[R] How to test the statistical significance of the difference of two univariate Linear Regression betas?

[Bert Gunter]

1. Is this homework? -- we don't do homework.

2. This is not an R question -- posting to stats.stackexchange.com or
other statistics websites is usually more appropriate for such non-R
statistical questions

3. General approach: Combine all data; model it with both a simpler
(fewer parameter, single slope) model and a more complex (separate
slopes for different groups of data); test difference in models (e.g.
via likelihood ratio which reduces to anova for the normal theory
case).

4. Better approach: Ignore 3, because the test has not been
pre-planned, suitable power has not been  designed in, or the
hypothesis is post hoc, etc., so that P values are therefore likely
just nonsense with no sensible interpretation. The correct answer is:
The slopes _are_  different (entropy is on my side here -- a very
powerful ally that one should avoid messing with). The relevant
question then becomes: Are they different enough to matter in your
context (which if it's homework is -- who cares?) .

5. Perhaps the best approach: Ignore the rantings of a grumpy
statistician and consult your local statistical resource for help,
which you clearly need more of then can be provided here.

Cheers,
Bert

On Wed, Mar 14, 2012 at 9:24 AM, Mark Leeds <markleeds2 at gmail.com> wrote:
> Hi: I'm jot sure if it's exactly what you want but check out Hotelling's
> paper from 1940. It
> should be in the archives because I answered this question before ( not
> from you ).
> If you can't find it, I'll find the title .... actually, here's the title:
>
> Hotelling, The Selection of Variates For Use in Prediction with Some
> Comments on the
> General Problem of Nuisance Parameters", Annals of Mathematical Statistics,
> 11,
> 271-283.
>
>
>
>
> On Wed, Mar 14, 2012 at 11:21 AM, Michael <comtech.usa at gmail.com> wrote:
>
>> How to test the statistical significance of the difference of two
>> univariate Linear Regression betas?
>>
>> Hi all,
>>
>> There are two samples of data: D1 and D2.
>>
>> On data D1 we do a univariate Linear Regression and get the coefficient
>> beta1.
>>
>> On data D2 we do a univariate Linear Regression and get the coefficient
>> beta2.
>>
>> How do I test the statistical significance of (beta1-beta2)?
>>
>> Could you please recommend packages/commands in R for doing this?
>>
>> Thanks a lot!
>>
>>        [[alternative HTML version deleted]]
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
>        [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.



-- 

Bert Gunter
Genentech Nonclinical Biostatistics

Internal Contact Info:
Phone: 467-7374
Website:
http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm