On Jan 10, 6:00 pm, Michael Press <rub...@pacbell.net> wrote: > In article > <e210e360-0b75-4c59-9225-50a0133a5...@px4g2000pbc.googlegroups.com>, > Ray Koopman <koop...@sfu.ca> wrote: > > [...] > > > > > > > It all depends on what you want. Look up the Gauss-Markov theorem. > > To justify the usual OLS estimates of the regression coefficients, > > the errors need only to be unbiased, uncorrelated, and homoscedastic, > > but to justify all the usual p-values and confidence regions, the > > errors must be iid normal. > > > However, that's considering only the theoretical justification. > > In practice, what matters is not whether the assumptions are right > > or wrong, but how wrong they are -- they're never exactly right. > > > Normality is probably the least important assumption. The most > > important things to worry about are the general form of the model > > and whether it includes all the relevant predictor variables. Then > > you ask how correlated and/or heteroscedastic the errors might be. > > Finally, you might wonder about shapes of the error distributions. > > Minor departures from normality are inconsequential. Nothing in the > > real world is exactly normal, and any test of normality will reject > > if the sample size is big enough. > > Assuming that the errors are normally distributed is > equivalent to assuming that the errors have mean zero > and fixed variance (using the new word I heard today: > homoscedastic) in that those assumptions least affect > how close our analysis gets to discerning the > parameters of interest. Normality is a bad assumption > only if we are suppressing some knowledge of how the > errors are distributed beyond the initial assumptions. > If it somehow turns out that a different set of > assumptions about the errors is better, for some value > of better, then that is called scientific discovery, > not bad assumptions. We should get to the point where > we cannot wring any more meaning out to the data and > are left with errors normally distributed around zero. > > It is not that I said anything more than you about the > mathematics and statistics---only voiced my perspective > on the process. If you see that I am in error, normal > for me, I welcome hearing about it.
I learned the word "heteroscedasticity" today. still trying to pronounce it without tripping.
Thanks for the perspective on the relative importance of normality, and why.