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| From | Roger Newson <r.newson@imperial.ac.uk> |
| To | "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu> |
| Subject | Re: st: RE: one-tailed tests |
| Date | Thu, 8 Jul 2010 17:39:49 +0100 |
The confidence region is defined (at least approximately) as the set of parameter values that pass the test. Most of these applications work best when the tests are 2-tailed. In the case of confidence intervals, the test must usually be 2-tailed for the confidence interval to have both an upper limit and a lower limit. In the case of multiple-test procedures, it helps if the underlying tests are 2-tailed, because, that way, the P-values are non-negatively correlated (even if the test statistics may be negatively correlated), and this makes the multiple-test procedure less conservative. Occasional exceptions arise when the distribution of the test statistic, under some hypotheses, really is one-tailed. This typically leads to confidence intervals bounded only on one side (eg confidence intervals for odds ratios extending from a lower limit to infinity), or to a requirement for conservative multiple-test procedures (eg the Holm procedure).
I hope this helps. Best wishes Roger Roger B Newson BSc MSc DPhil Lecturer in Medical Statistics Respiratory Epidemiology and Public Health Group National Heart and Lung Institute Imperial College London Royal Brompton Campus Room 33, Emmanuel Kaye Building 1B Manresa Road London SW3 6LR UNITED KINGDOM Tel: +44 (0)20 7352 8121 ext 3381 Fax: +44 (0)20 7351 8322 Email: r.newson@imperial.ac.uk Web page: http://www.imperial.ac.uk/nhli/r.newson/ Departmental Web page: http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/ Opinions expressed are those of the author, not of the institution. On 08/07/2010 15:01, Nick Cox wrote:
I don't know why anyone would want to do any test if you can get a confidence interval. After all, most of the best science should be quantitative, and a confidence interval is a report on the measurement scale of interest: it summarizes information, it indicates uncertainty and it can be compared with your qualitative ideas on sign or direction quite easily. If you think that something should be positive, or increase, or whatever, you can see whether the c.i. lies the correct side of zero, or whatever. In contrast, a yes-no test decision or even a P-value is a more cryptic and problematic reduction of the data. Actually, I don't know why anyone would get a confidence interval if you can put most or all of the data on a graph. After all, a good graph shows the main features of the data and detailed departures from those features, and it can give you ideas on what next to do. I have to estimate the extent to which Eric or Roger was talking tongue in cheek, and you will have to do the same about this. Nick n.j.cox@durham.ac.uk Eric Uslaner Bea Potter asked how to do one-tailed tests and Roger Newson responded: "I don't know why anybody would want to do a 1-tailed test, except if the distribution of the test statistic, under the null hypothesis, really IS one-tailed." I don't understand why anyone would do a two-tailed test. If you have a theory, that theory is directional: The more A, the more B. A two-tailed test is completely inappropriate for this. E.g., in studies of voting behavior in political science, we usually posit that party identification is the dominant force behind voter choice. So if you are a strong Democrat, you will vote Democratic. A two-tailed test would imply that a strong Republican would be equally likely as a strong Democrat to vote Democratic. This is plain silly. If you don't have a theoretical focus, you don't have a research design worth submitting anywhere. So I don't understand why anyone does two-tailed tests and why Stata (together with other statistical programs) report them as defaults. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/
* * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/