Now, I mentioned this idea of factor rotations earlier. It's not going to change the underlined results themselves but it may help you as far as the interpretation, how we look at them. And literally what we're doing is we are going to rotate the axis. So as an example let's go back to that retail illustration, that first example that we had looked at. We said questions one and two were related to each other, question three, four, and five were related to each other. But if we had a set of axis that looked like this, notice that it doesn't really lie on the horizontal or vertical axis. But it'd be a lot easier for us in talking about the results if they did. It'd be nice to say, okay, items one and two lie on one dimension Items three, four, and five lie on another dimension. Well, we can make that happen mathematically. All we have to do is turn and rotate our axis and we haven't changed the spacing between any of the survey items. All we've done is kind of tilt our heads and change how we're going to look at the results. And that's what we're going to do with our factor analysis. We're going to take the original result, we're going to rotate that mathematically to ease interpretation. All right, and once we do that what we're going to be the most interested in are those factors scores. And which survey items tend to move together. Which survey items relate to particular factors. The way we are going to be doing this again we going to look at that factor loading matrix to decide on a critical value around, a magnitude of say 0.4 or 0.5 as cut off and we are looking for the big factor loadings, anything In magnitude greater than that. All right, and we're going to say those items where the magnitude is greater than that critical value, we're going to say that they load on to a particular factor. And we're going to look at the original survey items, say all right, what do these items that load on to a particular factor have in common with each other? So let's take a look at what that looks like. So we're going to go back to doing our data analysis. I'm going to rerun this analysis again, but this time I'm going to tell it that we want nine factors. So let's make that happen. Okay. Now, when you do the rotation and factor analysis, it's going to give you two sets of results. We're going to see the unrotated result which is going to mimic what we had done before. And then we're going to see our rotated results. And we're going to have to scroll down quite a ways to get to that. So again, initially we have the unrotated results, and then we're going to move on to find, after the factor scores. What we're interested in, now notice the percentage of variation that's not being affected here against, it's going to affect this factor loadings but its going to ease our interpretation not really change the underlying structure. All right. So, what do we looking for and Excel status made this a little bit convenient, for us based on it's own analysis it highlights. Of course, I believe, Excel stat uses a cut off of 0.5 in magnitude. So, it's highlighted those factor loadings that exceed that threshold. And I'm going to expand this column just a little bit so we can see which items actually load together, all right. And so this is our first factor, the first rotated factor. And it's the questions about not being in debt being able to pay for things in cash, spending for today, letting tomorrow bring what it will. Not using coupons, confidence about the interest rates being low, both tend to all move together, and that's probably not too surprising. All tend to relate to that financial health aspect. The second factor. So column D2, the items that tend to load onto that are about the skeptics being wrong. I can do anything I set my mind to. I'm going to have higher income in the future. All tend to load together. Maybe that has something to do with the level of optimism or positive outlook. The third column is about society today, being fine and not having time for volunteering. Maybe some degree of indifference towards society. The fourth factor about domestic cars being worse. Being positive about restricting trade. Being positive about being American. All voting together, so maybe some construct relating to patriotism. Self-confidence, being a leader, helping others in a jam all relating to each other. So, perhaps that leadership or self-confidence dimension, being stylish, being fashionable, being in a good physical condition; may be an image orientation. So, this process that we are going through, of looking what's the survey question, and which survey questions tend to move together, this is something that we haven't managed to automate yet. This is really where the analyst has to add the value. The computer can tell you these survey items moved together. That's what the algorithm is designed to tell you. It can't tell you necessarily what these items have in common with each other, all right. But that is the fact, that's the big set of results from this factor analysis. So nine survey items really capturing the meat of this particular survey. So nine constructs capturing what took us almost 30 items to capture. All right. Now, something else that we should do, is we should look at the quality of fit. That is, how good a job is this survey doing. Well, or how good a job is this factor analysis doing in explaining the survey. And we've looked at this a little bit already. We've looked at how much variation from the original survey is being captured. All right, so that's an overall measure of performance. So think about as being akin to looking at the R squared in a regression analysis. The closer to a hundred percent the better job we're doing. But keep in mind again, we went from thirty survey items down to nine factors. So we've got 20 fewer items almost. We're not expecting to get to 100 percent. Now that's evaluating the overall analysis, what about each particular survey item? How good a job are we doing at capturing that? Well that's what a measure called, referred to as uniqueness can help us reveal. What's the uniqueness, what's the unique variation that is not being captured by factor analysis? So let's go back to our Excel results to take a look at that. And the way that this is going to be reported is going to vary from software package to software package. Some of them are going to report it as uniqueness. Others are going to report it as a measure of commonality. Think of commonality as how good a job is the common factor solution doing at explaining this survey item. Mathematically commonality is defined as one minus the uniqueness. So what we're looking for, either one of those measures can tell us. And so we have the initial commonality, what we're ultimately interested though is that final commonality measure. And notice here we have specific variance, that's effectively the uniqueness. So what is ideal for us is where we have a high measure of commonality or low measure of uniqueness. Now what that would indicate is the common factor solution is doing a good job of explaining that particular survey item. And you can see, generally, we see numbers for commonality 0.8, 0.8 over 0.5 doing the decent job. Here are a couple of questions where the factor solutions are not doing that great a job at explaining those particular survey items. And this depends on here's another item the work hard play hard question. We are not doing a great job of explaining that. And this is ultimately, it's going to be a judgment call. If these particular items are very important for understanding the consumer, the factor analysis isn't doing a good job for you. So on the other hand, if these items turn out to be extraneous as revealed through our subsequent analysis, these might be targets early in the survey process to say perhaps, these are items that we can eliminate because they're not telling us anything that's particularly useful.