Re: Simple binomial test question

David Winsemius wrote:
DZ <14206@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote in news:21359@
1719926613.3193910774.11894.25589.1170:

David Winsemius <doe_snot@xxxxxxxxxxx> wrote:
"Phil Holman" <piholmanc@yourservice> wrote
"Jack Tomsky" <jtomsky@xxxxxxxxxxxxx> wrote
he refuses to ever accept the null hypothesis or to accept the
alternative hypothesis.
One never accepts the null hypothesis, one only decides whether
or not to reject it. In this particular case, one would use a
lot more coin tosses to reduce the likelihood of making a type
II error.
Phil, I have only a handful fo statistics books in my office.
However, every single one says that the null hypothesis can be
either accepted or rejected.

"Let the decisions of accepting or rejecting H be denoted by do
and d1, respectively. A nonrandomized test procedure assigns to
each possible value x of X one of these two decisions and thereby
divides the sample space into two complementary regions S0 and
S1. If X falls into S0, the hypothesis is accepted, otherwise it
is rejected."

Lehmann, Testing Statistical Hypotheses, p. 60

"More precisely, let Wn be a set in the sample space Rn which
does not depend on theta such that if (x1, ..., xn) belongs to
Wn, we reject H, otherwise we accept H."

S.S. Wilks, Mathematical Statistics, p. 395

"The two decisions, one of which the statistician must make on the
completion of the experiment, are d1, the decision to accept the
hypothesis and say that theta belongs to w, and d2, the decision to
accept the alternative and say that theta belongs to W-w,"

D.A.S. Fraser, Nonparametric Methods in Statistics, p. 70

"Since Cp,m,n(alpha) > 1, the hypothesis is accepted if the left-hand
side of (42) is less than Chisqp,m(alpha)."

T.W. Anderson, An Introduction to Multivariate Statistical Analysuis,
p. 308
Ok, it looks like there are differing schools of thought on this,
but in context with this particular problem, I would hardly jump
to accepting it as a fair coin with only two out of ten heads. The
null hypothesis is that the coin is fair and we have not enough
evidence to prove otherwise. Yet if we obtained the same ratio for
a moderately larger number, say 3 out of 15, we'd reject it. The
problem with low number samples is they are very susceptible to
not rejecting the null when it is false.
Somehow, just somehow, I think Jack might already be aware of that
problem. I also suspect he is going to take Lehmann and Wilks'
perspective over yours when it comes to hypothesis testing.
But these definitions tell little about their perspective. If I'm
going to accept a hypothesis without having a slightest idea about my
chances of being wrong in making that decision, then why bother?

Your somewhat plaintive objections suggest to me that you have not yet resolved (or may be unaware of) the Bayesian v. N-P debate. My comment merely meant that I thought that Jack knew that any test woud have low power when sample sizes were low. That is a perspective that defines type I (failing to reject a true null) and type II (failing to accept a true alternative) errors.


Type I is failing to *accept* a true null (i.e. false positive).
.

Relevant Pages

  • Re: Simple binomial test question
    ... I have only a handful fo statistics books in my office. ... "Let the decisions of accepting or rejecting H be denoted by do ... to accepting it as a fair coin with only two out of ten heads. ...
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  • Re: the type II error has not nothing to do with *** accepting H0 ***
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  • Re: Simple binomial test question
    ... questing I posed: is cachechy evident. ... I have only a handful fo statistics books in my office. ... to accepting it as a fair coin with only two out of ten heads. ... number samples is they are very susceptible to not rejecting the null ...
    (sci.stat.math)
  • Re: Simple binomial test question
    ... questing I posed: is cachechy evident. ... I have only a handful fo statistics books in my office. ... to accepting it as a fair coin with only two out of ten heads. ... number samples is they are very susceptible to not rejecting the null ...
    (sci.stat.math)
  • Re: A misleading question
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