Re: Simple binomial test question
- From: Art Kendall <Arthur.Kendall@xxxxxxxxxxx>
- Date: Mon, 30 Apr 2007 17:58:14 GMT
In many disciplines the null hypothesis is about [the status quo, the current, the default, the presumed] proposition, practice, or policy.
In the social and behavioral sciences, it is analogous to the US legal presumption of innocence. It is retained (stayed with), rather than newly accepted.
The proposer of the alternative hypothesis seeks to replace the null hypothesis, i.e., to have the alternative accepted. If the evidence is sufficiently inconsistent with the null hypothesis, the alternative is asserted. In US criminal proceedings, the accused is found guilty.
Art Kendall
Social Research Consultants
Jack Tomsky wrote:
."Jack Tomsky" <jtomsky@xxxxxxxxxxxxx> wrote in
message news:632568.1177647489114.JavaMail.jakarta@xxxxxxxxxxx
thforum.org...one is never allowedJack Tomsky repeat his post, not answering the
questing I posed: is cachechy evident.
Jerry Dallal is clear at this point
www.tufts.edu/~gdallal/sigtest.htm
_______licas (Luis A. Afonso)
Under the Afonso theory of statistical inference,to make a decision if there is any chance that thedecision could bewrong. That's why in hypothesis testing, herefuses to ever acceptthe null hypothesis or to accept the alternativehypothesis.
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 H
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
Jack
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