Q: dichotomous variables

Hi!

Two questions about dichotomous variables:

1) Some elementary books present (exploratory) factor analysis as a
parametric method where the variables have to be continuous, at least in
interval scale, and with normal distribution (which view is rather
dogmatic). However dichotomies have been used in factor analysis with
certain things in mind. Gorsuch (Factor Analysis 2nd Ed. , 1983) and
Rummel (Applied Factor Analysis, 1970) give such examples and present
some difficulties but do not deny the use of dichotomous variables
categorically. I know that LISREL, Mplus and other programs offer
sophisticated solutions to the problem. However PCA or PFA (setting
communality iteration value low) give quite consistent results. Would
you happen to have other EFA books or other sources where this question
is dealt with or enlightened opinios?

2) Long ago it was quite clear to me, that methods like one-way ANOVA
and cross-tabulation with khii-square gave very similar results (when
testing the differences in proportions). Recently I calculated from a
real material the p-values with three methods: khii-square, logistic
regression, and one-way ANOVA. The tables were 8*2. Highest frequency in
8 categories was 55 and lowest 21 and the proportions were regularly
lower than .5 in the dichotomies. I did 38 real data calculations. The
obtained p-values between khii-square and one-way ANOVA correlated (to
my surprise) .99996. Range of p-values was from .885 to .005 thus the
values were practically identical. Number of cases was 350. Correlation
with logistic was .871 thus similar but not the same. I understand that
with larger data sets the above mentioned khii-square and one-way anova
are identical. What bothers me is that basic texts present the anova
requirements in a very categorical way so that the reader is ready to
adopt the view "anova is basically wrong and gives definitely wrong
results" in testing differences in proportions (percentages). Comments
and possible references to this second problem are wellcome as well.

Cheers, Erkki

<http://www.helsinki.fi/people/~komulain/>
.