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

Bruce Weaver wrote:
Reef Fish wrote:
Richard Ulrich wrote:
---- snip ----
I can't picture myself writing it that way.
I think I would have to say something like, "exceeding
the 20% cutoff, which we previously justified for this case."
Or some such.

The use of the technical language of Acceptance and Rejection,
together with the underlying meanings of alpha and p-values,
no special language is required to re-explain what is understood.

In the particular case, the 0.150 is the PROBABILITY that the
K-S Test Statistic is "more extreme" than the observed D, when
the null hypothsis (that the data is from a normal distribution) is
TRUE.
But I stumbled, slightly, when reading this sentence, because of the
present tense "is" -- It scans better for me like this,
"... probability that the K-S Statistic will be [or 'would be']
more extreme than the observed D, ..."

In that context, "is" and "will be" means exactly the same. :-) It
comes from the definition of p-value which is the
Probability ( Test Statistic > observed value of the Test Statistic
when
Ho is true).


Bob, I have two nit-picks.

1. I would say that definition works for one of the two directional
alternative hypotheses. For the other directional alternative, it would
be "less than", not "greater than". And for the non-directional
alternative, you would either have to invoke absolute values, or
describe it as "more extreme than the observed test statistic".

2. Isn't it really "EQUAL TO or greater than" rather than "greater
than"? I know that for test statistics that have continuous sampling
distributions, the difference is trivial. But not so for those with
discrete sampling distributions. Here's a binomial problem, for
example, with a non-directional alternative hypothesis:

X = number of successes in N = 13 trials
p = p(success)
q = 1-p = p(failure)

H0: p EQ 0.5
H1: p NE 0.5

Observed X = 2

X p(X|H0)
---------------
0 .0001
1 .0016
2 .0095 <-- observed X
3 .0349
4 .0873
5 .1571
6 .2095
7 .2095
8 .1571
9 .0873
10 .0349
11 .0095
12 .0016
13 .0001
---------------

I was taught to include the 0.0095 when computing the p-value:

p = (0.0095 + 0.0016 + 0.0001)*2 = 0.0224

Do you agree? Thanks for clarifying.

--
Bruce Weaver
bweaver@xxxxxxxxxxxx
www.angelfire.com/wv/bwhomedir

Agresti (1996, p 42), speaking of a test statistic that is highly
discrete: "the P-value equals the probability of a value this large
or larger...." He then goes on to argue for what he calls the "mid P-
value", which is "half the probability of the observed result, plus
the probability of more extreme results."

.

Relevant Pages

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