Talk:Statistical significance

calculation problem in example

What is the matter with this second Bayesian example I tried to make:

Example of a coin flip that comes up heads in none of four tosses:

${\text{Bayes Factor}}\ =\ {\frac {\left({\frac {1}{2}}\right)^{4}\ *\ \left({\frac {1}{2}}\right)^{0}}{\ \left({\frac {4}{4}}\right)^{4}\ *\ \left({\frac {0}{4}}\right)^{0}}}\ =\ {\frac {\frac {1}{16}}{0}}={\text{Infinity}}$

Thanks - Robert Badgett 06:44, 4 August 2009 (UTC)

What is wrong, is that 1^4 0^0 = 1, not zero. The Bayes factor is 1:16

If initially a coin is equally likely to be fair, or to be certain always to fall heads, then after 4 tosses all gave heads, the coin is 16 times more likely to double-headed than to be fair. Richard D. Gill (talk) 14:17, 20 February 2021 (UTC)

this article is much too restricted in scope

The present article is mainly based on expository papers in the medical literature. Statistical significance tests are used throughout empirical science (and very much misused, since not well understood by many practitioners). One big problem is that many null-hypotheses are composite, that is to say, the null hypothesis does not specify the probability distribution of the test statistic uniquely. In that case, denoting the data by X, and the statistic by T = T(X), and supposing that large values of T are supposed to be unlikely if the null hypothesis is true, then if we observe T = t, the p-value is the largest value of P( T >/= t) when P is allowed to vary throughout the null hypothesis.

For example, suppose we have the following background assumptions: we observe the value x taken by a random variable X which is known to have the normal distribution with mean mu and variance 1. The mean mu is however unknown. Suppose we want to test the null hypothesis that mu is less than or equal to zero. Large values of X are intuitively thought to contradict the null hypothesis to a greater or smaller amount, depending on just how large they are. The p-value based on the observed value x is by definition the maximum value of P(X >/= x | mu) as mu varies throughout the null hypothesis. In this case, it is found by putting mu = 0, ie, on the boundary of the null hypothesis. Richard D. Gill (talk) 15:30, 20 February 2021 (UTC)