WEBVTT 00:00:07.840 --> 00:00:10.874 Correlation is actually quite an interesting topic, 00:00:10.874 --> 00:00:16.954 perhaps not directly relevant to user experience in many cases, but it certainly does have its uses. 00:00:16.954 --> 00:00:23.249 And it's where we're trying to decide whether there is any kind of relationship between two different variables. 00:00:23.249 --> 00:00:29.440 So, for example, in user experience we might be tempted to find  out whether the longer that somebody spends 00:00:29.440 --> 00:00:34.880 on a particular page the more they spend at  checkout or the more they donate to our cause   00:00:34.880 --> 00:00:38.797 or whether there's an inverse relationship, which  is where the opposite would happen, 00:00:38.797 --> 00:00:44.560 or if there's no relationship at all; so, by way of real-world example, if we look at the connection between 00:00:44.560 --> 00:00:48.896 people's heights and weights, they *are* correlated, 00:00:48.896 --> 00:00:56.856 but there's no real direct relationship. People who are taller also tend to be heavier; it's just the way the world works. 00:00:56.856 --> 00:01:02.129 But that doesn't define the weight, by any chance – you can't predict somebody's weight from their height. 00:01:02.129 --> 00:01:08.023 But the scattergram, it's called – it's literally every  point plotted on both dimensions. 00:01:08.023 --> 00:01:13.246 On the right-hand side here, we have heights and weights, and every dot represents a person. 00:01:13.246 --> 00:01:17.386 It tends to show that as people get higher the weights go up. 00:01:17.386 --> 00:01:23.434 So, that is by way of a correlation. It's also called a *scatter plot* as I've named it in the slides. 00:01:23.434 --> 00:01:26.952 But the word "scatter" is the important one. 00:01:26.952 --> 00:01:32.932 And it's actually a very good way of looking at your data and trying to find out if there's anything interesting going on there. 00:01:33.000 --> 00:01:39.240 We're going to talk initially about a very common – or perhaps *the* most common – correlation test. 00:01:39.240 --> 00:01:45.615 And it's called Pearson's Correlation  Coefficient, and sometimes it's just referred to as "Pearson's r"; 00:01:45.615 --> 00:01:50.333 "r" is the name of the variable that's  always used for the correlation coefficient. 00:01:50.333 --> 00:01:54.991 And the way that it works is that r expresses the strength of the relationship 00:01:54.991 --> 00:01:59.288 from -1, which would be perfectly inversely correlated 00:01:59.288 --> 00:02:05.181 – that *would* mean that as the height went up the weight would go down in a very direct way 00:02:05.181 --> 00:02:14.640 – which, as you can see, is not really at all the case – or up to one, +1, which is where the weight goes up, the height follows directly and vice versa. 00:02:14.640 --> 00:02:18.908 And, of course, in the middle of all that is zero, where there is no correlation. And if there is no correlation, 00:02:18.908 --> 00:02:24.699 you'd expect to see that scatter plot  or scattergram having points all over the white space, 00:02:24.699 --> 00:02:27.268 not just towards the middle. 00:02:27.268 --> 00:02:30.291 The nature of the relationships are these. 00:02:30.291 --> 00:02:36.119 Now – certainly with Pearson's r, we're talking about *linear* relationships. 00:02:36.119 --> 00:02:41.011 So, if it's not linear, then Pearson's won't think it's correlated. 00:02:41.011 --> 00:02:44.931 But we can see the sorts of things that we might get as results from Pearson's. 00:02:44.931 --> 00:02:49.089 So, top-left-hand corner is a strong positive correlation. 00:02:49.089 --> 00:02:54.955 A bit to the right is a weak positive correlation where the points aren't quite following the straight line that we've drawn. 00:02:54.955 --> 00:02:59.930 The third on the right is a strong negative correlation, where the line is going down. 00:02:59.930 --> 00:03:07.577 So, as one variable increased up the  y-axis, the other decreased across the x-axis. 00:03:07.577 --> 00:03:12.964 Similarly, weak negative correlation – the points aren't quite as tightly packed around the line. 00:03:12.964 --> 00:03:20.448 And then, moderate, and finally no correlation, which is what I mentioned as being r equals or approximately equal to zero. 00:03:20.448 --> 00:03:24.885 Now, there is a kind of rule of thumb with correlation coefficients. 00:03:24.885 --> 00:03:32.416 And it's shown here; this is taken from "Statistics For Dummies". It is actually, in spite of its title, quite a good book on statistics. 00:03:32.416 --> 00:03:35.572 But this particular page is taken from their website. 00:03:35.572 --> 00:03:38.600 And you can see it runs from -1 to +1, as I said. 00:03:38.600 --> 00:03:43.121 And around about 0.7 plus or minus 1 is a strong relationship; 00:03:43.121 --> 00:03:46.240 0.5 moderate, and 0.3 weak. 00:03:46.240 --> 00:03:51.558 So, anything between 0.3 and 0 is more or less not very correlated. 00:03:51.558 --> 00:03:58.206 And anything between 0.7 and 1, whether it's positive or negative, is very strongly correlated. 00:04:00.456 --> 00:04:06.151 Let's have a look at correlation in user experience. Charts are from the Google Merchandise store. 00:04:06.151 --> 00:04:08.916 The top one is to do with the length of sessions, 00:04:08.916 --> 00:04:15.244 and the bottom one is to do with conversion value – the amount of money that people have spent at checkout. 00:04:15.244 --> 00:04:22.095 And while we don't need these to be normally  distributed for the correlation tests to work, 00:04:22.095 --> 00:04:27.519 it's a little bit unlikely that if you've got two  extremely different-looking distributions 00:04:27.519 --> 00:04:32.393 – maybe one's normal and one's not, or maybe they've got glitches in different places – 00:04:32.393 --> 00:04:37.237 the fact that they're different distributions means that they're not nearly as likely to be correlated. 00:04:37.237 --> 00:04:43.278 So, looking at a particular instance, the conversion value – the very first column – is labeled zero. 00:04:43.278 --> 00:04:49.190 That's somebody's checked out with presumably very little; actually, it's not quite zero, is it? It's a little bit above zero: 00:04:49.190 --> 00:04:56.106 a few pounds or dollars. There are not many of those, but if we look at a similar location in the session lengths, 00:04:56.106 --> 00:05:00.922 the zero- to ten-second session  length is the most common by a long way. 00:05:00.922 --> 00:05:05.600 And, of course, we know the reason for that, and the reason  for that is that lots of people come to a website   00:05:05.600 --> 00:05:10.982 and decide it isn't really where they wanted to be; so, they've left quite quickly. 00:05:10.982 --> 00:05:15.554 And it needn't necessarily be a problem. We'd actually have to try this. 00:05:15.554 --> 00:05:20.793 But the point is that we're interested in the correlation between session length and conversion value. 00:05:20.793 --> 00:05:24.442 And there is no conversion value for people who have not gone through the checkout. 00:05:24.442 --> 00:05:29.357 So, we almost certainly are going to be throwing out that 0- to 10-second column, anyhow. 00:05:29.357 --> 00:05:32.945 So, we might still find some correlation there. 00:05:32.945 --> 00:05:38.541 Note that there are many more than just one correlation test. 00:05:38.541 --> 00:05:41.763 Pearson's r is just the most common, most used. 00:05:42.000 --> 00:05:45.543 Pearson's r is very much a linear correlation test, as I've mentioned; 00:05:45.543 --> 00:05:52.480 so, if the relationship between your two variables is not linear, then it's not going to find much in the way of a correlation. 00:05:52.480 --> 00:06:01.541 Another very common and popular test is called the Spearman Rank Coefficient, and that is *not* sensitive to linearity. 00:06:01.541 --> 00:06:07.154 It doesn't have to be a linear relationship. So, this scatter plot shows a very strong correlation result: 00:06:07.154 --> 00:06:10.166 0.92, which is getting very close to 1. 00:06:10.166 --> 00:06:15.675 But it's certainly not a linear relationship. You can see it's curved; curvy linear is the proper term; and so, 00:06:15.675 --> 00:06:19.280 that might actually be more relevant  if you're not sure exactly what kind of   00:06:19.280 --> 00:06:23.120 relationship you're going to have; or if you look at a scattergram and you can see that it's   00:06:23.120 --> 00:06:27.895 certainly not a linear relationship although there  is some kind of correlation going on there.