Re: Two nit-picks re definition of p-value (Was: goodness of fit ?)

Reef Fish wrote:
Anon. wrote:
Reef Fish wrote:
David Winsemius wrote:
"Reef Fish" <Large_Nassau_Gr0uper@xxxxxxxxx> wrote in
news:1157159157.724558.200410@xxxxxxxxxxxxxxxxxxxxxxxxxxx:

Ha: > p-value = P(TEST STAT. > observed TS)
Ha: < p-value = P(TEST STAT. < observed TS)
Ha: .NE. p-value = P(TEST STAT < - abs(observed TS))
+ P(TEST STAT > abs(observed TS)).

Completely unambiguous. 100% standard. I believe you missed
that part in your education about how to state "more extreme" in
p-values in hypothesis testing.
Note that the Ha I used (in the one-tailed cases) were all STRICT
inequality.


2. Isn't it really "EQUAL TO or greater than" rather than "greater
than"?
RF > It depends on the STATEMENT of the Alternative Hypothesis.
RF > If Ha is "greater than", the more extreme in p-value is "greater
RF > than":

RF > If Ha is "greater than or equal", the more extreme in p-value is
RF > "greater than or equal".

<snip>
I was taught to include the 0.0095 when computing the p-value:
But did your professor explain WHY? If he had bothered to, using
the definition of a p-value (as I'll show below), he would have
realized his own error. That's only one of the troubles of ROTE
teaching and ROTE learning, without understanding the reason(s)
WHY.

The Alternative Hypothesis is Ha: p .NE. 0,5

So, the definition of p-value for that problem would be
P(# Succeeses "more extreme" than the observed "2" successes)

= P (# Successes > 2 ) + P( # Failures < 2)

P(# Successes < 2) = .0016 + .0001.
P(# Failures < 2) is also .0016 + .0001,

which is why you multiplied by 2.


p = (0.0095 + 0.0016 + 0.0001)*2 = 0.0224
This is NOT correct. .0095 does NOT belong to the "more extreme"
definition of a p-value.

Do you agree? Thanks for clarifying.
You are welcome. You have to come back with better nits than
those!!
:-)

-- Reef Fish Bob.
<snip>
--------definitons from math stats texts------------
Cox and Hinkley says a "level of significance" p_obs is defined as:
p_obs= Pr(T >= t_obs;H0)
This is a CONTNUOUS r.v. where the = has probability zero.
However, D.R. Cox uses this same definition for the discrete case in his
"Principles of Statistical Inference" (CUP, 2006: get it whilst it's
fresh!). In section 3.3 he writes:

"With test statistic T, consider two p-values, namely

p+ =Pr(T>=t|H_0), p- =Pr(T<=t|H_0). (3.7)

Against WHICH Alternative Hypothesis?

This question makes no sense. p+ and p- are defined in equations 3.7, and are calculated from the assumptions in the null hypothesis.


In general the sum of these values is 1+P(T=t). In the two-sided case
it is then reasonable to define a new test statistic

Q=min(P+, P-). (3.8)

Q is a new test statistic for What Ho vs WHAT Ha ?

From the statement "In the two-sided case...", you should be able to work it out.


Your description so far made neither sense nor provide sufficient
information about the CRUCIAL Alternative Hypothesis.

To be honest, I'm surprised that you can't work out what the alternative hypotheses are.

Bob

--
Bob O'Hara
Department of Mathematics and Statistics
P.O. Box 68 (Gustaf Hällströmin katu 2b)
FIN-00014 University of Helsinki
Finland

Telephone: +358-9-191 51479
Mobile: +358 50 599 0540
Fax: +358-9-191 51400
WWW: http://www.RNI.Helsinki.FI/~boh/
Journal of Negative Results - EEB: www.jnr-eeb.org
.

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