What is a residual?

A residual is the difference between the predicted score and the actual score for one observation (usually one participant). If you’re using ordinary least squares regression (which includes ANOVAs, t-tests, typical regression, etc. – everything you do in a typical applied stats class) the average of all of the residuals will be zero. That’s why sometimes when we’re talking about stuff that applies to the whole dataset, we leave off the residual term altogether. For any individual observation, you can calculate the residual by getting the score your model would have predicted for someone in that situation (e.g. someone in that cell in your factorial ANOVA, or someone with that predictor score if you’re doing a regression), and then subtract that from their actual measured score.