Bonnie’s recent post on diversity of skill sets, knowledge base, and other student attributes in statistics classes made me think of diversity as the raison d’être for descriptive and inferential statistics.
Students beginning a statistics class often say something to the effect “I want to be a counselor, why do I need to take statistics? One of my favorite answers to this question is to ask students to imagine a world where every person is a clone of me. Everyone looks like me, acts like me, in fact, is identical to me in every way, physically, cognitively, and emotionally. Of course this scenario leads to gasps of horror, especially from the women in the class. With a little class discussion, however, the realization suddenly grows that in this world all behaviors would be normal because there would be no variability among people. There would be no standard deviation for any measure we might obtain. Hence, no counselors would be needed. No one would be handsome, beautiful, intelligent, arrogant, energetic, or helpful (I’m not implying that any of these adjectives actually describe me). No behaviors would be abnormal, criminal, empathic, altruistic, selfish, or whatever. Such concepts imply a diversity in physical appearance, intellectual functioning, behavioral actions toward others, and so forth. If we want to know anything about such a population, we need measure only one member of the population. A measure taken on one person would describe all other people. Descriptive statistics wouldn’t be needed in this world.
Students soon realize that diversity is the reason that statistics is a necessary discipline to understand and explain our world. When there is diversity no single term adequately describes everyone. Thus we have had to develop statistics that describe “typical” and the spread around the typical.
A similar discussion can lead to an understanding for the need for statistical hypothesis testing. Think how easy it would be to decide if an independent variable has an effect on behavior if every person’s behavior were identical. If we introduce the independent variable with one person, and it changes that person’s behavior from the state prior to its introduction, then we know it is effective. And it will have the same effect for everyone.
A world without variability wouldn’t require statistics, but it wouldn’t be much fun to live in either.