Speaker 1: So, in the next set of videos, we'll be looking at factor analysis, which is a different technique that's similar to cluster analysis in spirit, but it serves a very different purpose. Let's take a look at what that is. So in cluster analysis, we had some data, which I'm representing here, and we had a bunch of respondents. So each line was one participant, one respondent, and each column was a bunch of different variables. In cluster analysis, we tried to reduce the number of variables on this y-axis. So instead of having 100 unique individuals, we would say we had three separate clusters of individuals. Factor analysis does something very similar, but it does it on the other dimension. What we try to accomplish is we say that rather than having, say, 20 different unique variables that we're measuring, perhaps those variables represent some subset of constructs or some ideas. And so factor analysis will allow us to statistically take a large number of factors, lots of dimensions, and reduce them into a smaller set of dimensions. So factor analysis is a technique that combines questions or variables to create new factors. The idea is that if you've got lots of different questions, they might sum up into these individual factors. And the purpose is twofold. One is data reduction, to reduce the number of variables to a more manageable set of factors. And two, much more importantly, is substantive interpretation. The idea is to identify underlying constructs in the data, and this makes it easier to understand the data. Because if we're trying to understand a set of individuals on 50 different dimensions, that's very, very hard to do. But if those 50 dimensions really only represent a couple of underlying factors, that's a whole lot easier. For us to be able to perform factor analysis, there needs to be some sort of relatedness or correlation between the underlying variables. So imagine for a second that we have a set of data such that there are only two attributes, and there's four different responses, A, B, C, and D. If the responses are arranged in the way that they are in this graph in the bottom left, it's impossible to do a factor analysis. Because the level of attribute one does not depend on the level of attribute two, there's no relatedness. And so we'd say these four dimensions capture four unique traits that we're trying to measure. On the other hand, if we observe something like this, now this is obviously an extreme perfect correlation that doesn't have to be quite so perfect, but if we observe any kind of relationship, we might say, well, hold on a second. It looks like as you move up in attribute four, you also move up in attribute three. So maybe it's the case that attribute four and three are actually measuring something very similar, if not the same thing. And if there is any of this correlation, we could perform factor analysis. So what I want to do is before we get to SPSS, I want to show you what factor analysis does under the hood. That way you can understand what's going on when we actually do the analysis in SPSS. So imagine there was a survey conducted by Best Buy, and Best Buy identified nine different attributes of their retail stores and their service that influence consumer store choice, in other words, where they shop. Best Buy wants to know, do consumers think in more general evaluative terms, which are in fact composites of these nine specific attributes? In other words, is it really that there are nine unique different things that people care about, or do those nine things represent something smaller, some smaller subset of dimensions? And if that's the case, Best Buy can use those broader dimensions to define areas of planning and action, which is great. That's what we want. We want to help facilitate decision making. And so factor analysis is going to help us identify these broad dimensions, or factors as we call them, from data on detailed consumer evaluations. So imagine that Best Buy asked nine questions about their store and their service. They were measured on very good, very poor. So the questions were things like, how good is the price level, the store personnel, the return policy, and so on. And you might argue that these nine things are totally unique. But what factor analysis is going to do is it's going to statistically check and see if some of these are related to one another sufficiently to allow us to pool them into underlying factors. So what it's going to do is something like this. It's going to create a correlation table. We've seen these already. And it's going to pull out values that are particularly large. So I know that's hard to see here, so I'll circle them for you. What this is basically saying is something like A5, product quality, is very related to A1, price level. A3, return policy, is very correlated to A2, store personnel, and so on. If that's the case, what we could do is rearrange this table. So I'm going to leave the exact same correlation coefficients. And I'm going to rearrange this so that I group them. And what you see here is that it looks like these four questions here, A3, A8, A9, and A2, are all highly correlated with one another and to a lesser extent correlated with other dimensions. A6, A7, and A4 are all correlated with one another and to a lesser extent with other dimensions. And A1 and A5 are correlated with one another and to a lesser extent with other dimensions. And so what this tells me is that these four, these three, and these two questions somehow hang together. So let me put this on a different figure for you. And what we might do is say, well, what do these factors actually represent? So these four questions, return policy, in-store service, store atmosphere, store personnel, they seem to refer to the in-store experience. Whereas assortment depth, assortment width, and product availability seem to be related to something like product offerings. Finally, price level and product quality are related to something like value. So instead of having to think about nine different dimensions that Best Buy customers are evaluating the store on, we now only have to think about three. And if we found that there's some sort of inadequacy in any one of these three, we might be able to act and change that and make our consumers happier. So factor analysis assumes that the correlation between a number of variables is due to their all being dependent on the same underlying factor. So this is an assumption that we're making. So for instance, perception of in-store experience, like we saw a moment ago, is a function of these four related concepts. And this is what factor analysis is going to allow us to do. So what we're going to do is go through a couple of examples in SPSS in the next set of videos so you can get a feel for how this works with some real data.