More Summers Apology Stuff
King at SCSU Scholars posts about the Lawrence Summers flap I have posted on below. He focuses on the misinterpretation of statistical results and the reverse of the fallacy of composition - whatever is true for the whole must be true of the individual. It's a good read.
Every once in awhile when I mention that, on average, college graduates earn more than those who have no college degree, a student will say that he/she knows someone who has not completed college but does very well for him/herself. Bill Gates' name often comes up in such discussions. Yes, by the definition of the average, you will always find examples like this. The average is a measure of the middle value of a variable (and not the only measure) and thus has values above it and below it. But people sometimes forget to account for this. When we say one average is larger than another, all that we are saying is that this particular middle measure for one variable is higher than that for another variable.
It's also important to note, as King's post does, that the average, strictly speaking, is a measure of a middle value of observations taken from a sample. The population is a collection of everything of interest. The sample is a subset of the population. As such, the average doesn't account for every value in the population, only those "lucky" enough to have been observed in the sample. The larger the sample, the more representative it is of the population and the more likely that analysis of it will reveal the true nature of the population. Even if the sample is small, there are well-developed techniques that allow us to make statements about the population based on the sample. Moreover, the more we sample from the same population and the more techniques we use, the more we learn about it. Unfortunately, if people squelch some research because they find its direction or findings offensive, then repeated sampling will be less likely to occur and we will be less likely to learn about how things work.