Analyzing data from memory tasks - comparison of ANOVA, logistic regression and mixed logit model

Abstract

We compared three statistical analyses over binary outcomes. As applying ANOVA over proportions violates at least two classical assumptions of linear models, two alternatives are described: the binary logistic regression and the mixed logit model. Firstly, we compared the effects obtained by the three methods over the same data from a previous memory research. All three methods gave similar results: the effects of the tasks and the number of sensory modalities were observed, but not their interaction. Secondly, by using the bootstrap estimates of the parameters, the efficacy of each method was explored. As predicted, the bootstrap parameter estimates of the ANOVA had large bias and standard errors, and consequently wide confidence intervals. On the other hand, the bootstrap parameter estimates of the binary logistic regression and the mixed logit models were similar - both had low bias and standard errors and narrow confidence intervals.