta lagunarte onean zaudete, gaizki erantzuten dute.

This is my little diversion into my real passion, which is genetics.

Hau da nire pasioarekin, genetikarekin, lotuta nire dibertimentu txikia.

There's a connection between head-tail-heads and head-tail-tails in genetics,

Bada erlazio bat, aurpegi-gurutze-aurpegi eta aurpegi-gurutze-gurutzeren artean.

and it's the following.

Eta hau da.

When you toss a coin, you get a sequence of heads and tails.

Txanpona jaurtitzean, aurpegi eta gurutzeen sekuentzia bat lortzen duzu.

When you look at DNA, there's a sequence of not two things -- heads and tails --

DNA ikustean sekuentzia bat dago, baina ez bi gauzena soilik,

but four letters -- As, Gs, Cs and Ts.

lau hizkiena baizik, A, G, C eta T.

And there are little chemical scissors, called restriction enzymes

Eta guraize kimiko txiki batzuk daude, errestrikzio entzimak,

which cut DNA whenever they see particular patterns.

patroi jakin bat ikustean DNA mozten dutenak.

And they're an enormously useful tool in modern molecular biology.

Biologia molekular modernoan oso erabilgarriak diren tresna bat dira.

And instead of asking the question, "How long until I see a head-tail-head?" --

Eta "aurpegi-gurutze-aurpegi lortzeko zenbat jaurtiketa behar dira?" galdetu beharrean,

you can ask, "How big will the chunks be when I use a restriction enzyme

"zein tamaina izango dute adibidez G-A-A-G patroia ikustean mozten duten

which cuts whenever it sees G-A-A-G, for example?

errestrikzio entzimak erabiltzen baditut?" galdetu dezakegu.

How long will those chunks be?"

Ze tamainako pusketak izango ditut?

That's a rather trivial connection between probability and genetics.

Hau probabilitatearen eta genetikaren arteko azaleko lotura bat da.

There's a much deeper connection, which I don't have time to go into

Lotura sakonago bat ere badago, baina ez daukat hura aztertzeko denborarik,

and that is that modern genetics is a really exciting area of science.

genetika modernoa zientziaren esparru oso kitzikagarri bat baita benetan.

And we'll hear some talks later in the conference specifically about that.

Eta beranduago honen inguruko hitzaldiak entzungo ditugu.

But it turns out that unlocking the secrets in the information generated by modern

Baina teknologia experimental modernoek sortzen duten informazioaren sekretu batzuk jakiteko

experimental technologies, a key part of that has to do with fairly sophisticated --

gakoetako batzuk teknika sofistikatuetatik etortzen dira,

you'll be relieved to know that I do something useful in my day job,

jakin ezazute nire eguneroko lanean zerbait erabilgarria egiten dudala,

rather more sophisticated than the head-tail-head story --

aurpegi-gurutze-gurutzeren istorioa baino sofistikatuagoa,

but quite sophisticated computer modelings and mathematical modelings

eredu konputazional eta matematiko nahiko konplexuekin,

and modern statistical techniques.

eta teknika estatistiko modernoekin.

And I will give you two little snippets -- two examples --

Nire taldeak Oxford-en daramatzan bi proiekturen

of projects we're involved in in my group in Oxford,

zati txiki batzuk, adibide batzuk, azalduko ditut

both of which I think are rather exciting.

interesgarriak direla uste dut eta.

You know about the Human Genome Project.

Giza genomaren proiektuari buruz entzun duzue.

That was a project which aimed to read one copy of the human genome.

Giza genomaren kopia bat deszifratzea helburu zuen proiektu bat zen.

The natural thing to do after you've done that --

Hau lortu ostean, noski, beste proiektu bat doa,

and that's what this project, the International HapMap Project,

HapMap nazioarteko proiektua,

which is a collaboration between labs in five or six different countries.

5 edo 6 herrialdeetako laborategiek kolaborazioan garatzen duten proiektua.

Think of the Human Genome Project as learning what we've got in common,

Giza genomaren proiektuak zer dugun amankomunean aurkitu nahi du,

and the HapMap Project is trying to understand

HapMap proiektuak, pertsona desberdinen arteko

where there are differences between different people.

diferentziak non dauden ulertu nahi du.

Why do we care about that?

Zergatik axola digu?

Well, there are lots of reasons.

Beno, arrazoi asko daude.

The most pressing one is that we want to understand how some differences

Premiazkoena, zera ulertzea da, diferentzia batzuk nola egiten duten

make some people susceptible to one disease -- type-2 diabetes, for example --

batzuk gaixotasun batzuk izateko joera izatea, 2 motako diabetesa izatera adibidez,

and other differences make people more susceptible to heart disease,

edo gaixotasun kardiakoak izateko joera izatea,

or stroke, or autism and so on.

edo aplopejiak, autismoa...

That's one big project.

Hori proiektu handi bat da.

There's a second big project,

Badago beste proiektu handi bat,

recently funded by the Wellcome Trust in this country,

Wellcome Trust-ek berriki finantziatua,

involving very large studies --

genetika ulertzeko, ikerketa handiak, milaka pertsona

thousands of individuals, with each of eight different diseases,

8 gaixotasun desberdin, 1 eta 2 motako diabetesa,

common diseases like type-1 and type-2 diabetes, and coronary heart disease,

gaixotasun koronarioak eta nahaste bipolarra adibidez,

bipolar disease and so on -- to try and understand the genetics.

barne hartzen dituena.

To try and understand what it is about genetic differences that causes the diseases.

Ze desberdintasun genetikok sortzen dituzten gaixotasunak eta zergatik ulertzeko.

Why do we want to do that?

Zergatik egin nahi dugu?

Because we understand very little about most human diseases.

Giza gaixotasun gehienen inguruan ezer gutxi dakigulako.

We don't know what causes them.

Ez dakigu zerk sortzen dituen.

And if we can get in at the bottom and understand the genetics,

Eta oinarrira iritsi eta genetika ulertu ahalko bagenu,

we'll have a window on the way the disease works,

gaixotasunak nola jokatzen duen jakingo genukeelako.

and a whole new way about thinking about disease therapies

Eta terapiak eta tratamentu prebentiboak ikusteko

and preventative treatment and so on.

modu berri bat izango genukeelako.

So that's, as I said, the little diversion on my main love.

Beraz hori da, nire benetako maitasunaren barnean daukadan dibertimentu txikia.

Back to some of the more mundane issues of thinking about uncertainty.

Ziurtasunik ezaren inguruan egiten ditugun arrazoiketetara itzuliz,

Here's another quiz for you --

hona zuentzat beste askmakizun bat:

now suppose we've got a test for a disease

Imajinatu gaixotasun bat detektatzeko proba bat daukagula.

which isn't infallible, but it's pretty good.

Ez da hutsezina, baino nahiko ona da.

It gets it right 99 percent of the time.

kasuen %99an asmatzen du.

And I take one of you, or I take someone off the street,

Eta zuetako bat, edo kaleko norbait hartzen dut, zoriz,

and I test them for the disease in question.

eta proba hori egiten diot.

Let's suppose there's a test for HIV -- the virus that causes AIDS --

Demagun GIB-rako proba dela, IHESA sortzen duen birusa,

and the test says the person has the disease.

eta probak pertsona gaixo dagoela esaten duela.

What's the chance that they do?

Zein da gaixotasuna izateko probabilitatea?

The test gets it right 99 percent of the time.

Probak kasuen %99an asmatzen du.

So a natural answer is 99 percent.

Beraz erantzun azkarra %99 da.

Who likes that answer?

Nori gustatzen zaio erantzun hori?

Come on -- everyone's got to get involved.

Benga, guztiok parte hartu behar dugu.

Don't think you don't trust me anymore.

Ez pentsatu jada ezin duzuenik nigan konfidantza izan.

(Laughter)

(barreak)

Well, you're right to be a bit skeptical, because that's not the answer.

Ongi dago pixka bat eszeptiko egotea, hori ez baita erantzun zuzena.

That's what you might think.

Hori pentsa dezakezue.

It's not the answer, and it's not because it's only part of the story.

Baina ez da erantzun zuzena, historiaren zati bakarra baita.

It actually depends on how common or how rare the disease is.

Berez, gaixotasunaren hedapenaren araberakoa izango da probabilitatea.

So let me try and illustrate that.

Utzi iezaidazue erakusten.

Here's a little caricature of a million individuals.

Milioi bat pertsonaz osatutako lagina dugu.

So let's think about a disease that affects --

Pentsa dezagun gaixotasun bitxi batean,

it's pretty rare, it affects one person in 10,000.

10.000tik bati eragiten dion batean.

Amongst these million individuals, most of them are healthy

Milioi horretan, gehienak osasuntsu daude,

and some of them will have the disease.

eta batzuk gaixotasun hori izango dute.

And in fact, if this is the prevalence of the disease,

Berez, hori bada gaixotasunaren maiztasuna,

about 100 will have the disease and the rest won't.

gutxi gora behera 100 gaixo izango genituzke.

So now suppose we test them all.

Demagun proba guztiei egiten diegula.

What happens?

Zer gertatzen da?

Well, amongst the 100 who do have the disease,

Gaixotasuna duten 100 pertsonetan,

the test will get it right 99 percent of the time, and 99 will test positive.

Frogak %99tan asmatuko du, eta 99 gaixo detektatuko ditu.

Amongst all these other people who don't have the disease,

Gaixotasuna ez duten pertsonetan,

the test will get it right 99 percent of the time.

frogak %99tan asmatuko du.

It'll only get it wrong one percent of the time.

Kasuen %1ean erratuko da.

But there are so many of them that there'll be an enormous number of false positives.

Baina hainbeste osasuntsu daude, positibo faltsu asko egongo direla.

Put that another way --

Beste era batera esanda,

of all of them who test positive -- so here they are, the individuals involved --

frogak gaixo dagoela esaten duen horietan,

less than one in 100 actually have the disease.

ehunetik batek baino gutxiagok izango du gaixotasuna benetan.

So even though we think the test is accurate, the important part of the story is

Beraz froga zehatza dela uste badugu ere, garrantzitsua zera da,

there's another bit of information we need.

beharrezko den beste informazio bat falta dela.

Here's the key intuition.

Hau da ideia garrantzitsua.

What we have to do, once we know the test is positive,

Froga positiboa dela jakin ostean egin behar duguna zera da,

is to weigh up the plausibility, or the likelihood, of two competing explanations.

lehian dauden bi azalpenen probabilitatea aztertu.

Each of those explanations has a likely bit and an unlikely bit.

Azalpen bakoitzak zati probable eta zati inprobable bat ditu.

One explanation is that the person doesn't have the disease --

Azalpen bat pertsona gaixo ez egotea da,

that's overwhelmingly likely, if you pick someone at random --

hau oso probablea da, norbait zoriz hautatzen baduzu,

but the test gets it wrong, which is unlikely.

baina froga erratu egiten da, eta hau inprobablea da.

The other explanation is that the person does have the disease -- that's unlikely --

Beste azalpena, pertsona gaixo egotea da, inprobablea dena,

but the test gets it right, which is likely.

eta froga zuzen egotea, probablea dena.

And the number we end up with --

Eta topatu nahi dugun zenbaki horrek,

that number which is a little bit less than one in 100 --

ehuneko bat baino txikiagoa den horrek,

is to do with how likely one of those explanations is relative to the other.

azalpen batek bestearekiko duen probabilitatearekin du zerikusia.

Each of them taken together is unlikely.

Multzo bakoitza banaka inprobablea da.

Here's a more topical example of exactly the same thing.

Hona hemen gai bera jorratzen duen adibide berriago bat.

Those of you in Britain will know about what's become rather a celebrated case

Britainia Handikoak zateretenak jakingo duzue, kasua nahiko famatua egin baita.

of a woman called Sally Clark, who had two babies who died suddenly.

Sally Clark izeneko emakume batek bapatean hil ziren bi haur izan zituen.

And initially, it was thought that they died of what's known informally as "cot death,"

Hasieran informalki "sehaskako heriotza" deritzonarengatik,

and more formally as "Sudden Infant Death Syndrome."

formalki, haurren bapateko heriotzagatik hil zirela uste zen.

For various reasons, she was later charged with murder.

Hainbat arrazoirengatik, erahilketa leporatu zitzaion.

And at the trial, her trial, a very distinguished pediatrician gave evidence

Bere epaiketan, pediatra oso ezagun batek ebidentzia bezala esan zuen

that the chance of two cot deaths, innocent deaths, in a family like hers --

bi horrelako heriotza izateko probabilitatea, berea bezalako familia batean,

which was professional and non-smoking -- was one in 73 million.

profesionala eta ez erretzailea, 73 milioiren artean batekoa zela.

To cut a long story short, she was convicted at the time.

Laburtuz kondenatu egin zuten.

Later, and fairly recently, acquitted on appeal -- in fact, on the second appeal.

Geroago, bere bigarren apelazioan, errugabea zela erabaki zen.

And just to set it in context, you can imagine how awful it is for someone

Pentsa ezazue zer izan daitekeen norbaitentzat

to have lost one child, and then two, if they're innocent,

haur bat galtzea, gero bestea galtzea, eta errugabea izanik

to be convicted of murdering them.

erahilketa leporatuta kondenatua izatea.

To be put through the stress of the trial, convicted of murdering them --

Epaiketaren eta seme-alabak galtzearen estresa jasatea

and to spend time in a women's prison, where all the other prisoners

eta emakumezkoen gartzelan denbora pasatzea, beste preso guztiek

think you killed your children -- is a really awful thing to happen to someone.

zure seme-alabak hil zenituela uste duten bitartean. Horrez izugarria izan behar du.

And it happened in large part here because the expert got the statistics

Eta gertatu egin zen. Adituak estatistikak ereabiltzerakoan

horribly wrong, in two different ways.

bi akats egin zituelako.

So where did he get the one in 73 million number?

Beraz, nondik atera zuen "73 milioitik bat" zenbakia?

He looked at some research, which said the chance of one cot death in a family

Bapateko heriotzaren estatistika batzuk kontsultatu zituen, eta

like Sally Clark's is about one in 8,500.

Sally Clark-ena bezelako familia batean hori gertatzeko probabilitatea 8500etik batekoa zela ikusi zuen.

So he said, "I'll assume that if you have one cot death in a family,

Gero pentsatu zuen "familian horrelako heriotza bat izateak

the chance of a second child dying from cot death aren't changed."

ez du beste bat izateko probabilitatea aldatuko".

So that's what statisticians would call an assumption of independence.

Horri estatistikoek independentziaren aurretikoa deitzen diote.

It's like saying, "If you toss a coin and get a head the first time,

"Txanpon bat airera bota eta aurpegia ateratzeak,

that won't affect the chance of getting a head the second time."

ez du bigarren aldiz aurpegia ateratzeko probabilitatea aldatuko" esatea bezala da.

So if you toss a coin twice, the chance of getting a head twice are a half --

Beraz txanpon bat airera bi aldiz botatzen baduzu, bi aldiz aurpegia ateratzeko probabilitatea erdia,

that's the chance the first time -- times a half -- the chance a second time.

lehen aldiz aurpegia ateratzeko probabilitatea, bider erdia, bigarreneko probabilitatea, da.

So he said, "Here,

Beraz esan zuen, "demagun

I'll assume that these events are independent.

bi gertaerak independenteak direla pentsatuko dut,

When you multiply 8,500 together twice,

8500 bider 8500,

you get about 73 million."

73 milioi inguru da".

And none of this was stated to the court as an assumption

Eta guzti hau ez zitzaion zinpekoei suposizio gisa,

or presented to the jury that way.

edo modu honetara azaldu.

Unfortunately here -- and, really, regrettably --

Zoritxarrez, lehenik eta behin

first of all, in a situation like this you'd have to verify it empirically.

egoera horretan enpirikoki egiaztatu beharko litzateke.

And secondly, it's palpably false.

Eta bigarrenik, erabat faltsua da.

There are lots and lots of things that we don't know about sudden infant deaths.

Gauza asko dira bapateko haurren heriotzari buruz ez dakizkigunak.

It might well be that there are environmental factors that we're not aware of,

Posible da ezagutzen ez ditugun faktore anbientalak egotea,

and it's pretty likely to be the case that there are

eta oso litekeena da ere, ezagutzen

genetic factors we're not aware of.

ez ditugun faktore genetikoak egotea.

So if a family suffers from one cot death, you'd put them in a high-risk group.

Beraz, familia batek horrelako heriotza jasaten badu, arrisku altuko taldean sartuko zenuke.

They've probably got these environmental risk factors

Ziurrenik, ezagutzen ez ditugun arrisku faktore

and/or genetic risk factors we don't know about.

anbiental eta genetikoak izango dituzte.

And to argue, then, that the chance of a second death is as if you didn't know

Bigarren heriotzaren probabilitatea, informazio hori ezagutuko ez bazenukeenaren

that information is really silly.

berdina izango dela argudiatzea benetan inozoa da.

It's worse than silly -- it's really bad science.

Inozoa baino okerrago, benetan zientzia txarra da.

Nonetheless, that's how it was presented, and at trial nobody even argued it.

Hala ere, hala aurkeztu zen, eta epaiketan inork ez zuen eztabaidatu.

That's the first problem.

Hori da lehen arazoa.

The second problem is, what does the number of one in 73 million mean?

Bigarren arazoa zera da, zer esan nahi du 73 miliotik batek?

So after Sally Clark was convicted --

Beraz Sally Clark kondenatua izan ostean,

you can imagine, it made rather a splash in the press --

imajina dezakezue prentsan izan zuen oihartzuna,

one of the journalists from one of Britain's more reputable newspapers wrote that

Britainia Handiko egunkari errespatuenetako kazetari batek

what the expert had said was,

adituak zera esan zuela idatzi zuen:

"The chance that she was innocent was one in 73 million."

"Errugabea izateko aukera 73 miliotik batekoa zela"

Now, that's a logical error.

Akats logiko izan zen

It's exactly the same logical error as the logical error of thinking that

%99ko zehaztasuna duen gaixotasunaren froga eta gero

after the disease test, which is 99 percent accurate,

gaixotasuna izateko aukera %99koa dela pentsatzearen

the chance of having the disease is 99 percent.

errore bera.

In the disease example, we had to bear in mind two things,

Gaixotasunaren adibidean bi gauza izan behar genituen kontuan,

one of which was the possibility that the test got it right or not.

bat froga erratu zitekeela, eta bestea

And the other one was the chance, a priori, that the person had the disease or not.

a priori, pertsonak gaixo egoteko edo ez egoteko zuen probabilitatea.

It's exactly the same in this context.

Testuinguru honetan gauza bera gertatzen da.

There are two things involved -- two parts to the explanation.

Bi gauza daude, azalpenaren bi zati.

We want to know how likely, or relatively how likely, two different explanations are.

Bi azalpenek duten probabilitatea jakin nahi dugu.

One of them is that Sally Clark was innocent --

Bat Sally Clark errugabea dela,

which is, a priori, overwhelmingly likely --

a priori oso posible dena,

most mothers don't kill their children.

ama gehienek ez dituzte beren seme-alabak hiltzen.

And the second part of the explanation

Eta azalpenaren bigarren zatia

is that she suffered an incredibly unlikely event.

oso inprobablea zen zerbait pasa zela.

Not as unlikely as one in 73 million, but nonetheless rather unlikely.

Ez 73 miliotik behin bezain inprobablea, baina inprobablea hala ere.

The other explanation is that she was guilty.

Beste azalpena erruduna zela da.

Now, we probably think a priori that's unlikely.

A priori inprobablea dela pentsa dezakegu.

And we certainly should think in the context of a criminal trial

Eta horrela pentsatu beharko genuke epaiketa kriminal baten testuinguruan,

that that's unlikely, because of the presumption of innocence.

inprobablea dela, inozentziaren aurretikoari esker.

And then if she were trying to kill the children, she succeeded.

Beraz, seme-alabak hil nahi bazituen, lortu zuen.

So the chance that she's innocent isn't one in 73 million.

Beraz errugabea izateko aukera ez da bat 73 miliotik.

We don't know what it is.

Ez dakigu zenbatekoa den.

It has to do with weighing up the strength of the other evidence against her

Bere aurkako ebidentzia eta ebidentzia

and the statistical evidence.

estatistikoa aztertu behar dira.

We know the children died.

Badakigu haurrak hil zirela.

What matters is how likely or unlikely, relative to each other,

Beraz jakin behar dena bi azalpenen

the two explanations are.

probabilitate erlatiboa da.

And they're both implausible.

Biak sinesgaitzak dira.

There's a situation where errors in statistics had really profound

Estatistikako akatsak ondorio lazgarriak izan zituzten

and really unfortunate consequences.

egoeretako bat da hau.

In fact, there are two other women who were convicted on the basis of the

Izatez, beste bi emakume ere kondenatuak izan ziren

evidence of this pediatrician, who have subsequently been released on appeal.

pediatra honen ebidentziagatik, eta gero aske geratu dira, apelatu ere egin gabe.

Many cases were reviewed.

Kasu asko errebisatu ziren.

And it's particularly topical because he's currently facing a disrepute charge

Eta orain Britainia Handiko Kontseilu Mediku Orokorrean

at Britain's General Medical Council.

ospea galdu du.

So just to conclude -- what are the take-home messages from this?

Beraz, amaitzeko, zein da guzti honen mezua?

Well, we know that randomness and uncertainty and chance

Badakigu zoria, probabilitatea eta ziurtasunik eza

are very much a part of our everyday life.

gure bizitzako zati direla.

It's also true -- and, although, you, as a collective, are very special in many ways,

Egia da ere, nahiz eta zuek oso publiko berezia izan,

you're completely typical in not getting the examples I gave right.

oso tipikoa dela jarri ditudan adibide horiek ez asmatzea.

It's very well documented that people get things wrong.

Oso ongi dokumentatuta dago jendea gauza hauetan erratu egiten dela.

They make errors of logic in reasoning with uncertainty.

Logikako akatsak egiten dira ziurtasunik ezaren inguruan arrazoitzean.

We can cope with the subtleties of language brilliantly --

Hizkuntzaren txikikeriekin oso ongilan egin dezakegu,

and there are interesting evolutionary questions about how we got here.

eta hori nola lortu dugunaren inguruan oso galdera interesgarriak daude.

We are not good at reasoning with uncertainty.

Baina ez gara onak ziurtasunik ezaren inguruan arrazoitzen.

That's an issue in our everyday lives.

Hori gure eguneroko bizitzan arazo bat da.

As you've heard from many of the talks, statistics underpins an enormous amount

Hitzaldi askotan entzun duzuen bezala, estatistika

of research in science -- in social science, in medicine

ikerketa zientifiko askoren, gizarte zientzietan, medikuntzan...

and indeed, quite a lot of industry.

eta industriaren zati handi baten oinbarrian dago.

All of quality control, which has had a major impact on industrial processing,

Industriaren prozesuan inpaktu handia duen kalitate kontrol hori guztia,

is underpinned by statistics.

estatistikan oinarritzen da.

It's something we're bad at doing.

Gaizki egiten dugun zerbait da.

At the very least, we should recognize that, and we tend not to.

Gutxienez onartu egin beharko genuke, baina ez onartzeko joera dugu.

To go back to the legal context, at the Sally Clark trial

Testuinguru legalera bueltatuz, Sally Clark-en epaiketan,

all of the lawyers just accepted what the expert said.

abokatu guztiek adituaren hitzak onartu zituzten, besterik gabe.

So if a pediatrician had come out and said to a jury,

Beraz pediatra batek zinpekoei zera esan bazien:

"I know how to build bridges. I've built one down the road.

"Badakit zubiak eraikitzen. Kale horretan bat eraiki dut.

Please drive your car home over it,"

Mesedez, pasa bertatik zure autoarekin",

they would have said, "Well, pediatricians don't know how to build bridges.

zinpekoek erantzungo zuten: "pediatrek ez dakite zubiak eraikitzen.

That's what engineers do."

Hori injeniarei dagokie."

On the other hand, he came out and effectively said, or implied,

Baina horren ordez iritsi eta esan zuen, edo aditzera eman zuen:

"I know how to reason with uncertainty. I know how to do statistics."

"Badakit nola arrazoitu ziurtasunik gabeko egoeretan, badakit estatistikarekin lan egiten."

And everyone said, "Well, that's fine. He's an expert."

Eta guztiek esan zuten, ados, aditu bat da.

So we need to understand where our competence is and isn't.

Beraz gure konpetentziak non amaitzen diren jakin behar dugu.

Exactly the same kinds of issues arose in the early days of DNA profiling,

Horrelakoxe gauzak atera ziren DNA sekuentziatzen hasi zirenean,

when scientists, and lawyers and in some cases judges,

zientzialariak, abokatuak eta epaileak ere

routinely misrepresented evidence.

sistematikoki frogak desitxuratu zituztenean.

Usually -- one hopes -- innocently, but misrepresented evidence.

Orokorrean, uste dugu, maliziarik gabe, baina frogak desitxuratu zituzten.

Forensic scientists said, "The chance that this guy's innocent is one in three million."

Zientzialari forenseek esan zuten "hau errugabea izateko probabilitatea 3 miliotik batekoa da".

Even if you believe the number, just like the 73 million to one,

Zenbakia sinistuta ere, 73 miliotik bat bezala,

that's not what it meant.

ez du hori esan nahi.

And there have been celebrated appeal cases

Eta apelazio famatuak egon dira horregatik

in Britain and elsewhere because of that.

Britainia Handian, eta beste lekuetan.

And just to finish in the context of the legal system.

Eta lege-sistemaren testuinguruarekin amaitzeko.

It's all very well to say, "Let's do our best to present the evidence."

Oso ongi dago "ahalik eta ongien froga aurkeztea".

But more and more, in cases of DNA profiling -- this is another one --

Baina gero eta gehiago, batez ere DNA-ren azterketen kasuetan,

we expect juries, who are ordinary people --

zinpekoak, pertsona normalak direnak,

and it's documented they're very bad at this --

eta jakina den arren horretan oso txarrak direla,

we expect juries to be able to cope with the sorts of reasoning that goes on.

arrazoitze modu horrekin lan egiteko gai direla uste dugu.

In other spheres of life, if people argued -- well, except possibly for politics --

Bizitzaren beste esparruetan, jendeak ilogikoki argudiatuko balu,

but in other spheres of life, if people argued illogically,

beno politikoak kenduta, beste esparruetan jendeak ilogikoki argudiatuko balu,

we'd say that's not a good thing.

ez dela ona esango genuke.

We sort of expect it of politicians and don't hope for much more.

Politikoengandik espero dugu, baina ez beste inorrengandik.

In the case of uncertainty, we get it wrong all the time --

Ziurtasunik ezaren kasuan beti erratuta gaude, eta

and at the very least, we should be aware of that,

gutxienez kontziente izan beharko genuke.

and ideally, we might try and do something about it.

Eta idealki horen inguruan zerbait egin beharko genuke.

Thanks very much.

Mila esker.