In article <[EMAIL PROTECTED]>,
Rich Ulrich <[EMAIL PROTECTED]> wrote:
> I agree, if you don't have "statistical power," then you don't ask
> for a 5% test, or (maybe) any test at all. The JUSTIFICATION for
> having a test on the MIT data is that the power is sufficient to say
> something.
The reason why one should NOT do a significance test on this data, at
any level, and regardless of how much power the test would have, was
explained by me a while ago in the post I have repeated below.
If you think there is something wrong with my reasoning, I suggest you
explain the flaw.
Radford Neal
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I think the statistical issue in this discussion can be boiled down to
a question of how to calculate standard errors for regression
coefficients.
What regression? Well, there isn't one, because there isn't any data,
but the discussions seems to presuppose the possibility of data that
for each faculty member gives their salary (the response variable, y),
their gender (x1, coded as a dummy variable), and some indicator of
performance (x2). The question is whether one has evidence that the
regression coefficient for the dummy gender variable (x1) is non-zero.
This will require computing the standard error for the estimate of
this regression coefficient.
The accepted procedure for computing this standard error involves the
sample correlation between the two predictors, x1 and x2. When the
sample correlation is high, the standard errors for the regression
coefficients will tend to be high, making it more difficult to
conclude that the coefficient for gender is non-zero.
The procedure apparently being advocated by some posters is to perform
a test of the null hypothesis that the correlation between x1 and x2
in the population is zero, and if there is not sufficient evidence to
reject this null hypothesis, compute the standard errors for the
regression coefficients as if the predictors were uncorrelated.
I believe that this procedure is not generally accepted, for very good
reasons.
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Radford M. Neal [EMAIL PROTECTED]
Dept. of Statistics and Dept. of Computer Science [EMAIL PROTECTED]
University of Toronto http://www.cs.utoronto.ca/~radford
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