对假设检验使用中一个常见错误的澄清

Clarifying a Common Mistake in Using Hypothesis-test

是否接受某个假设应该取决于这个假设成立的概率.当从实验获得样本观察值X之后,假设H成立的概率就是P(H/X).所以,应该把P(H/X)≥e(e是一个足够大的概率常数)规定为接受假设H的条件并进而规定为确定H接受域的方法.这个方法对备择假设和零假设是同样适用的,据此可以证明:零假设的接受域不是备择假设接受域的余集.

Whether we will accept a hypothesis should be determined by the probability that the hypothesis is right. When we obtain the observed value X of a sample from an experiment, the probability that hypothesis H is right is P（HIX）. Therefore, the qualification for receiving H and thereby the method for prescribing the receiving area for H should be P（HIX）≥e （e is a large enough probability constant）. The method is true not only for alternative hypothesis but also for null hypothesis, so it can be proved that the receiving area for null hypothesis is not the surplus set of the receiving area for alternative hypothesis.