Can ANOVAs or Student tests be conducted on any summary statistic at the individual level?

Question

I am wondering if ANOVAs or Student tests can be performed on any summary statistic of performance at the individual level without any effect on type 1 and type 2 error.

For example, consider a simple experimental design with a categorical independent variable and a continuous dependent variable. For instance, human participants either drink an alcoholic or a non-alcoholic beverage, and then perform 100 trials of a detection task. The variable of interest is the response time (RT) in each trial. Researchers generally compute the mean RT for each subject, and run an ANOVA or a Student test on these individual means. Would it possible to instead compute the median RT for each subject, and run an ANOVA or a Student test on these individual medians? I think this alternative approach is valid so long as assumptions of the test are satisfied, but maybe I am missing something.

Answer 1

I wouldn't collapse any within-subject repeated measurements of RT into a mean or median, since they're correlated. The within-subject correlation among repeated measurements affects the overall difference between subjects (B), within subjects (W), and their interaction (BW) and therefore needs to be preserved during the analysis.

Collapsing into anything throws away the valuable information related to within-subject correlation. Repeated Measures ANOVA (RMANOVA) can easily handle this. Otherwise use a longitudinal regression method that can handle all the repeated within-subject RTs, as well as the categorical grouping (treatment) variable.