Welcome back to principles of fMRI. In this module we're going to introduce group analysis. We're first going to give a background and then we'll talk about moving from a single GLM analysis to the group analysis setting. In a multi-level analysis fMRI experiments are often repeated for several runs in the same session, several sessions on the same subject, and several subject, or a number of subjects now drawn from a population. And just to remind us, we've seen this before, but this is the hierarchal structure of the state. So now what you see is we have boxals within images within runs. Run one to K. Runs within sessions potentially, this could be a time one, time two, pre, post-drug intervention. And then sessions within subjects. So for group analysis we run multiple subjects, started with maybe a handful of subjects, but now, it's common to run tens, or even hundreds, or sometimes thousands of subjects nested within groups. Group might be a patient versus control, for example. So the data has this hierarchical structure. And in a multi-level model we, as we said before, do a first level analysis which deals with individual subjects. So we run a model on each subject. And then a second level model deals with groups of subjects, and that could involve patients versus controls, it could involve individual differences and relationships between brain activity and personable characteristics like age or performance. So here's a depiction of the group, and within a group there are subjects, each subject has their own time series. For every voxel, and we're still dealing with inferences that are performed in the mass user variant setting. So we're stealing with one voxel at a time. So here's an overview of the GLM analysis process again, we talked before about design specification or model building in several lectures, we talked about estimation of the design at the first level, that's for every voxel for a subject, and we talked about, defining contrast, which are effects of interest that you care about, and identifying contrast images for each person. Those contrast images for each person, and taken and combined with the contrast images from other subjects, into a group analysis, and that's what allows us to make inferences about which areas are activated in the population, and this is our framework. So we're going to work backwards from a group result to a individual subject result, and this is also rear view. So here there are some true signal mixed with noise, which yields a mixed map of signal plus noise. And if we do a statistical test in the group, then we end up getting a test statistic at each voxel, that could be a T value for example. And we threshold that, correcting for multiple comparisons. And we get some results, which we then interpret. So working backwards again, from the results at one voxel in a group analysis the most basic kind of group result is contrast values between task and control, where each dot here that you see is a score from one subject, and I'm interested in whether those scores, those contrast values, are significantly different different from zero in the group. So there's that group analysis again. Each of those scores then in the group analysis, each individual subject score is resulting from a contrast in a general linear model analysis. So this is an example with two regressers within that individual subject which yield beta 1 and beta 2, two regression perimeter estimates. Those are multiplied by a contrast of interest, this case the difference let's say between the two, one minus one, which yields a contrast value for each subject. So, what we're going to see next is a movie that takes us all the way through the analysis process, from individual subject, design and contrast at one voxel, repeated over a group of subjects, and then the process of doing the group analysis using the very simple one sample T test. So here we go, we're looking at one voxel, now this is a partial fit for trial type A and B within one subject to one voxel, there's the fit all trial types together. Now in the bottom left, we're going to see this difference between trial type one and trial type two, in terms of the human endemic response, the greater the difference is, then the greater the contrast value. Now that's going to be translated into dots, over on the right panel. So we see subjects being repeated. Now we're repeating the analysis several times. The first analysis is where we have all the subjects are actually identical, and the only differences across the subjects are in the actual fMRI random noise, the noise realization. So that's the black line, and that's only one source of air. Then we're going to repeat the analysis and that's the middle row, column of gray dots. And with that, we have two sources of noise. We actually have the design varying as well. So we've randomized the ordering of the events. And the design is randomized. So now we have a little bit greater spread in those points. So we have a little bit greater noise variance. And then in the third case, we've also added the idea that there are real differences across individuals. So now there are individual differences as well, and that adds an additional noise component. And so the spread in the points is greater. The greater the spread, the more that hurts us in terms of statistics, so that's the noise that we have to overcome. But that's a realistic situation. So the realistic idea is really what's happening on the right side, where we have variation due to random noise in the scanner, variation that's related to the design matrix itself, and what I've induced with the design, and then variation that's related to the individual differences in true levels of activation across people. So that's the overview of how the analysis works at one voxel, from soup to nuts. And we'll go back over this now in more detail, and explain it more completely in the next modules. This analysis maps onto a repeated measures analysis from traditional statistics in which we have one or more within person predictors. Now we have just one simple within subject contrast. So that's a generalized linear model, and we'll deal first with this sort of summary statistic case, which has the one simple T test and we'll deal later with models that count more completely for correlated errors and time series models. That's the end of this module. In the next couple of modules, we'll talk more about group analysis.