[R] t-statistic for independent samples

[Kevin E. Thorpe]

On 04/17/2013 06:24 PM, David Arnold wrote:
> Hi,
>
> Typical things you read when new to stats are cautions about using a
> t-statistic when comparing independent samples. You are steered toward a
> pooled test or welch's approximation of the degrees of freedom in order to
> make the distribution a t-distribution. However, most texts give no
> information why you have to do this.
>
> So I thought I try a little experiment which is outlined here.
>
> Distrubtion of differences of independent samples
> <http://msemac.redwoods.edu/~darnold/math15/R/chapter11/DistributionForTwoIndependentSamplesPartII.html>
>
> As you can see in the above link, I see no evidence why you need a pooled or
> Welch's in these images.
>
> Anyone care to comment? Or should I put this on Stack Exchange?
>
> D.

Admittedly, I just skimmed the page, but one thing stands out.  Your 
standard deviations are really quite close to each other.  Try your 
simulations again with variance ratios exceeding 2 and see what happens.


-- 
Kevin E. Thorpe
Head of Biostatistics,  Applied Health Research Centre (AHRC)
Li Ka Shing Knowledge Institute of St. Michael's
Assistant Professor, Dalla Lana School of Public Health
University of Toronto
email: kevin.thorpe at utoronto.ca  Tel: 416.864.5776  Fax: 416.864.3016