Re: JACK TOMSKY: an HISTORIAL of nonsense

On 19 Mar, 15:19, "Luis A. Afonso" <lic...@xxxxxxxxxxx> wrote:
Richard Atkins:

In the coin problem you posted to the Readers must be indicated (do fill the blanks)
_____H0 :
_____Ha :
_____Significance level =

_________licas (Luis A. Afonso)

In fact this was just to illustrate the point I was making.

H0: p = 0.5
HA: p > 0.5
alpha = 5%

This is a much simplified situation compared to a proper equivalence
trial but it serves to illustrate the point that a non-significant
test result can provide support for a null hypothesis.

If I recall correctly, I selected the sample size to give a 97%
probability of obtaining a significant result (p<.05) if the true
value of q was .51 Therefore, given the results I previously
mentioned (equal heads and tails in 100000 tosses) I conclude my coin
is unbiased (by which I mean it has so little bias that it doesn't
matter - whatever bias is present is below the level of 'clinical'
significance that I chose at the start).

I appreciate the language is not ideal here but please understand that
(a) prior to testing I have constructed my mathematical model assuming
a null hypothesis that q is algebraically equal to .5 (b) having
completed the test, I am not concluding that the true value of q is
algenbraically equal to .5 but (c) I am saying the weight of evidence
favours the null hypothesis (as opposed to the alternative hypothesis)
so I conclude my coin is de facto unbiased.

I think the key thing is to appreciate the difference between studies
that are adequately powered and those where no power analysis has been
done. It is clear that Parkhurst was fully aware of this. Note that he
comments that reasons for a non-significant result can include too
small a sample. He later mentions the idea of making a decision based
on a statistical test using a predetermined "biological
importance" (obviously used to calculate sample size). Parkhurst is
clearly aware of the implications of sample size and of power
analysis. I think the reason he largely glosses over these it to keep
the explanation simple enough that the users of statistics to whom
this piece is directed can pick up on his central message, which I
interpret as follows:

In the absence of a properly powered study, a non-significant result
means your study has failed to provide evidence either way.

As regards his point that we can never prove a null hypothesis - in a
way this is simplification to the point of silliness since, by the
same argument you can never prove an alternative hypothesis either.
However it is understandable because I have also had occasions when I
have resorted to similar simplifications to get these ideas over to
students and researchers who have minimal statistical training.

.

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