How to interpret chi2 results?

[Nienke vHoof]

I'm sorry for bothering you with this small detail, but couldn't seem to figure it out..

I'm trying to figure out of the result for ArticleAppearance on wtradingvolume is larger for larger firms. This is done by creating size3 and size4 out of the variable size. (With size3 being the 'lower' half of the results, and size4 being the 50% highest results)
The code I used is the following:

 regress wtradingvolume ArticleAppearance wlagReturns size3 wleverage wcashtoassets wbooktomarket Ratings i.GlobalCompanyKey i.DayofWeek i.MonthofYear i.sic3
  estimates store regr_A
  regress wtradingvolume ArticleAppearance wlagReturns size4 wleverage wcashtoassets wbooktomarket Ratings i.GlobalCompanyKey i.DayofWeek i.MonthofYear i.sic3
  estimates store regr_B
  suest regr_A regr_B, vce(cluster Ticker)
  test [regr_A_mean]ArticleAppearance==[regr_B_mean]ArticleAppearance

Results that I get are:

 ( 1)  [regr_A_mean]ArticleAppearance - [regr_B_mean]ArticleAppearance = 0

           chi2(  1) =   12.88
         Prob > chi2 =    0.0003

Now my stupid small question: How to interpret my results?
I can't seem to figure out what Stata picks as H0 and H1, and so what to conclude from the results..

Many thanks in advance,
Nienke

[Maarten Buis]

The null hypothesis is stated above the test, i.e. the difference between the two parameters is zero, which is equivalent to the hypothesis that the two parameters are equal. So in your case you can reject the hypothesis that the two coefficients are equal.

[Carlo Lazzaro]

Nienke:
the null hypothesis (H0) is: [regr_A_mean]ArticleAppearance=[regr_B_mean]ArticleAppearance. The alternative hypothesis (i.e. H1) is that they are different: [regr_A_mean]ArticleAppearance-[regr_B_mean]ArticleAppearance≠0.
According to the results of your chi2 test, there is evidence that the compared coefficients do differ (i.e., the null ihypothesis is rejected, as p-value=0.003, is well below the customary 0.05 cut-off value).

Kind regards,
Carlo

[Carlo Lazzaro]

When I replied, Maarten's advice was still unreported on the list.
Sorry for the redundancy.

Kind regards,
Carlo

[Nienke vHoof]

Carlo and Maarten, thanks a lot for your responses, helps a lot!

Kind regards,
Nienke

[Clyde Schechter]

I'm sorry to muddy the waters, but I don't see how the chi square test that Nienke has performed answers her stated question: "whether the result for ArticleAppearance on wtradingvolume is larger for larger firms."

The chi square test tests whether the coefficient of ArticleAppearance is the same in two different regression models. Those regression models are seen to be identical except that one conditions on a variable size3, and the other on a variable size4. The description of what these two variables are is, to me, confusing. But in any case, it does not appear that we have two regressions, one carried out for "small" and the other for "large" units of observation. Rather we have two regressions carried out using different representations of size as a covariate. Even if I knew exactly what size3 and size4 are, it is hard for me to imagine how this approach would lead to any answer to the stated question.

I think the easiest approach to her question would be to run a single model that includes an interaction between size and ArticleAppearance. If the implied homoscedasticity is unacceptable using that approach, a two regression approach followed by -suest- could work, but I would think it would involve generating a dichotomous variable that indicates large vs small size, and the two regressions would be differently conditioned: -if large- and -if small-, respectively.