```Date: Wed, 30 May 2007 00:13:03 -0300 Reply-To: Hector Maletta Sender: "SPSSX(r) Discussion" From: Hector Maletta Subject: Re: hypothesis testing with correlation? Comments: To: Pushpender Nath In-Reply-To: <4b72890a0705291908n5945f48ax3202eeaa5be322b3@mail.gmail.com> Content-Type: text/plain; charset="us-ascii" You should distinguish between statistical significance and substantive relevance or importance. Statistical significance asks whether your sample results enable you to say something about the corresponding population, and of course that depends on the size of the sample. A correlation of 0.20 may enable you to say (with probability higher than 5%, say) that the population correlation is probably greater than zero, if your sample is composed of 10,000 cases, but you may be unable to reject the null hypothesis (that the population correlation is zero) if your sample were only 100 cases. In any case, your analysis is just about the relationship between your sample and your population, and has nothing to do with the substantive importance of your findings. Substantive relevance is something totally different. Suppose you can actually reject the null hypothesis, i.e. you are reasonably confident that the population correlation is greater than zero (probably not much greater, since your sample correlation was just 0.20). Now you may ask ABOUT THE POPULATION: what is the meaning of this finding? If you are 95% confident that there is such a correlation (say about -0.20, give or take a confidence interval of several percentage points) between the blood concentration of drug X and the frequency of symptom Y, can you prescribe drug X to patients in order to reduce the frequency of the symptom? This question is about the substantive relevance of the finding, and it is about what is happening in the population where your sample comes from, whereas statistical significance deals with the question whether your sample finding is representative of the population facts. If your sample is large enough, even minuscule differences or correlations may be statistically significant, but they may be substantively worthless. Increasing sample size will increase statistical significance, but will not change the substantive meaningfulness or relevance or importance of a finding. Hector -----Mensaje original----- De: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU] En nombre de Pushpender Nath Enviado el: 29 May 2007 23:08 Para: SPSSX-L@LISTSERV.UGA.EDU Asunto: hypothesis testing with correlation? Dear listers, Can we test hypothesis with the help of bivariate correlation with *t *test, where decision is based on the significant, not significant value of the *t *test. Should we chech the absolute value of correlation too, or merely the *p *value of *t *test applied on correlation? Sometimes a correlation of 0.2is also significant at 0.05 level. What should be done in that case? -- Regards Pushpender Nath Saini ```

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