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Encyclopedia > Alternate hypothesis

The alternate hypothesis (or maintained hypothesis) and the null hypothesis are the two rival hypotheses whose likelihoods are compared by a statistical hypothesis test. Usually the alternate hypothesis is the possibility that an observed effect is genuine and the null hypothesis is the rival possibility that it has resulted from random chance. In statistics, a null hypothesis is a hypothesis set up to be nullified or refuted in order to support an alternative hypothesis. ... Look up likelihood in Wiktionary, the free dictionary. ... One may be faced with the problem of making a definite decision with respect to an uncertain hypothesis which is known only through its observable consequences. ...

The classical (or frequentist) approach is to calculate the probability that the observed effect (or one more extreme) will occur if the null hypothesis is true. If this value (sometimes called the "p-value") is small then the result is called statistically significant and the null hypothesis is rejected in favour of the alternate hypothesis. If not, then the null hypothesis is not rejected. Incorrectly rejecting the null hypothesis is a Type I error; incorrectly failing to reject it is a Type II error. Statistical regularity has motivated the development of the relative frequency concept of probability. ... In statistical hypothesis testing, the p-value of a random variable T used as a test statistic is the probability that T will assume a value at least as extreme as the observed value tobserved, given that a null hypothesis being considered is true. ... In statistics, a result is significant if it is unlikely to have occurred by chance, given that a presumed null hypothesis is true, but is not improbable if the null hypothesis is false. ... Type I errors (or Î± error, or false positive) and type II errors (Î² error, or a false negative) are two terms used to describe statistical errors. ... Type I errors (or Î± error, or false positive) and type II errors (Î² error, or a false negative) are two terms used to describe statistical errors. ...

Bayesian statisticians would challenge this approach in that it takes no account of a priori beliefs in the two hypotheses or the different consequences of taking a wrong decision; there may be good reasons (extraneous to the statistical data) for believing the null hypothesis to be correct. This must be weighed against the damning evidence of a low p-value before the null hypothesis can be rejected. Bayesian inference is statistical inference in which evidence or observations are used to update or to newly infer the probability that a hypothesis may be true. ... The terms a priori and a posteriori are used in philosophy to distinguish between two different types of propositional knowledge. ...

An example: In the trial of Sally Clark, a solicitor accused of killing both her babies, pediatrician Sir Roy Meadow testified that the probability of two infants in the same family dying of natural causes was 1 in 73,000,000. If natural death is the null hypothesis and murder the alternate hypothesis, then the p-value is 1/73,000,000. The smallness of this value means that the null hypothesis that the deaths had had natural causes should be rejected and therefore murder concluded. For other persons named Sally Clark, see Sally Clark (disambiguation). ... Pediatrics (also spelled paediatrics or pædiatrics) is the branch of medicine that deals with the medical care of infants and children. ... Professor Sir Samuel Roy Meadow (born 1933) is a former British paediatrician. ...

The problem was that even if the 73,000,000 figure were correct (this calculation was itself challenged as being flawed by the ecological fallacy), double murder is a rare event and there is therefore a good a priori reason for believing the null hypothesis. The standard hypothesis test was therefore not a good indicator of Clark's guilt. The ecological fallacy is a widely recognised error in the interpretation of statistical data, whereby inferences about the nature of individuals are based solely upon aggregate statistics collected for the group to which those individuals belong. ...

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 Alternate hypothesis - Wikipedia, the free encyclopedia (374 words) The alternate hypothesis, or alternative hypothesis, together with the null hypothesis are the two rival hypotheses whose likelihoods are compared by a statistical hypothesis test. Usually the alternate hypothesis is the possibility that an observed effect is genuine and the null hypothesis is the rival possibility that it has resulted from random chance. Incorrectly rejecting the null hypothesis is a Type I error; incorrectly failing to reject it is a Type II error.
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