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I'm trying to learn ANOVA and see how it applies to a certain experiment. In the experiment we are trying to predict if a certain brain signal is predictive of whether a mouse would do the correct or wrong action. For simplicitly, let us assume that the signal is a scalar real number.

So, there are two classes of interest: correct and mistake. There are also several nuisance parameters:

  • Experiment is performed on multiple mice. There is variance among mice
  • Each mouse performs a task, say, 100 times each day for 10 days. For each mouse there may be variances among days.
  • Mice actually perform one of two different tasks, call them Task1 and Task2. The tasks are very similar, as for both there is a correct and wrong solution. While it is an interesting parameter, for this particular question the task type is a nuisance parameter

So, the goal is to check if the signal is predictive of the classes (Correct/Mistake), excluding the effects of categories Mouse, Day and Task.

After reading on ANOVA, I learned that in case there is one nuisance category, one can perform blocking over that category, and exclude it by means of procedure called Two-Way ANOVA.

Questions

  1. If I have multiple nuisance categories, what is a good way to exclude their effect? Should I perform blocking over every combination of the categories?
  2. The number of days and number of tasks per day varies across mice. Is this sort of variability a problem for ANOVA?
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