Getting blood from a stone: Improving brain-behavior inferences without brain data

In recent years, the cognitive neuroscience literature has come under criticism for containing many low-powered studies, limiting the ability to make reliable statistical inferences. Typically, the suggestion for increasing power is to collect more data with neural signals. However, many studies in cognitive neuroscience use parameters estimated from behavioral data in order to make inferences about neural signals (such as fMRI BOLD signal). In this paper, we explore how cognitive neuroscientists can learn more about their neuroimaging signal by collecting data on behavior alone and using alternative estimators designed to leverage this information. We demonstrate through simulation and mathematical derivations that knowing more about the marginal distribution of behavior can improve inferences about the mapping between cognitive processes and neural data. We analyze the magnitude of this benefit, finding that it depends on the desired estimand and several underlying study parameters. While in many cases the absolute gains in precision can be modest, our results demonstrate that, in realistic settings, additional behavioral data can lead to the same improvement in the precision of inferences more cheaply and easily than collecting additional data from subjects in a neuroimaging study. This means that when conducting a neuroimaging study, researchers now have another knob to turn in a design analysis: the number of subjects collected in the scanner and the number of behavioral subjects collected outside the scanner (in the laboratory or online).