# [S] r and rho

Shawn Boles (shawn@luthien.ori.org)
Thu, 12 Feb 1998 13:55:00 -0800

Frank:

The correlation coefficent r is a statistic for a sample and estimates
population parameter rho. The test of the null hypothesis Ho: rho=0,
will of rejected if the sample statistic is unlikely to have been
drawn from a population with a true rho of 0. In the case where r
is _exactly_ 0, Ho: will not be rejected. As r diverges from 0, probability of
rejecting Ho: increases as sample size increases.

hope this helps -

Shawn Boles

Oregon Research Institute Internet: shawn@ori.org
1715 Franklin Blvd. Voice: (541) 484-2123 Ext. 225
Eugene, Oregon /97403-1983 USA Fax: (541) 484-1108

....................... non nova, sed novae .........................

fro11@lycosmail.com writes:
> I have two simple (maybe stupid?) questions about hypothesis tests, for example in correlation and regression.
>
> 1.
> The significance test in correlation analysis asks if there is a significant correlation in the population, i.e., you test the null hypothesis rho = 0. If you reject the null, you conclude that there is significant correlation. However, the correlation coefficient itself indicates whether there is a correlation (if zero, there is no correlation).
>
> If the conclusion of the hypothesis test is that the null should not be rejected, you conclude there is no correlation. But what is the difference between this conclusion and having a zero correlation coefficient in a significant correlation? Do they mean the same thing?
>
> The question is whether failure to reject the null amounts to the same conclusion, a conclusion of no relationship?
>
> 2.
> The question for regression is basically the same: does an insignificant regression imply that that there is no relationhip (of the kind specified in the regression, for example, linear) between the variables?
>
> Of course, I understand that for correlation or linear regression, the conclusion is that there is no *linear* relationship.
> Frank O'Hare
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