Re: st: significance of the variables based on t-test or f-test

["Seed, Paul" <paul.seed@kcl.ac.uk>]

Dear Statalist, 

In László's present model, it is likely that the linear and 
quadratic terms are highly correlated, and the tests 
do not make sense taken separately.  Hence the need to rely on the 
F-test for the whole model.  It's weakness suggests nothing much 
(compared to the size & power of the data set) is going on.

Maarten's main conclusion notwithstanding, 
anyone facing a similar problem to László may wish to 
look at using orthogonal polynomials (Stata command -orthog-).
Reference: Golub, G. H., and C. F. Van Loan. 1996.  Matrix 
Computations. 3rd ed.  Baltimore: Johns Hopkins University Press.
László might also want to do this if cleaning and transforming 
the data improves the overall F test.

A sequence such as the following might show something. 
Higher degrees can also be used.
	orthog xi, poly(xi_) degree(2)
	regress y xi_1 xi_2



2012/8/30 Maarten Buis <maartenlbuis@gmail.com>:
> The main conclusion is that you cannot reject the hypothesis that
> screening intensity is neither linearly nor quadraticly related to
> risk adjusted performance.
>
> I would look at a scatter plot of performance against screening
> intensity and look if you can see any anomalies. If that does not
> work, than you'll just have to live with the fact that your data tells
> you that the two are unrelated.
>
> -- Maarten
>
> On Wed, Aug 29, 2012 at 6:59 PM, László Németh wrote:
>> Dear Statalist Users,
>>
>> I would like to analyze the relationship between the risk-adjusted
>> performance (DV) and the screening intensity of the SRI funds (IV). In
>> the first model I assume a linear relationship between these two
>> variables:
>> y = B0 + B1*xi+ui
>> The t-statistic of screening intensity is here 0.84
>>
>> Then I use a second model, where I add the square of screening
>> intensity (Xi2) as a second independent variable: y=B0 +
>> B1*xi+B2*xi2+ui
>> The t-statistic of Xi is 2.02, whereas the t-statistic of Xi2 -2.17
>> is. Based on this results I assume that there is a quadratic
>> relationship between the risk-adjusted performance and the screening
>> intensity of the funds. However, if I run an F-test with the two
>> independent variables I got a p-value of 0.1008.
>>
>> Now, I am not sure how I should interpret these results. Based on the
>> t-statistic, I think that there is a quadratic relationship, but the
>> results of the F-test make me uncertain. That is why I would like to
>> ask for your help in the interpretation of these results.
>> Thank you very much in advance for your help.


Paul T Seed, Senior Lecturer in Medical Statistics, 
Division of Women's Health, King's College London
Women's Health Academic Centre, KHP
(+44) (0) 20 7188 3642.


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