All data analysis – all statistics – involves a mathematical ‘model’. This statistical modelling can be very simple. If we hypothesise that male and female gerbils differ in weight, we might use a model like weight_for_this_gerbil = mean_weight + sex_effect_for_this_gerbil + error_for_this_gerbil, or more generally (across all the gerbils we measure): weight = mean_weight + sex_effect + error. By ‘error’, or ‘residual’, we mean ‘what’s left after we’re done explaining’. We could compare this to a simpler model, weight = mean_weight + error, in which sex plays no explanatory role. If our model is any good – if sexes differ in weight – then the model with sex_effect will predict better than the model without.