Speed vs reaction time as a measure of cognitive performance

Choosing mean reaction time or mean speed (it's reciprocal) as the dependent variable in cognition experiments is frequently done for no better reason than convenience. It is shown that sometimes this choice is crucial in determining the order of the obtained effects. Moreover, it is proved that when the order of the effects is dependent upon the choice of the transformation, the assumption of homogeneity of variance is not true and hence ANOVA may not be justified. Alternative strategies are proposed to deal with this data-related problem.