[speaker001:] effect using pi squared. I'm doing a handout now. I'm gonna do it for everybody, not just the joint management. Er it'll probably be about a fortnight before we get it back, okay? So I'm gonna send it down to shortly. Right, somebody asked a little while ago parametric and non-parametric stats. It was in the tutorial on Friday. Erm I won't look them out. Erm if you still don't understand it, come and see me at the end of the lecture, okay? You won't get anything on it here but if you haven't been told. Right, we're gonna look at correlation over the next couple of weeks. We're gonna look at the Pearson's cross product or product moment correlation and Spearman's rank order... Before we do, I'll just put this on and make sure it's working... okay. We've looked at pi squared and we've talked about the, the term I used was association. Now the reason I used the word association is that it's different from correlation which is what we're gonna talk about shortly. No what we said was that if you were interested to see if two variables are associated, this is for a pi squared... you might look at sex differences, men and women, and smoking or non-smoking... now if they were associated what we've said is that you might for example ex in fact women'll probably smoke more than men. Anybody know the figures?... well, let's pretend they do. What you might find is that out of er fifty women, thirty smoke, twenty don't smoke. Out of men you might get twenty smoke, thirty not-smoking. Now if you did a pi squared on that it might come out significant, I don't know. But what you might find is that there's an association between smoking and non-smoking. So we've used the word association. What it means is that if you know that somebody's or if you know somebody's sex then you've got a better than chance bet at guessing whether they smoke or not. So what you're saying is that these are associated. Now correlation, in a similar way, measures something similar to association but it gives you a bit more detail. Erm, let me think, reaction time and intelligence are correlated. What this means is as your reaction time increases it's believed or been shown that your intelligence quotient or I Q measure decreases. Now what it means if if you know somebody's reaction time, you can have a guess of how good their intelligen or the value of I Q that they obtained. Er, for example incomes, as people get older they earn more so they're related. Now there's a difference between correlation and. If you get a correlation between two variables it may be because one causes the other, or directly influences it, or it may be that it's just cha it's just a chance fluctuation and the two have occurred together, or it may be a combination of the two. Now the correlation or the calculation of a correlation coefficient or carrying out the correlation statistical test doesn't tell you about the nature of the relationship, whether it's caused or whether it's erm by chance or whatever. Now, it's alright, I'm looking at people and they're smiling and it's throwing me. Erm... that's right, exactly, erm. Now, to illustrate the difference between sort of causation, one of my favourites is if you take the number of new born babies in Holland and you take the number of storks, they're found to significantly correlate. That is, as the number of storks increases, so does the number of new born babies. Now some of you s might still believe in Santa Claus are about to be disillusioned. I don't think that people would posa is a actual direct link between the two to bring the baby. It turns out that there's a common variable in between them which is nest sites. Erm as erm more housing sites are built, young people move in or young couples, and they start families so you get an increase with the number of new buildings or new homes i the number of babies. What you also get is the storks have got nest sites in chimneys so you get the storks, so what you've got is nest sites for people and storks increase together, so there's an intervening variable. But sometimes you can't even identify an intervening variable, they just seem to have occurred together or arise in some way. Right, so correlation is is different from causation. Let's try and do a little graph. I'm gonna turn some lights down I think, unless you can read that. Now what we've got there is income increasing with age. That... can you see that at the back? I can't hear you, yeah? yeah
[Barker:] Fine. Now what you've got is income is increasing in that direction. Age is increasing in that direction. Now what we've got, if you take this little point here, that means that somebody has a sort of quite a young age and quite a low income. This person is about the same age but earns a bit more and so on and so forth, so your age increases. Each one of these represents an individual, in this case person, who we ask about their age and we ask about their income. Now, as you can see from the dots, the relationship isn't perfect in that everybody who's older than somebody else necessarily earns more but there's a sort of trend or a general pattern... So there seems to be a relationship between the variables of age and income. Interestingly, in this country, if erm you're classified as manual worker, your peak income occurs in your forties. If you're not a manual worker, your peak income occurs in the fifties. So as you get older, your potential to earn increases... Now in this case, because age is increasing and income is increasing, I E they're getting bigger together, it's said that there's a positive correlation... In the case of reaction time... and intelligence quotient, as reaction time gets bigger I E gets worse... I Q increases, so in fact many people would say that their in I Q and R T are negatively correlated in the sense of as your I Q gets better, your reaction time gets worse. It depends how you measure things whether increasing positive is good or bad relatively speaking. I'll give you some graphs in a minute... Now for those of you I w I what I want to get across to you is the concept of correlation, positive correlation, negative correlation. I'm speaking fast in the hope you might not write it down erm and how to interpret a correlation coefficient and what it means. Erm the sums behind it I'm not too bothered about but I'm gonna go through them because they're quite instructive and I dare say there's some poor souls here who'd actually quite enjoy me to do that so we're gonna go through some of the sums, not now but a bit later on. Right? Let's take the top one... okay, that's what we've just had, where you've got A and B both increasing. If you'd worked out the correlation coefficient or some measure of correlation, you would expe you'd say that they're positively correlated.... If you're uncertain about correlation coefficient it's always worth doing a scatter plot. That's what that's called. It's where you just draw the two axis for the two different things and then plot the people's scores on them... scatter plot... Now I'll put that there just to. The alternative is, where A and B are still, look at the axis, A and B are still getting bigger as they go along the axis but the relationship is different. As A increases,s as B increase, is that right? Have I got that right? What I'm trying to show is a negative relationship As A increases That's right, so as B increases, A reduces. Or you can say it the other way round... That'll be a negative correlation... Now the alternative would be when you plot them you get a circle almost, you get, there appears to be no systematic relationship between the two... So what you'd be tempted to say is, no correlation... Now I'm gonna try and move towards how we might measure, how might we actually measure, get a measure of correlation because what you'd be able to say is, well they're more correlated or less correlated. Now what we can do is do that mathematically which is the exciting bit for some of you. Erm for those who don't understand it, just write it down and come and see me if you really want to but I'm not gonna be testing you as to whether you understand it... Right, just a little bit of recap... You don't need to write this down but it's there in case you do. Erm for each case or subject, there are two scores. If they are correlated in some way, then we should see a pattern when we consider the sets of scores across several people. Sometimes you have the same person and you have lots of different scores for them and you see whether they're correlated but most o more often than not what we're talking about is a number of people and to see whether the pairs of scores in some way are related... Now... this is probably a bit more important. If there's a positive relationship okay I d I mean that was just recapping something I said before so if you got it you've probably got it down twice now... Okay, if you knew that there was a positive relationship between two variables and we said that their score on one of the variables was high... then we would expect, although not necessarily, because w it's not true in every case but it i there's a general trend, we would expect that their score on the other variable would also be high. So n I it's just re-interpreting what correlation co positive correlation is. Now a way of determine determining if if a score is relatively high compared to the rest of them, is to look at the Z score... yeah? That's one way of doing it. You know that if the score's above the mean... don't worry, I've got an overhead for this, that's if the score's above the mean then i you know relatively speaking to the mean it's high right? And the further th away from the mean, the higher, relatively speaking, it is. Now a Z score is a convenient way of encapsulating that and this is a way that we're gonna g work out the correlation coefficient... okay?.... Whoops I'll put that on the... Somebody left a highlighter in my office on Friday, a yellow one? No? If you wanna pick it up... God, you must have good eyesight. I can only just make it out and I wrote it... No charge for the free eye sight test. D'you want me to read these out if you're at the back? Or are you c you happy? Happy?... Oh God, it's appalling written, which one?
[speaker001:] [whispering] It must be []
[Barker:] Okay, sorry, I'd forgotten I've I've lapsed into notation. Positive, negative, and the thing at the end is a Z, of sorts... All scores above the mean, if you converted them to a Z score you would expect them to be positive. All scores below the mean, if you converted them to a Z score you would expect to be negative. If the two sets of scores are positively correlated, then we would expect positive Z scores to occur together and similarly negative Z scores should be paired. So if you were to convert the pairs of scores to their relative Z scores then what you would find is that the positive Z's, if one score is positive, then the other score should also be positive. In fact the more positive one is, the more positive you would expect the other to be. Okay. Can I move this off? Move it up to about there?... Now what I've done here is just put that in a table saying that if score A has a negative Z score, then you would expect score B to have a negative score. Similarly, if score A has a positive Z score then we would expect variable B to have a variable Z score. Do I say that the same way twice? No? That's unusual. Now that's if they're positively correlated. If they're negatively correlated, then you would expect the Z score for one to be positive and the other to be negative, or negative and positive. You'd expect them to have opposite signs.... If there was no correlation, well you'd expect them to be mixed up a bit so that negatives might occur with negatives or they might occur with positives vice-versa... Now, I'm g try and give you a feel for how these numbers, how we work out the correlation coefficient in terms of Z scores. If you consider what I've just said about Z scores, let's assume that there is a positive correlation because if we have a Z score of one on A, let's assume we also get a Z score of one on B. These numbers in fact can't happen in practice. They wouldn't add up to the sorts of things that we've got. Why I'm showing, I mean this is just the same as the table you had before but this time what I'm showing you is the product of A ti A times B, the product of the two. Now because score A has plus one, B has plus one er then it's negative, negative, slight difference there on the negatives but both negatives and both pos both positive, what you'd say for those sets of scores are that there's probably a positive correlation between A and B and if we look at the total of each one of those multiplied together, it comes up with about plus eight. Now, what we'll do is do exactly the same but this time for a negatively correlated score, and you might expect the Z scores to be paired up like so.... When you have a positive Z score for one, you'd expect a negative for the other. Negative positive negative positive positive negative. And if you multiply those together, you end up with a negative total. We ended up with plus eight for the positive cases where they're positively correlated, we ended up with minus nine for the negative cases.... Now, if there was no correlation between the two, then the patterns of the Z's paired Z scores would be quite arb arbitrary in that there'd be no consistent pattern. So, for example, we've got a positive with a negative, then we have a positive with a positive, a negative with a negative and a negative with a positive. And you'd pi be tempted into saying that they were probably not correlated, either positively or negatively. And if you look at the sum of the two Z scores times' d each other, you end up with something close to zero. So you begin to get a bit of intuitive feel. If you g if you take the two Z scores, convert the paired scores into Z scores and multiply both of them, you get a big positive number if they're positively correlated at the end of the day. If they're negatively correlated you get a big negative number. If they're not correlated, you get something approaching zero.... Is it cold in here? Well I never, first time. It is... Okay, now what I'm trying to tell you is that th a measure of association or, as we're gonna call it, correlation They are but I'm just I mean y'know it's cos it's not really correlation yet so I'm sort of u that's why I've put quotes round association. Now, you can't see them both. I mean I I I'm confusing the notation but I've put little quotes round it. It's just that it's not quite a correlation yet. We haven't evolved the mathematics to where I'd call it correlation, yeah? Cos otherwise people'll tell me that this is how this is the correlation coefficient. I don't want you to do that so it's I've just association wi. I suppose you could put correlation with quotes round it if you prefer, yeah?... Now don't forget the sigma means the just the grand total. Now I'm not gonna bother to put the N sort of equals one to N equals N or something on the top yeah? What it means is that we're just adding up all the products for all the paired scores, right? As we did in the example before... Now there's a bit of erm recreational or diversional mathematics coming up which you don't have to understand but for those of you who are keen on it, it's there. What I'd like you to think about, if I can find a rubber, is... we've said if you take the sum of Z X's times Z Y. They were A and B before, I think I might have confused that. Right, that's all the Z's multiplied by their corresponding Z's on the pairs and you add them all up. What's interesting to know is, what is the maximum value that that can attain? Alright? Now, I think it's M minus one, I'll just check, yeah. The answer will be N minus one where N is the number of paired scores, so the maximum value that that can obtain is N minus one. Now, there's a proof for that and I'll give it to you but but you're not expected to know it, but it's there for those of you who want it. Well, you're gonna have to take something on trust already. Erm the maximum score of that expression is obtained when Z X equals Z Y. So, the maximum time is when the two paired standard scores are a exactly the same, not just they're both positive or both negative, but they're exactly the same value as well. Now those of you into differential calculus, your time has come, cos you can prove that on Friday night. Maxima and minima, but I'm not gonna bothered with that one... Now what I suggest you do is just jot this down. I'm not gonna bother to explain it too much. Erm if Z X equals Z Y is when that's the maximum, then Z X times Z Y is either could be put down as Z X times Z X or Z Y times Z Y cos they're both the same.... If the two scores, or the two Z scores were identical, then it would be a straight line of points for X and Y. There'd be no little scattergrams, there would be no little dots about the line, the line would run perfectly through them. That would be when you get a maximum value of this product of the Z scores, Z X times Z Y.... Now, the tricky bit comes back to remembering what Z actually equals, okay? Z X al a Z score is the deviation from the mean divided by the standard deviation. So, let's assume that we've gone down the line of saying that, for a maximum value, Z X times Z Y equals Z X squared. Right, let's assume that we've done that. We substitute those into the Z scores... and lo and behold, at the bottom of the page, you end up with the maximum value of those of the product of X Y, sorry Z X and Z Y is N minus one.... Now that's if they're positively correlated. I drew the diagram and they were positively correlated... Now, you don't have to know that proof but if you ever wonder where it comes from or you wanna tell your grandchildren one day... Mummy, what did you do in the stats classes? Wrote my other essays is an answer that I... For those of you that believe that statistics and research matters is about hard sums, you can endorse that view... okay.... Okay, can I put the other one on? The max value em... So the max value, if there's a positive correlation, if there's an ideal perfect correlation between X and Y, the maximum value of this standard score X times standard score Y, the maximum value that can take is N minus one, right? Restating it, so, the max value of that product is N minus one... Now, if you wanna know what the maximum value and negat if the score's are negatively correlated rather than positive, you end up with exactly the same expression, N minus one, but lo and behold it's negative. That's an exercise for the students to do themselves if they want to, is to derive the negative version. Now that would be the minimum vale, but what we mean by that is the th maximum negative correlation cos if there was not correlation you'd expect it to be zero.... Don't forget N, in this case, is the number of paired scores. It's typically the number of subjects but sometimes it's it's not subjects all the way through, so it's the number of paired scores. Now, there's a certain attractiveness to this number, there is,ther there is, because, as you shall see, right?... Right, the correlation coefficient is given by da da R equals, now we've already met this, this is your old friend the product, and what we're gonna do is divide it by N minus one... Now if you think, I'll wait til you've got that down [whispering] let's see if I can find this bloody rubber [].... Now, if we've said that the correlation coefficient is the product that we've been working out... and we've said the maximum positive value that this little expression here can obtain is N minus one, N minus one divided by N minus one is plus one. So the maximum value a coeffic correlation coefficient can obtain is plus one, and that would be when there's a total positive correlation... Conversely, the minimum value it can obtain is when this expression on top is minus N minus one, so it goes down to minus one for a complete negative correlation and it's zero if there's no correlation and then there's the values in between That's just saying what I've said.... If a correlation coefficient obtains a value of minus one, or plus one, it means that you only need to know one of the scores of the two and you can say exactly what the other one will be. It enables you to perfectly predict what the other score would be. It means if you know one score, you automatically know the other. Of course, in true life, real life, things like that don't happen. You quite often get correlation coefficients in the order of about point three, R equals point three, R equals minus point three. If you're really lucky, you get up to about point six. Now in social sciences you very rarely get a correlation coefficient going about point six or seven, very unusual. But, if it's positively associated, it means as one score increases, the tendency is for the other score to increase. If it's negatively correlated, it means as one score increases, the tendency is for the other one to decrease, and if it's virtually zero it means there's no relationship between the two. Now, that's the first sort of introduction to correlation. I've got s don't go yet, we've still got a bit to get through. Erm, what we're gonna do now is look at some number crunching and what I'll do is give you Pearson's erm formula for calculating the correlation coefficient. It's not very nice. It's in your text books. There's lots of different formulas for this by the way. You take whichever one's most appropriate.... I suggest you use this version because it's one of the easier ones to calculate. They all end up the same way but you do it by different ways. For example, you could actually work out all the Z scores but this equation you don't have to, but you could if you wanted to. You could actually work it out the longhand way, the way that we've described it... Yeah I think you'll find that that's meant to be X and X The B's are supposed to be Y's. I do apologise, I nicked it, the B's are meant to be Y's and the A's are meant to be X's. I thought I'd got rid of them all but I hadn't, right? W you've got two scores, X and Y, for every subject, yeah? X X Y, now the B's should in fact be Y's... It's what comes of talking about it in A's and B's and then changing to X and Y's. I mixed it up when I wrote it down... If you find something in the text books looks about right and similar to that, use the text book version, I might have written it down wrong. This is not an X, it's a times. That's actually a times, multiply, so what you do is that N times that bracket times N times that bracket and then the whole lot is square rooted... I'll come on to that shortly... Another way of thinking about erm the product moment correlation is that what it's doing, it's putting the line of best bet through the data. It's finding the best straight line through the scatter plot. Now it's another way of thinking about it. That way of thinking about it will become very useful for things like linear regression, which we may touch on, and erm for the notion of variants accounted for, which we certainly will touch on shortly... Now, there's different sorts of correlations. There's, somebody's mentioned Spearman's Row, I'd already mentioned it before I think. Erm, this is known as Pearson's and there are certain assumptions regarding it. Have you written that down? Yeah?... Okay... Assumptions for Pearson's are... It assumes that there's an n an approximate linear relationship between, in other words you could cos what it's trying to do is draw a straight line through it. If it goes all over, if the relationship is curvier linear then you have problems with Pearson's, so it's gotta look like there's a straight line relationship in the first place. Approximately that now I've it's very y'know woolly, most people don't bother but you should really do the scatter plot to see whether a relationship is linear as opposed to something like that which would be curvier linear.... it's a repeated measures design. Now it doesn't have to necessarily be the same subject but in some way it's a repeated measures, that's where you. It assumes that the scores have been derived from random samples. It assumes that there's interval level data. It assumes that you've deri derived the samples from normal populations and it assumes there's a home between the two. So what you're doing is making assumptions about the population from which your samples were drawn, so therefore this is known as a parametric technique... Nearly there... Now, another interpretation of Pearson's R, or the correlation coefficient generally, is variants... If you square the correlation coefficient... it equally the proportion of variants in X accounted for by Y. Now that is actually a very good measure of how good a correlation is. If you get a correlation of about point seven, it means that you're only accounting for forty nine percent, less than half, of the variants in the other var the other sets of scores... Think about it, if it's a positive, if you've got a correlation coefficient of one, what it means is that you account for a hundred perc or or sorry, if you're gonna make convert it to a percentage, you times it by a hundred, it's the proportion there. So, if it comes out as one, one squared is one so you've accounted for a hundred percent or all of the variants in the other variable which means that if you know X you automatically know Y, or if you know Y you automatically know X. When you're doing a correlation study, it's very hard to work out what's the dependent and what's the independent variable because by it's nature you don't know. Little aside. Very last overhead, and you've only got to look at half of it. We're gonna do Spearman's next week... For those of you who want to, what you can do, you can take the correlation coefficient. I've called it R P to distinguish it from Spearman's which we're gonna do next week, but you can convert the value of R to a T score and if you've got a T score you can look it up in T tables to work out whether it's significant. Most tables, though, in fact already give you correlation coefficient. So what we're saying is that you can take the correlation coefficient, multiply it by N minus two divided by one minus R, square root it first, and you convert it to a T. R P is the correlation coefficient ca calculated by the way we've j that that's just a little squiggle has no meaning as far as I am aware. That's where I fell asleep probably. And next week Spearman's rank order... I'll stay behind for about five minutes if anybody wants to ask any questions
[speaker001:] ...
[Barker:] [shouting] Don't forget, some of you've got a lab class n erm from five til six []
[speaker001:] last Monday
[Barker:] That's right, did you miss the start of this?
[speaker001:] No, I just came in when you were saying
[Barker:] That's right yeah they'll be about all night
[speaker001:] Oh right, that's alright then
[Barker:] Okay
[speaker001:] do you mind if I get the stuff for perception
[Barker:] Er is it?
[speaker001:] Yeah
[Barker:] I mean I'll bung them in to you at some point
[speaker001:] Yeah, that's alright yeah
[Barker:] It's one of the non-urgent jobs unfortunately [humming] Are there any absent friends who're sort of gonna appear imminently? Oh, here's one... Have you just had a lecture? Just had a lecture? Oh right, just had lunch? Breakfast?... Is there erm here? Did you get a copy of the,, that's what, I don't know what's gonna happen with that because nobody's got back in touch with me at all Oh right but is I went to t I said to them, d'you wanna scrap it yeah? I said there's y'know it was a couple of minutes late and they said erm it had to be processed through the proper channels. Waste of my time for an hour, waste of whoever's gonna have to sit on the committee for even more, ridiculous. It's a w new way of the system I'm afraid. It was a waste. I just went over there and said it was okay,th I'd put in a letter and they still couldn't just take it off. They said it all had to be processed so it's gonna have to go bef but I mean I will get very angry if that gets taken any further cos it's ridiculous, isn't it? [shouting] Is there a course work deadline today? Fine, just in case I'm running over a little bit. [] We don't want to cause any body some distress. Okay, H P only. It's alright, I'm just checking. Apparently last week there was a course work deadline, I didn't realise. Erm Schumann psychology first years erm, that you isn't it, H P one? You're the only ones who have to do the essay for perception. Combined honours don't. That's my understanding from the book. Is that correct? Okay well H P one's on your notice board you've got four titles of possible essays. You can pick any one of those four. You can pick more than one of those four but the second one won't be marked. Yeah?... Anybody else gonna turn up? No? Right Can I borrow a sheet of paper off someone just t. Front row's packed today Well you turned it off there Okay we started off and we was talking about the fact that when we perceive things they start off in origin as energy signals in the environment and we detect those changes in the energy and somewhere in the process they get converted into our experiences of perception. We perceive the objects, or patterns, or whatever. In the handout pattern perception is synonymous with object recognition. Object recognition is a case of pattern recognition I suppose. Now, we talked about attention as being a process whereby we could explain how it is that, with all the information that we receive, or our senses receive, that we only process part of it, and we saw that within the information processing model. Now in, is it Matlin? Matlin? Maitlin? Maitlin erm you'll notice that it concentrates on spatial frequencies which is a particular interpretation of the type studies where you look at the responses of the brain to particular stimuli. Now, as I said in one of the quotes that we were talking about, a psychological explanation does not need to rest on physiological causes. In other words you can have what goes on in the brain at the hardware level does or at the level of nuance doesn't necessarily have to correlate with what goes on at a high level description. So, leaving aside the hardware involved, is feature analysis one of the processes involved in object perception? Now what we're doing is a sort of historical sidestep. We evaluated erm the neurological feature detection, the work of grandmother cells and we said that in fact that probably wasn't what was happening, we were looking at spatial frequencies instead. Now, when their findings came out that the cell there were cells that appeared to correspond to feature detectors in the real world, a number of theories immediately popped up which tried to take this into account. So a number of theories of perception erm came on to the market as a response to the work of people like in the fifties and towards the end of the fifties we started to get theories of perception which were based on feature detectors. Now there's loads of these different theories. There was a whole whole sort of I don't know, what's the word, clutch of them, that came into being. Er I'm gonna talk about a couple because it'll give you a bit of a flavour on perhaps some of the more popular works that you'll find in some of the text books. Now the first one was Selfridge's Pandemonium model. Pand it's actually pan dee mon ium which is quite interest I couldn't work out what it really meant, pan demon, across demons, well that doesn't make much sense but you'll see why it's called pandemonium, in the conventional sense, model. There were two key components to this, there were things that er were labelled feature demons and there were things which were labelled cognitive demons. Now the feature demons corresponded to feature detectors. So, for example, what you find is that they're a number of features are detected by the feature demons, such as straight lines, which are either vertical, horizontal, at an angle, angles that intersect at ninety degrees, half circles, small circles, so they it was hypothesised that there were a number of feature detectors that erm were detecting features early in the pr the perception process... When these features were detected or, well when these features were detected, this information fed into cognitive demons which started to respond. So if y there would be the cognitive demon which was the letter A and what would happen is, it would start looking at the features that were coming into the system and it would say, are they the ones associated with A? And if some of them are, then the A cognitive demons start shouting that by analogy and that's why it's the pandemonium muddle because many letters share similar features so that there would be lots of different little cognitive demons jumping up and down saying, hey it's me, as more features become apparent, or more features are detected. The decision demon, which is this one over here, which is p is a cognitive demon, looks at the cogit the output from the cognitive demons, sees which one's shouting loudest and then decides that that's the letter. Now, as you can see, that maps quite well with the sort of hierarchical feature extraction. You start off with a stimulus, which is here, there are the various bits that feed into the feature detectors. The feature detectors fire, higher cognitive demons start selectively responding to the features that're fired. The more features that're fired, the more likely it is that you'll get an out or the higher the activity level of the cognitive demon and then the more likely that the decision demon will decide that that's the appropriate character. I think that was fifty nine, Selfridge's model, that was the year it was published. It was at the end of the fifties, fifty eight, fifty nine... Now, I don't know whether you've done language yet. I'm n have you done anything on language? Erm you'll find that there's something known as the Logagun model, which was proposed by John Morton, which is analogous to this which is a feature detector for sound. It's when it's it's known as word recognition. It's for recognising words rather than features or objects, visual. This i was taken to account for visual in particular of word recog letter recognition through the visual system. Morton's model was concerned with how we recognise wor auditory words and that was an a sort of analogous process to this. If you have a look at it, it's quite sophisticated and you'll come across it certainly by the end of your second year. And that was the Logagun models... For about ten years feature models were quite popular in perception. Erm I'll talk about one of the later models, which was Gibson's, E Gibson as opposed to J J, which again was concerned with letters and whether or not we construct letters by recognising features from them. Can I take this one off?... Okay... Although I'm referring to Gibson's work, I mean this was typical of the time, there were a number of other researchers who were using similar ideas and notations. Erm, the idea is that letters are uniquely sep specified by different combinations of features, but certain letters would share more features than others... So the idea is that you might consider that the letter X is made up of two features... line going that way, whoops, yeah, and a line going that way, which when they're viewed together make the letter X. The letter Y is made up of a line going that way and a line going that way. They are holistic features, that is one feature that is detected. Now we're not su we're not sug er Gibson didn't suggest that that was the feature that was specifically detected by erm perceptual cells. It's just that we can think that that is a feature that is detected by the perceptual system. It wasn't said that there were cells that actually corresponded to those features, not but nonetheless the output from the system could be thought of as a feature detection system. Now the ideas was that if you presented the letters X or Y very quickly... that people would tend to confuse them. If you present the letters very rapidly, just so they could only just be detected, erm you'd find that sometimes X and Y would be confused, whereas X and P were very rarely confused. Now they used something called a tachistoscope, I'm not sure about the spelling of that, which you don't come across these days, it tends to be computers that're used. But a tachistoscope was a bit like an oscilloscope or a screen where you could flash a word up for a very shore period of time. There's a lot of work done on tachistoscopes in the sixties and the seventies. By and large they've been replaced by computers now. But you often hear the expression, tack iss stock ope, tachistoscope as presented by a tachistoscope, right, there you go. Some letters were found to be more often confused with other letters and these letters were deemed to share similar features E G, B and P were often confused whereas B and X weren't so you'd be flashing either a series sequence of letters up, some of which shared features, some of which didn't, or we thought shared features, and then we saw whether they were confused or not, and this was taken to support the idea that features were extracted from the input, or that's how we constructed the letters or characters that we were perceiving. Interestingly enough, when you come to language, we'll find that that's a far more complicated topic. Erm, how do we recognise letters and words and you'll come into a lot of other factors influence that. But one of the earlier findings which began to cause problems was that the sound of the letters, as well as the features, determined whether or not they were confused so B and D, for example, sound similar therefore they tended to be confused. You could also find some letters that were confused, they didn't share common features but they sounded the same and they tended to be confused as well There was a lot of enthusiasm from the work of the neuro-psychologist th with the discovery of cells which appeared to be sensitive to particular features. Erm, that over a period of about ten years, began to wane and by and large now I think feature analysis per se has been abandoned as a as a model for understanding human perception. Interestingly, it does feed into some of the later ideas that were associated with computational modelling, I E using computers to recognise objects on model processes, in particular perceptual ones. The rip there're a number of problems with feature analysis and you can read books on them. Erm, I'll try and summarise them... A perce an understanding of perception, whereby we say that i features are hierarchically extracted, is unable to deal with ambiguous input. If the input information is slightly ambiguous then a feature analyser would be confused and unable to deal with it, a pure feature analysis. For example, if we take those words there, I I hope that most of you can work out that that says, the cat, right, some of you can be difficult and say that you can't but I should think that most of you can. But if you look at the H and the A's, they're in fact, feature-wise, identical but you're able to work out that one's er an H and one's an E based on the context. So any feature analyser would have to deal with context so therefore they started to look at the role of context and we're gonna look at contextual effects later on, probably next week or the week after. So the way that we process or extr it cannot just be we take a we take the information an and build up the letters by extracting the features from it because if you did that then the H and the A would come out the same both times but they don't. So there're other processes that're going on. Right, in a simple sentence, contextual influences are not easily accommol accommodated by feature analysis... [sigh]. When you look at certain letters, you can see that they've got exactly the same features involved in them. Take the B P and D. You often see that the P's, the D's du du and the B's share similar features. They've each got ideally a circle and a line so they have identical features but they're different letters so clearly, I mean it's quite obvious, it's not only the features present but also their relationship to the other features that're present that determines what type of letter is recognised... So any model of perception would have to take that into account.... Another thing, when you look at how people recognise characters, it's not a the features that they pay attention to, but the overall shape. Quite often when you're looking at people's handwriting, you can tell by the overall shape rather than the single features. So, a feature analyser would also have to take into account the overall shape of the letters so it's becoming a bit more complicated already in terms of the model that would have to account for it. Now, all of those criticisms come about on the work that's been done which has mostly been done on the recognition of characters and letters. Erm,wh most of these criticisms would become far more exaggerated or far more relevant if you considered what happens in the real world. What are the essential features in the real world?... So these problems and similar ones to them are generally led to an abandonment I suppose, or a lack of interest in feat in a pure feature analysis view to how we build up and recognise objects.... The next topic we're moving on to in a way w is is erm speaking in terms of time, precedes the work of the feature analysis, the feature analysists. Erm it dates back to the twenties, perhaps a bit earlier than that. We're gonna look at psychology and what they had to say about, or the school had to say about perception. They were far more interested in how the whole image, or the whole perception came about. Rather than being concerned with the minor details being elaborated into a more complex picture, they were just interested in how we come to group erm features together for want of a although they weren't thinking about them as features. Most of you have probably come across the saying, the whole is greater than the sum of its parts. Now to some extent what that's acknowledging in the role of perception is the fact that perception isn't a bottom-up driven process. Th it's not a case of everything's contained within the stimulus that's coming in and we elaborate it into whate the object. Er we bring ideas er concepts and knowledge, which are very important in interpreting information. So they were in a way acknowledging th that sort of work or approach. Now this psychology, there's absolutely loads of stuff on it so and the Maitlin book's got quite a good coverage of it, so I'll go over it quite quickly, alright? Generally it falls, although I've used as the sub-heading, I suppose the overall title of this area is perception organisation, the way that erm things become organised, how we perceive them as an organised whole. Okay, with objects are perceived as structured coherent wholes rather than as discreet component parts. So they were quite interested in that process... Most people are probably aware that the school produced a load of laws that were associated with perception. Interestingly, they also influence memory. I don't know if you've covered the influence school on memory, have you? In your memory lectures? Is that a yes or a no? No. What lectures did you say? Oh. Well anyhow the had something to say about memory as well erm which is quite interesting. Most of the ideas, or the laws that were were derived which erm pertaining to to the school, derived from something called the law of, now would anybody care to pronounce that? Pregnence, pregnance? Anybody here do German? No? Does anybody here actually speak German? Okay, what does that mean? Pragnance, any idea? Progna I s to be quite h I've forgotten, it used to me it means something quite interesting and I've forgotten. So thirty five of several geometrically possible organisations that one will actually occur which possesses the best, simplest and most stable shape. So that's the guiding principle of the view of perception. Most of the other laws if, in a way, follow on from that one... You'll notice that I've sort of spaced the writing out today so you haven't got to do so much. Same number of overheads to keep me happy, but you've gotta write less to keep you happy, there you go. Now the sorts of laws that they came up with were things like the law of proximity, the law of similarity, the law of common fate, good continuation and closure. Right now the I mean there's loads more as well if you wanna look them up. They're the more common ones, or the more popular ones.... It's a very sad sight y'know to see all these empty seats. It's quite, I'm sure they were fuller at the start, alright? I mean is this a general tendency in most lectures, or just mine? I've noticed [LAUGHTER]. You can be brutal... Koffka K O F F K A... Okay? Can I take this one down?... A picture that you'll find to sort of try and ex give you an example of some of the l a the text books have got some great pictures on these particular sorts of examples of the laws in practice. we have here, well, what do we have here? That's an interesting question, eh? Okay, what we actually have are a selection of dots arguably, those little well sort of funny looking dots, elongated dots, there you go. Yeah, dots. We have those sort of things. But in fact the dots are seen as lines due to the laws of proximity and similarity. They were looking for the principles of organisation, how it is that we organise things like dots into a meaningful whole... Why is it that we tend to see two lines crossing in the middle rather one two than two V's? Law of good continuity... Then you tend to get things like closure where, instead of seeing four separated lines, you tend to see a square or a rectangle or whatever. The law of closure. The books are full of good examples. They've also got some lovely illusions erm figure and ground illusions wh ambiguous figures. Y'know, the old hag and the young lady as Victorian sort of principles.... Now when you look at the stuff it looks qui it's plausible, it seems to describe what you see in practice. It seems to be a good account of it. But when you start to think about it in terms of erm sort of psychological explanation as you're becoming used to, then it becomes perhaps not such a good way of thinking about perception... Matlin's got some very examples in it of this of those sorts of things... By and large were concerned with people's experience, self-reported experience quite often, of the phenomena saying well tell me what you see when you look at it rather than being based on the sort of lovely stuff that we love, good solid empirical data, yeah? So being psychologists who can't get enough of it, empirical solid data, we tend to erm be a bit dismissive of the methods that were used by the... Although these laws tend to describe what th what's happening, they don't actually tell you how they're achieved. W what mechanisms, what processes underlie these laws of perception? It doesn't really tell us very much about those at all. They weren't concerned with that, although they did come up with some electro um electro-static field, or electro magnatic magnetic fields in the brain or something. It wasn't really erm a very satisfactory explanation and it lost favour quite quickly... There's lots more Matlin lists a load of problems. These are sort of a summary of them erm I may have missed one of the minor ones out. The laws, whilst they're pretty good at applying to things like erm visual illusions and two D and dots on pieces of card, they're not very good at really applying to solid objects. It becomes very difficult to apply the laws to solid objects. Surprisingly, considering a lot of the illusions that were provided, in fact rely on contextual information. What I'm gonna say may seem strange but they don't allow for certain contextual influences. Now y'know you can come up with a description of that as an ellipse but in exactly the same shape, in a slightly different context, yeah, you know it's actually circular and it's a hoop and your perception of the object is different. They don't really give erm much of an account for w how it is that erm similar objects which're grouped according to their laws erm can be perceived differently in different contexts. For those who came in late, the essay titles are up on the first year notice board. Essentially the four areas are computational modelling, what contribution a don't write these down because they're not the same as the ones on the board, but it's looking at the role of computational modelling in perception, although you could start off with a broader definition of it within cognitive psychology. Erm, we're looking at the modern approach to th or modern evalu evaluation of the approach. Looking at visual illusions and perceptual errors and I ca what was the oth oh and the role of attention in perception. They're the four areas. Some of which we haven't done yet, some of which we have, so it's up to you. You can either do what we've already done or you can base it on stuff that we'll do in the future. Either way it should be helpful... Now, interestingly... people, more recently, and by that the late seventies and the eighties, have attempted to actually operationalise and measure the principles and they've come up with some fairly ingen ingenious experimental designs to take tha to explore these avenues. Er I'm gonna give you one here, although there are several more which you'll find references to in text books, okay? Now this is a lovely quote I think. It really gets over. Percepts I think are sort of breaking things into their sort of components if you like. them on the floor and watch them shatter into natural pieces, di dum di dum di dum, in the absence of such a direct technique, more indirecti more indirect alternatives must b must suffice. They're saying is, it'd be nice if you could take something that's a holistic perception and fragment it into the component parts. But of course that's very difficult. the notion of getting hold of a sort of re a perceived object and dropping it on the floor and watching it split into it's component parts is quite appealing... If you take a, if you imagine, you could take an object that you're perceiving, yes? And you could break it into its fundamental component parts, yeah? It's just what I said before. Yeah... Now Pomerance, who's one of the people in the quote, has done a lot of work recently er by that in the last five six years, looking at how we can investigate the, or objectify, the measures that w or the laws that were used by the. I'll talk to you about one of his experiments to give you a sort of flavour of it, although other people and himself and others have done a lot of interesting work that's similar. Right. Let's have a look at this. What've we got? If you, in case A, if you imagine that you're presented with with a piece of paper or card and it has two symbols on it, right? It could have it like those, like those, like those, or like those... So that would be one deck of cards that you'd be given and they'd have the four types of symbols on them, separately of course. Now, the alternative deck of cards in B would be those four. Your task is, regardless of the symbol that appears on the left, to sort the cards into the four shapes, right? So you ignore that symbol and you just decide which deck to pu pile to put them on based on those f the four first symbols. Now, in deck A it was argued, or proposed, that there is the symbols are similar, whereas in group B the symbols aren't similar. So, Pomerance argued it should be easier to process just the right hand signal if they're not grouped together, if they if the processing system doesn't tend to group them as a single entity. So the it should be qu easier to sort these than it is to sort those. Sorry, the other way round. It's quicker to sort those rather than those because what tends to happen is that you process them as an entity rather than as single figures. It's a very difficult task when you come to do it, if you want to have a little play at home. You can even entertain the kids. Okay, the task was to ignore the right hand bracket and to sort cards based on the left hand bracket... In fact you'd sort them into two piles, not four. He did a load of different experiments, this is just an example of one of them. They're all very similar... He, or they, manipulated the notion that similarity, they manipulated proximity by varying the distance between the two brackets, the two pair of brackets. So how far away did you have to put them before you no longer saw the interference?... What Pomerance and others are attempting to do is to operationalise definitions for proximity, similarity, closure and those type of measures and then they're seeing whether or not they're using visual processing time or decision task or attention task to as v as ways of investigating the similarity or otherwise... Take this one off or?... Now, another notion, we talk about the idea of bottom up versus top down processing. Bottom up processing is where you start with the input information, whatever that might be... and then you, based on that input information, you extract or inp or extract more meaning from the input until you end up with whatever it is that you recognise. So the process starts with the data and it's totally determined by the contents of the data, right? An it's a notion that you'll come across again and again in cognitive psychology. The alternative notion is the idea that you impose meaning on the input, in which case it's a top down process and it relies on contextual information and information that you already have i on previous knowledge. In perception, you tend to find models of perception that're based on top down or bottom processing. Now the feat hierarchical feature analysis that we've done so far was predominantly a bottom up data driven process. Whereas most of the models today that we think of we regard them as a mixture of the two but with a he and, depending on the type of or the piece of perception that we're working on, we have either one the other. We tend to have, but they never, they very very rarely occur in isolation. There's always a little bit of bottom down and there's always a bit of top up, regardless. So you th this distinction isn't a pure one. There there's no idea of a pure bottom up or pure top down process. By and large most cognitive processes are a mixture of the two and in fact it depends on the context that you're operating them in, we tend to be able to split from one to the other. Now, in perception, as we've we've mentioned that you've got bottom up and top down driven processing but what you've also got is something called global versus local processing. Now, this isn't a very good impression and I think you'd go to the doctors if you had something like this. The idea is, I'll present it you and you you can I won't try and astound you with it because it is hard to do that under these contexts. What we've got is a shape here and a series of shapes there. Now isolated they look fairly meaningless and it's very hard to work out what they are. That might be a letter or something. What you've actually got if, if you bung them together, well you've got a sort of face. If you had a face like that you'd be down for plastic surgery tomorrow wouldn't you? I mean, look at it. But er yeah rhinoceros man, mhm?... Down? There you go. I think you c well you c that's it. There's only global versus local processing above that... A and B only make sense when seen together. A provides a context for B but B serves to provide context for A. These are known as local features, and that's known as a global feature. Within perception you quite often get erm a local processing going on simult apparently simultaneously with a global processing and the two sort of mutually influence each other. So, that's distinct from top down or bottom up. There's another sort of notion of whether you process the global feature or whether you process the local features and you attempt to find out they it dep vary between processes and which one they use, but it's another way of distinguishing the sort of processing that goes on. I've only come across this with perception. You don't tend to get it in memory and problem solving, although you get the forest for the trees in problem solving so I suppose it's there in a way. Do you pay attention to local features to build up global or d the other way round? Well it seems that the two interact. It's hard to say it's one or the other. But it's another way of looking as processing. You could describe it as global or local.... Next we're gonna look at the role of context or computational modelling. I'm not sure which one is better to present to you first. Ah computational modelling is easier for me to present to you but then the role of context might become more important so you can appreciate it, in which case I shall give you that first. I don't know, I'll have to think about it. Normally I do the computational modelling first then context but I might do it the other way round, right? So it's one or the other next week. I've run out of things to say
[speaker001:] [LAUGHTER]
[Barker:] Thanks a lot By scientific revolutions How're you spelling kuhn as well?
[speaker001:] K U H N?
[Barker:] Yeah that's fine
[speaker001:] Erm, long report, can you do the short report?
[Barker:] Yeah
[speaker001:] Yeah?
[Barker:] That was easy wasn't it?