On 14 Dec 1999 08:40:18 -0800, [EMAIL PROTECTED] (William B. Ware)
wrote:
> As I recall, there was an article by Lunney et al that appeared in the
> Journal of Educational Measurement that examined the use of ANOVA with "1"
> and "0" as the DV. I believe that they concluded that distortion was
> minimal when the distributions were within an 80/20 split... I think that
> the article was in the early 70s, perhaps 1971.
>
> As Don has noted, proportions are means... which will be symmetrically
> distributed when the split is about 50/50. Apparently, the Central Limit
> Theorem applies as long as sample size is sufficiently large...
< ... >
The problem that I am aware of has nothing to do with the Central
Limit Theorem -- and I'm not positive what that problem is supposed to
be -- and everything to do with additivity and linearity.
If you have a 2x2 table, and the four groups have means on the
dichotomous outcome, of (1%, 4%; 4%, 16%), do you decide that this is
additive and has an interaction, or do you label it a simple pair of
multiplicative main-effects? - The interaction apparent by ANOVA
does not exist in the log-linear model. So it may be worth using the
ANOVA computer-procedure, and ignoring the interaction, if it is a lot
simpler to use that computer program. I am willing to use the
systematic absence of the interaction as evidence that the
multiplicative model is the better one.
The linearity-artifact does not exist for a simple t-test, one-way
ANOVA, or regression with small effect size (low R-squared, AND low
Odds ratios). So far as I know, you can do those ANOVA analyses with
proportions that may be beyond 20%, with very little loss of power.
Further, you should note, you have the risk of similar
linearity-artifacts when you analyze continuous variables that have
been re-expressed as their *rank-transformed values*. That applies
for essentiall the same set of models -- multiway, multi-variable, or
high R-squared.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
