 Non i chi dweud at y cy里adau yn bwysig sy'n meddwl ychynig i ddageddio'r gwrs yn ychydigion yn bwysig, drwych chi'n meddwl i'r meddwl yn ei bod, ac mae'n dweud nowe ac mae'n will yn ychydigion sy'n ddiddorol yn dda, mae'n ddiddorol yn ddiddorol yn ddiddorol. Roeddwn i ddim ohel o'r ddiddorol, oherwydd oedd yn ddiddorol yn ddiddorol. Yes, your chance of generating truths and interesting insights goes up, but the amount of bullshit that's generated also increases and at an even faster rate. Problems like false correlations, for example. Correlation is actually a very weak measure in many ways. Also things like what are occasionally called confounding variables. In other words, there's another variable that you don't have which is causing the correlation. ac ydyn nhw'n cyfleu i ddweud o unrhyw gwasanaethau ar hyn o'r ddweud o'r ffordd yn gwybod. Ac oedd cyfleu i ddweud o'r ddweud yn y rhan y blaen. Gwyddoedd yn ei hunain o'r byd yn ddweud. Rwy'n ddych yn cael cyfnod o'r ddweud yn unrhyw gofio o'r ddweud. Rwy'n ddweud yn cael cyfnod ffaint o'r ddweud o'r ddweud ffaint o'r ddweud o'r ddweud. a mae'r dweud o gynhau dweudio'n dweud. Mae'n dweud o'r ffordd arall ddim yn cymryd ar gyfer gwirioneddol. A dyfodol arall o'r ddechrau sydd yn hynny, mae holl o'r ddweud o gwaith. Dyfodol o ddwych yn digwydd amddangos yn ymgyrch yw ddweud, efallai maen nhw o'r ddechrau a'r ddweud. Mae'r ddweud o'r ddweud yn hwnnw i'r ddweud o ddweud. Mae'r risg, a ddweud hynny'n dweud hynny ymgyrch ddweud ar gyfer, chi'n fath o gweithio'r pwysig yn trafod yn iawn i'ch gweithio, ond yn y gallu feddwl. Fy ddweudio'r dweudio'r dda wedi'u cyfnodd, ond yn y dda'r gweithio'r ddau sy'n gweld yn dweud yn ddweud a phobl yn ddod yn osio'r ddweud yn y ddweud. Fy ddweudio'r ddwyng y cwyl yn ddweud yn yn teimlo'r ddweud sy'n ddweud yn ddweud. A'u gweithio yn ddweud, Rhaid o'r ffordd tellanion gwahanol anodd, oedda'n bwysig mor hwn. Mynd i'r ddweud ydw i g olikaid bwysig yn meddwl y dda am ddelfindio cael amsgolon, a'r sefyllfa'n mewn gwisig wrth ei wneud. Yna, ar ôl gwnaeth arweithio cyfredin hyn ar hyn yn i'w ddweud yr hyn o'ch wneud. Yn dweud y 12 oed, byddwch i gyd yn y fwrdd fath. Mae'n fwrdd y ffordd Fyhl, byddiogelffaeth, felly mae'n ddiolch yn y ffordd wedi gyda'u ffordd Petyl i fynd i'r ffordd. A dda i'r ffordd'r ffordd i ym 3 yrdydd, y ffordd y mae eu ffordd yn ffordd, yw'n ymgyrch o'r ffordd yn ddweud gan gweld. Mae'r ffordd i'r ffordd i'r ffordd. Felly, mae'n ddweud, ych definedd dda i lyfr yw gweithio, fel ddweud i'r ddau. Felly, mae'n ddweud ei wneud yn go ar y syniad sy'n dod yn cael eu gwirionedd, o'r fwy o'r cyffredinol. Rydym yn dweud y gweithio dyna yw ddweud yn cyfyrdd yn cyfyrdd y ffêl oedd yn creu'r ddweud i'r gwirionedd yn y cyfyrdd ychydig i'r ddweud yn ôl, i'r ddweud i ddweud i'r ddweud. Dyna, mae'n meddwl ar gyfer ffêl a'r ddweud i'r gwaith yn y ddweud i'r rhaid drif. sydd angen, hen, sydd y gweithio'n gweithio'n gwahanol gwaith appearedol i'r unrhyw o'r gweithio, a'r gweithio sefydl iawn. Mae'r angen yn gwasanaeth cyflodiadau pan o'r mwyfyr i mi ac rhaid gela, a r emergingol wedi cael gwneud ar gyfer y cyfaint, a'r angen yn fawr yn teimlo arweinio Instancaethol, ac mi'n rhaid gweithio'n gweithio'n gweithio'n cyflodiadau mewn gwahanol, ac yn dod yn hunau o rhaid gweithio am y mwyfyr. Definitely, they were just making suspicies from my neighbours. Now, it turns out that the two things that had happened before the company had started presenting more of the MPG data. One of which is that I've taken a brief trip to France, and you can't use the card in France, and on another occasion I think in the very early days I had forgotten to use the card. So they were two periodswas before the MPG data started to beán produced. My car was actually twice as economical as it really was because I'd done twice the number of miles between visible fill-ups. Once I realised that's what it was, of course I realised that actually what was happening was effectively a form of regression to the mean. I stopped being paranoid. But it would have been very, very easy for me to start lavishing accusations at my neighbour that they were siphoning fuel off, based simply on this data, without the understanding how one or two rogue variables, just one or two rogue variables which you don't notice can cause information to go wonky. Average is really dangerous because the average doesn't really exist. I wrote about this recently in the spectator. When they tried to design an average cockpit for high-speed jet pilots, the expert they brought in who is a physical anthropologist was already sceptical because he'd done work on the measurement of human hands and said that actually the number of human hands that are average across a range of dimensions is surprisingly few. Nearly everybody's hand is weird or an outlier on a few of these dimensions. And sure enough they found the same as true of pilot's body type. And what they found was that not a single pilot out of 4,000 was average across all ten dimensions that they measured. And so his recommendation was you don't need an average seat, you need an adjustable seat, and that you need adjustable controls so that depending on anomalies like the length of your forearm or the length of your legs or the width of your arse or whatever, you can actually adjust the seat accordingly because the solution for average is actually not a solution for everyone, it's a solution for nobody. And I think that's one thing we've got to be really careful of, that we tend to think that when we average we're dealing with more numbers and therefore we have better information. Of course when you average you lose information because the very act of adding disguises things like variance, second order factors which may be the more important thing. So other fears are there are a lot of people who are quite good at statistics by which I mean bad enough to be confident, good enough to be confident that everything they think statistically is true but bad enough to make real schoolboy errors. And there are cases, I mean this is a major problem when you're presenting evidence in court because even quite expert people, very famous case the Sally Clark case in the UK where a solicitor was accused of double infanticide when it was almost certainly a double cop death and a doctor who was an Oxford professor, he was no slouch academically went and basically said the odds that she is responsible for murdering at least one of her children will basically multiply the odds of a double cop death together, square it and then we'll subtract that incredibly unlikely event from one and the odds therefore that it was a double cop death were declared to be something like 80 million to one against. So essentially it said she's definitely a murderer. Now it was appalling by the way because first of all there were both males which increases the odds significantly, they were both children of the same mother and father. Now if there's a genetic basis to cop death which there probably is that further reduces the odds, they were both in the same house so if there were an environmental factor like a strange sort of plastic material in their bedding that could have been again a common variable but worse than that in correct statistical practice you don't compare the chance of a double cop death against everything else you have to compare it against the odds of a double infanticide and double infanticide is really really rare too. Once you make that comparison the odds that she was a murderer are not actually 80 million to one against or whatever they were I mean a near certain thing the odds are actually something like two to one in her favour that she's innocent. I'll give you another example of misuse of statistics now the reason I tell these stories is in lots of areas of maths we can be a bit wrong but our instincts aren't that bad so if you ask me to calculate the surface area of a cone and you ask me to cut an area of cloth that would cover some sort of cone simply instinctively I'd be within an order of magnitude of the right answer I'd be somewhere right just using a hunch with statistics you can literally be wrong as I think the man's name was Roy Meadows Professor Roy Meadows was highly educated people with a room full of baristers he was later censured by the Royal Statistical Society but a whole room full of extraordinarily educated people can be wrong by a factor of millions because they don't understand what's going on and a second case of this is the interesting misuse sometimes called the prosecutor's fallacy sometimes called the defender's fallacy in the O.J. Simpson case because previously Mrs Simpson had wrung the police claiming her husband was beating her up okay and the defence simply said okay, when we get people who ring up the police and say my husband's beating me up how often does that lead to a murder and it was something like one in a thousand times so they convinced the jury to regard that evidence as completely insignificant because it only implied guilt at a level of 0.1% okay however we've got to think about this differently because Mrs Simpson was already dead and if you reverse the question when someone is murdered who has previously complained about abuse from a spouse in what percentage of occasions was the spouse responsible for the murder in those cases it's significantly more than half so you can literally be wrong by a factor of not fives or sixes a factor of a thousand and yet be completely confident in what you're saying and have really intelligent people not contradict you so you really really care about statistics I mean a friend of mine O.L. Peters at the London Mathematical Laboratory makes the point that all of economics is based on a fallacious understanding of probability which is the assumption of ergodicity now I won't go into this look up ergodicity because it's a whole area of discussion from theoretical physics to probability to economics now but essentially there's the assumption that what's good for ten people doing something once is good for one person doing something ten times in a row so if ten people do something once and it's good on average therefore that's good for you to do ten times in a row now if I take a very exaggerated example if I offered everybody watching this course a million pounds to play Russian roulette once a few people would probably say yes one in six chance of death five in six chance of getting a million there'd be quite a few people who go I'll take those odds everybody's going to take almost any amount of money to play Russian roulette say six times in a row or ten times in a row there was one person apparently who would take a billion pounds to play Russian roulette ten times in a row you're almost certainly going to be dead I would say that's a terribly bad bet even though on average obviously you end up richer and I've suddenly realised that using this misunderstanding of ergodicity has been really useful in problem solving you go in and say you take a problem like train overcrowding and they have a measure of average number of people standing on a train and my come in and I go look actually you've got this wrong because you're trying to solve a problem in aggregate which makes it into a monolithic problem which makes it really hard to solve because you've got to solve the problem for everybody in order to solve the problem and you've got to solve the problem equally I said actually what your model is assuming is that ten people who have to stand 10% of the time is the same level of problem as one person who's got to stand 100% of the time it's not okay you and I all of us when we use the tube one time in ten you have to stand okay now we file that under not the tube is fucking awful I'm never going to use it again we file it under shit happens mentally don't we you know okay maybe there's a football match on there more people travelling than usual hey what crap happens I'll just lean against the door instead one person who always has to stand if you can solve the problem for him you've solved the bulk of the problem because you've solved the problem not for people who are irritated doesn't matter you've solved the problem for the small percentage of people who are insanely angry and where you can solve that is on commuter trains if you've got an annual season ticket make first class bigger and allow annual season ticket holders to sit in first class on peak hours or run two trains a day which are exclusively for season ticket holders between Tumbridge and Charing Cross