On 21 Apr 2000, Kermit Rose wrote:
> The following is my proposed methodology for analyzing survey data for a
> professor in criminology at Florida State University.
>
> I'd like someone experienced in categorical data analysis to review it and
> email me comments, or criticisms, or suggestions.
[ KR: Please post any response to the edstat list as well as to me.
I may not have the leisure to continue this conversation, and others
on the list may have better advice for you in any case. -- DFB. ]
To begin with, you have not told us what the professor in criminology is
trying to find out, and why; without that information, no-one can offer
you (or the professor) useful advice on data analysis.
Your proposed procedure seems unnecessarily cumbersome. So far as I can
tell from all that algebra, you're effecitively substituting a whole
bunch of 2x2 tables for a single RxC table (R = number of rows, C =
number of columns) with R>2 and(/or?) C>2. Or, for each of several RxC
tables.
Why do you not first do the obvious contingency table chi-square
to see if there's anything worth following up? (And if I were doing it,
the follow-up(s) would be in the RxC format as well.)
Your #1 null hypothesis is that two dichotomized variables are
independent. I don't believe the test statistic you propose -- more
about that later -- but this is the formal null hyp. for the usual
contingency table chi square.
> The dependent variable is a multivalued categorical variable.
So far, so good.
> The model dependent variable is an interaction variable. It is the
> interaction of some subset of the 10 two-valued dummy variables
> representing the dependent variable. The 10 values of the dependent
> variable are choices of preferential treatment for affirmative action.
Here it begins to get sticky. I cannot tell whether you mean the
same thing by "interaction" that I would mean. In particular,
there seems to be no difference between "interaction variable",
in your terms, and "indicator variable", in my terms.
> The model independent variable is also an interaction variable. It is
> the interaction of two-valued dummy variables representing some subset
> of the predicting variables.
< snip, details of standard construction of indicator variables >
> Suppose R is an ordinal level variable with values r1 < r2 < r3 < r4.
> Then R is converted to three variables S1,S2,S3 with
>
> S1 = 1 if R = r1 and S1 = 0 otherwise.
> S2 = 1 if R = r1 or r2 and S2 = 0 otherwise.
> S3 = 1 if R = r1 or r2 or r3 and S3 = 0 otherwise.
Possible, but doesn't seem necessary. Why not leave R as it is instead
of constructing dichotomies?
< snip, details of argumentation >
> We define parameters t,I,D and N as follows.
>
> t is the number of cases where both the model independent and model dependent
> variable are true.
>
> I is the number of cases where the model independent variable is true.
>
> D is the number of cases where the model Dependent variable is true.
>
> N is the total number of cases.
Somewhat more briefly, and a good deal more clearly for me, you are
defining a 2x2 table thus:
Independent Dependent variable
variable 1 0 | TOTAL
----------------+-----------------------+--------
1 | t . | I
0 | . . | .
----------------+-----------------------+--------
TOTAL | D . | N
with the values marked "." determined by subtraction.
(You defined a "Col pct" as t/D, which is not a % but a proportion.)
< snip, tedious definition of above table >
< snip, definitions of covariance, variances, r^2;
which I did not really follow >
> Chisquare of crosstab of model independent variable with model
> dependent variable is
>
> (t - D*I/N)*( N/[D*I] + N/[I*(N-D)] + N/[D*(N-I)] + N/[(N-I)*(N-D)] )
No, I don't think so. Your formula is of the form A*B. B is
nonnegative. A may be positive or negative, so the product is positive
or negative depending on A. Chisquare cannot be negative.
> The significance number that is calculated for a statistic is the
> predicted probability that the null hypothesis is true.
I very much doubt it. This certainly does not conform to the standard
statistical definition of "level of significance", which I assume to be
what you want us to understand by "significance number".
> There are two different null hypotheses of interest.
>
> null_1:
> The dependent variable does not depend on independent variable.
Discussed above.
> The significance of null_1 is (D - t)/N
Can't imagine why it would be. In any case, one doesn't speak of
"the significance of an hypothesis" (null or otherwise), one speaks of
the significance of a test, or of a test statistic; and one is thereby
referring to a sampling distribution of the test statistic in question.
You seem to have no sampling distribution in mind.
> null_2:
>
> There is not a bidirectional relationship between the independent
> variable and the dependent variable.
What do you mean by a "bidirectional relationship"? Whatever you mean,
it cannot be different, so far as I can see, from null_1, for a 2x2
table. You've only got one degree of freedom for detecting whether there
is ANY relationship of any kind; you have zero d.f. for detecting
whether a relationship, once found, is of one kind or another.
> The significance of null_2 is (I+D-2*t)/N
See comments above on "significance of null_1".
-- DFB.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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