airbear wrote:
I did not misunderstand the context. I am simply stating this: if a distribution curve is positively skewed, then it is not normal. And I think we would agree that the men's distribution more closely approximates normal than does the women's distribution, although perhaps neither of them meets requirements for normality necessary for the application of parametric statistics.
I'm not disagreeing with your statement that "if a distribution curve is positively skewed, then it is not normal." But I am disagreeing with the assumption that the men's distribution more closely approximates normal than does the women's distribution -- not because I know that the men's distribution isn't more closely approximated by a normal curve, but rather because the assumption isn't justified by the observation that the "spreads" between top-end performances are wider in the women's distribution than they are in the men's. (The distribution of women's marathon times is probably much closer to the distribution of men's marathon times fifty years ago than is the distribution of men's marathon times today. At what point did the distribution of men's marathon times become "normal"?)
Again, however, whether the distribution of times or performances is approximated by a Gaussian curve says very little about whether any of these models are accurate or useful in assessing performances among reasonably good athletes, since almost anyone who trains and competes seriously is going to be at the far end (right or left, depending on the parameter used for the x-axis) of the distribution curve. |