AW: st: Chi-squared test for independence of observed and expected frequencies

["Marc Michelsen" <marcmichelsen@t-online.de>]

Thank you very much for all the valuable comments. Having read all that, I
will probably skip the analysis.

-----Ursprüngliche Nachricht-----
Von: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Steve Samuels
Gesendet: Samstag, 17. Juli 2010 00:24
An: statalist@hsphsun2.harvard.edu
Betreff: Re: st: Chi-squared test for independence of observed and expected
frequencies

Marc Michelsen  wants to use the Chi Square test of independence in a
contingency table of two of his predictor variables, because the test
occurs in a reference. Stas  and Maarten suggested alternatives.  But
he wants to test the "significance of each of the frequencies".

This would have been ill-advised but possible.  See the section
"Nevertheless, it would be quite helpful to determine the relative
importance
of the two explanatory variables (dimensions), i.e. prior stock return
(divided into quartiles) and credit rating outlook (positive, negative,
stable)."

Agreed, but the chi square test for independence of the two
explanatory variables says  _nothing_ about their relative importance
as predictors.  The same logic applies to a test for the correlation
of two continuous predictors in ordinary regression.  Correlation
(multicollinearity)  will make it difficult to disentangle the effects
of the involved predictors, but it says nothing about the relative
importance of any of them

The authors of Marc's reference might have had other reasons for
studying the association of the two predictors.  They might have also
tested a single cell with the residual shown on page 81 of A. Agresti,
2002, "Categorical Data Analysis", Wiley Books.

Steve


On Fri, Jul 16, 2010 at 4:22 AM, Marc Michelsen
<marcmichelsen@t-online.de> wrote:
> Stas, Maarten,
>
> many thanks for your comments.
>
> The complete reference is: Dittmar, A., and A. Thakor. "Why do firms issue
> equity?" Journal of Finance 62 (2007), 1-54.
>
> You are totally right, the authors use this analysis only as an add-on /
> robustness test. The main body of the paper are multivariate analyses.
> Nevertheless, it would be quite helpful to determine the relative
importance
> of the two explanatory variables (dimensions), i.e. prior stock return
> (divided into quartiles) and credit rating outlook (positive, negative,
> stable). Do you have any idea how the authors have tested the significance
> of each of the frequencies?
>
> I will have a look at your three proposed alternatives and see how fancy
> they are.
>
> Regards
> Marc
>
>
>
> -----Ursprüngliche Nachricht-----
> Von: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Stas
Kolenikov
> Gesendet: Donnerstag, 15. Juli 2010 23:52
> An: statalist@hsphsun2.harvard.edu
> Betreff: Re: st: Chi-squared test for independence of observed and
expected
> frequencies
>
> On Thu, Jul 15, 2010 at 10:33 AM, Marc Michelsen
> <marcmichelsen@t-online.de> wrote:
>> I am trying to copy the approach of Dittmar/Thakor (2007) "Why do firms
>> issue equity?" p. 27: The authors divide their sample of debt and equity
>> issuers into quartiles based on two explanatory variables, i.e. building
a
>> matrix. Specifically, they examine the observed number of firms that fall
>> into one of the four categories and compare them to the expected
>> frequencies. After that, they apply a chi-squared test for independence
to
>> determine if there are more or fewer firms than expected in each
category.
>> Untabulated results show that each of these frequencies is significant.
>
> I agree with Maarten: that's a strange approach. Not that it is
> totally inappropriate... but it smells like 1960s when computations
> were essentially restricted to how much handwriting you can fit onto
> two sheets of paper. Propagating strange approaches does not do a good
> service to whatever discipline you are in (finance?).
>
> If those are continuous variables, you can use two-sample
> Kolmogorov-Smirnov tests to compare the distributions. I am pretty
> sure that bivariate versions of K-S tests exist, but they are not
> implemented in Stata. If the explanatory variables are categorical,
> you can compare the samples using -tabulate variable debt_vs_equity-
> as they are.
>
> If you want a fancier analysis, you can run -qreg- (or rather -sqreg-)
> over a set of quantiles, with debt/equity as the explanatory
> variables, to gauge whether the distributions of the continuous
> variables are the same for two types of firms.
>
> --
> Stas Kolenikov, also found at http://stas.kolenikov.name
> Small print: I use this email account for mailing lists only.
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-- 
Steven Samuels
sjsamuels@gmail.com
18 Cantine's Island
Saugerties NY 12477
USA
Voice: 845-246-0774
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