Monday, April 26, 2004

Evolving Variances

Asking, "Can Drug-Free Baseball Stars Smash Records?", Stephen Metcalf evokes Stephen J. Gould's "Why No One Hits .400 Anymore." Again, it takes good questions to provoke good discussions. Gould paid attention to changes in variances and came up with a good story. Not only are offensive and defensive abilities, on average, both improving but there are reasons to think that variances are getting smaller and fewer outliers are to be expected.

In most social science and related discussions, it is natural to focus on trends in mean values. Much less investigation is focused on whether variances have evolved in interesting ways.

Anomalous prices have shorter life spans in the global economy. But, this means there are more and better reasons to avoid price competition and product differentiate if at all possible. But quality advantages will be more easily emulated.

Evolving means are the staple of any and all statistical absracts. In a better world, we would also be looking at data on evolving variances. These data exist but are seldom published.