<HTML>ISHMAEL wrote:
>
> A much more plausible (but still incorrect) scenario
> proposed (in jest) by one of my students is that divorce
> leads to a greater need for housing, which in turn leads to a
> greater demand for sinks, the majority of which will be steel.
> ---------------
>
> That is actually an excellent idea.
>
> My point was only that the more perfect a correlation, the
> greater the odds in favour of there being a relationship
> between the two. Thus we should not dismiss a connection
> between sink sales and the divorce rate simply because it
> appears patently ridiculous.
And we should not accept it unless there is supporting evidence of a proposed mechanism of causation. In this case there is no 1:1 causal mapping of divorces => housing demand (the moving divorcee often moves in with new partner). If you think htat there is a causal relationship at work, demonstrate it with data, not with argument by scenario.
This has been an excellent example (thanks, Alice!); no relationship outside the statistical correlation has been shown, yet we <i>still</i> have someone arguing for it.
> -----------
> Please describe how you would differentiate statistically
> between a perfect correlation that occurrs by chance and one
> that does not.
> -----------
>
> A theoretical *perfect* correlation (in the absolute sense)
> has a chance factor of zero
Incorrect.
> (but of course, *perfect*
> correlations never exist,
Incorrect.
To address the two incorrect statements above:
I hypothesise that to give credence to the OCT you have to be dead from the neck up. If, to test this, I put 100 live OCT acolytes into a room and decapitated them, there would be a perfect correlation between the number of severed heads and the number of dead OCT acolytes (thus disproving my hypothesis -- oh well, can't win 'em all...).
> A sufficiently minimal chance factor produces a
> "statistically proven" case for a relationship.
Incorrect. Correlation <b>never</b> implies causation (or relation beyond correlation); other evidence must be found.
May I suggest that you read and understand M.J. Moroney's somewhat dated but still excellent little book, <i>Facts from Figures</i>; it may save you the embarrassment of making more incorrect pronouncements on this subject.</HTML>
