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Dear Mike > I've been following this very interesting and enlightening conversation, as it potentially applies to some atlas-based techniques we're interested in in my lab. I'm a bit confused about one point (probably just misunderstanding something). You and others have pointed out that the registration is not informed of the design, which seems crucial. Is that really true, though? Isn't it possible for the design to correlate strongly with the features being used for normalization, even if it is not set up that way a priori? > > To use your example with groups A and B, in the real world they are not likely to actually be arbitrary. If I knew that group A was generally higher in value than group B, I could probably make the means closer together by nudging the higher values down selectively, even without knowing your actual assignments. This would correspond for example to a healthy control vs. multiple sclerosis study -- where we expect FA to in general be lower in MS, and simultaneously use FA to drive the normalization. the discussion has been exclusively about false positives and control of false positives (which is what classical statistical testing aims at). What we mean by a false positive is “to detect a difference when in truth there is no difference”. The way to do that is to compare the statistic (for example a t-value) one observes to a null-distribution. The null-distribution is the distribution of your test-statiistic under the null-hypothesis, i.e. if indeed there is no difference. To get an idea of what the null distribution is, imagine that case where there is no difference between your groups, imagine that you have done the experiment and that you have calculated your test-statistic (t-value). What do you expect that t-value to be? The “expectation” is zero, but for any given experiment you are very unlikely to get zero. You will get some small value, say for example that you get t=0.9. Imagine now that you repeat the experiment with two other groups that there are no difference between. Do you think you will get the same value this time? Not likely, you will get some other small value, maybe this time you get t=-0.34. If you now keep repeating this experiment over and over you will eventually have a distribution of values, and this is the null-distribution. In your example above you have predicated that there _is_ a difference between A and B, i.e. that the null-hypothesis is false. If the null-hypothesis is false, there can be no such thing as a false positive. Only a true positive or a false negative. I hope that helps. Jesper