View Full Version : Re: Stats Power. Report Confidence Limits - p values

01-26-2005, 12:42 AM
I am in complete agreement with Dr. Allison's summary of statistics.

In response to the question below I would add that the p value is the
probability (assuming all the statistical assumptions are valid) of
obtaining the observed outcome by chance alone. This probability is
compared to the alpha level to determine statistical significance. The
reason that there is no such thing as "highly significant" or the even
more annoying "trending towards significance" is because the
experimental p value is the outcome of only one experiment. If the p
value of that experiment is sufficiently rare (less than alpha) we have
confidence in concluding that the observed phenomenon was _probably_ not
due to chance (not a Type I error). Our level of confidence is reflected
by the alpha level. In effect, alpha is a predetermined probability of
the correctness of our conclusions. If alpha is .05 then we can state
with confidence that our conclusions will be wrong 5 times out of 100,
we just don't know if this is one of those times. Since alpha is our
pre-established cutoff, one p is as good as another. Remember, you
cannot know if the null hypothesis or research hypothesis is correct.
You can "reject the null hypothesis" (palpha),
which is not the same as concluding that the null hypothesis is correct,
but rather that the null hypothesis (random chance) is a good at
explaining the data as the research hypothesis and that you therefore
have no reason to prefer the research hypothesis.

What we really want to do, in our own work and in our evaluations of the
works of others, is to justify alpha and not blindly insist in the .05
level. This level is probably not the most appropriate alpha for every
experiment and every data set.

Thomas M. Greiner, Ph.D.
Assistant Professor of Anatomy
Department of Health Professions
University of Wisconsin - La Crosse
4054 Health Science Center
1725 State Street
La Crosse, WI 54601-3742

Phone: (608) 785-8476
Fax: (608) 785-8460
Email: greiner.thom@uwlax.edu

-----Original Message-----
From: * Biomechanics and Movement Science listserver
[mailto:BIOMCH-L@NIC.SURFNET.NL] On Behalf Of Bryan Kirking
Sent: Tuesday, January 25, 2005 4:46 PM
Subject: Re: [BIOMCH-L] Stats Power. Report Confidence Limits - p values

To comment and question some of Dr. Allison's insight:

>>My understanding of the arbitrary "line in the sand" of 0.05 was
>>originally due to the choice of the original tables (pre computer)

I have heard this too. It was very tedious to calculate probabilities
Personal Computer) as is done now, so the investigator would pick the
appropriate values to simplify the calculations.

>>The p value reflects the probability of the observed change happening

Isn't this only correct if the null hypothesis is correct (not
rejected?). This is why (as explained to me by statisticians - I won't
claim authority here) it is considered incorrect to differentiate
"significant" from "very significant" from "highly significant"? I
this point because of your comment about relating the alpha level to the
seriousness of the outcome.

Bryan Kirking
ProbaSci LLC
tel. 512.218.3900
fax. 512.218.3972

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