Re: Explaining significance to laypersons: why the tails?


Herman Rubin wrote:
> In article <d6dfmo$d61$1@xxxxxxxxxxxxxxxxx>,
> bill <please_post@xxxxxxxxxx> wrote:
> >In <1116347367.023147.263230@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>
clemenr@xxxxxxxxxx writes:
>
>
> >>bill wrote:
> >>Is that somewhere in the ballpark?
>
> >Halfway there! I was about to reply that this argument would not
> >do because it relies on an arbitrary significance level of 0.05,
> >which does not mean much to the layperson; he/she would simply
> >counter "just redefine your cutoff for significance to something
> >well below 0.01783901".
>
> The choice of cutoff needs to be more complicated than that.

In particular, if the distribution is not symmetric then in an extreme
case a single cutoff might reject the hypothesis only in a tiny area
under the upper tail, but reject huge amounts under the lower tail. I
realise that the original poster is not arguing for the cutoff, but
discussing a hypothetical layman's argument. But, drawing a picture of
a highly asymmetric distribution and colouring in the regions where
they null hypothesis is rejected might answer that comeback.

If the distribution has multiple peaks then things would be even worse.
If t(x,a,b) is the value for x of a triangular distribution non-zero
between points a and b, then for some constants d, e and f, the
following would be a probability distribution:

f(x,a,b,d,e) = ( t(x,a,b) * (1+sin( d x + e )) ) / f

I don't even want to think of using a fixed cutoff for f(x,...) in
hypothesis testing for a distribution like a very hilly version of this
:-)

Cheers,

Ross-c

.

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