On Sat, 1 Feb 2003, David C. Howell wrote in part: > This morning I sent out the message below. I still have basically > the same question, but when I went back and looked at my resampling > program, I discovered an error. When I corrected that, the > distribution is normal. But I still don't know what is wrong with my > argument that it shouldn't be normal.
Might it have to do with assuming values of X to be fixed, not random, in the regression model? The distribution of r is commonly derived, I thought, on the assumption that both X and Y be normally distributed. But if X be considered to have fixed values, and therefore not to be a random variable, the usual distribution of r presumably would not apply. I suspect your question arises because beta and r have the same *value*; but to say that the *value* of beta is equal to the *value* of r is not necessarily to say that the *distribution* of beta is the same as the (usual) *distribution* of r, is it? > ***************************************** > This morning's message [condensed -- DFB]: > > Yesterday I received a query asking about the sampling distribution of > beta, the standardized regression coefficient. < snip > > > Let's ... look at the sampling distribution of b <snip> > > [References cited, and arguments presented, stating and/or proving the > assertion that b is normally distributed.] > > BUT, suppose that we standardized our variables. [Then] the slope is > equal to the standardized slope (beta) [which] is equal to the > correlation coefficient. So [for] standardized variables ... r, b, > and beta will all be numerically equal. > > [Comments on sampling distribution for r.] > > So now I have shown that the sampling distribution is skewed, though I > began by quoting experts I respect saying that it is normal. < snip > > > So where did I go wrong? The sampling distribution of b cannot be both > normal and skewed, at the same time. ----------------------------------------------------------------------- Donald F. Burrill [EMAIL PROTECTED] 56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
