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

 From Stas Kolenikov To statalist@hsphsun2.harvard.edu Subject Re: st: Chi-squared test for independence of observed and expected frequencies Date Thu, 15 Jul 2010 16:51:59 -0500

```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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