Estimating efficiency a priori: a comparison of blocked and randomized designs

This technical note deals with a priori estimation of efficiency of functional magnetic resonance imaging (fMRI) designs. The efficiency of an estimator is a measure of how reliable it is and depends on error variance (the variance not modeled by explanatory variables in the design matrix) and the design variance (a function of the explanatory variables and the contrast tested). Changes in the experimental design can induce changes in the variance of estimated responses. This translates into changes in the standard error of the response estimate or equivalently into changes in efficiency. One consequence is that statistics, testing for the same activation in different contexts (i.e., experimental designs), can change substantially even if the activation and error variance are exactly the same. We demonstrate this effect using an event-related fMRI study of single word reading during blocked and randomized trial presentations. Furthermore, we show that the error variance can change with the experimental design. This highlights a problem with a priori comparison of efficiency for two or more experimental designs, which usually assumes identical error variance.