Herman Rubin wrote:
>
> In article <[EMAIL PROTECTED]>,
> Joseph McDonnell <[EMAIL PROTECTED]> wrote:
> >I may be wrong, but I thought that Gerhard was asking something like "If I
> >perform a linear regression but with a dichotomous dependent variable, do
> >I get 'garbage' results?"
>
> The results must be at least partly garbage. We can
> consider the dichotomous variable to be 0 or 1, and,
> using expectation, should interpret an answer between
> 0 and 1 as a probability.
>
> However, what meaning can be given to <0 or >1? The
> TRUE "linear regression" does not give the conditional
> expected value of the dependent random variable given
> the independent random variables, here the probability
> of 1, as it does in a linear model..
>
> >Joseph
(1) Perhaps part of the problem is in the premise.
The subject header specifies "ANOVA".
With 2 groups, Student's t test applied to a binary outcome for
large samples is, for all practical purposes, the square root of
Pearson's chi-square statistic for homogeneity of proportions.
I have some simulation results for more than two groups which
suggests that ANOVA can be liberal in the 2xc case with nominal
levels of 0.05 being closer to 0.03.
(2) Regression of a 0/1 variable on a continuous predictor is
Fisher's version of discriminant analysis. What Professor Rubin
says about the possiblity of misinterpretation is true, but that
doesn't invalidate the technique for use as Fisher intended.
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