RV: hypothesis testing with correlation?

[Hector Maletta]

To correct a small typo that may be confusing to some: the parenthetical
remark in my second paragraph "(with probability higher than 5%, say)"
should actually be "with probability higher than 95%, say)".

Hector

  _____

De: Pushpender Nath [mailto:[hidden email]]
Enviado el: 30 May 2007 00:41
Para: Hector Maletta
Asunto: Re: hypothesis testing with correlation?



Thanks a lot dear Hector. It was useful.

On 5/29/07, Hector Maletta <[hidden email]> wrote:

        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: [hidden email]
<mailto:[hidden email]> ] En nombre de
Pushpender Nath
Enviado el: 29 May 2007 23:08
Para: [hidden email]
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




--
Regards

Pushpender Nath Saini