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For such a hypothesis the sampling distribution of any statistic is a function of the sample size alone. Composite hypothesis Any hypothesis which does not specify the population distribution completely. [4] Example: A hypothesis specifying a normal distribution with a specified mean and an unspecified variance.
In statistical hypothesis testing, this fraction is given the Greek letter α, and 1 − α is defined as the specificity of the test. Increasing the specificity of the test lowers the probability of type I errors, but may raise the probability of type II errors (false negatives that reject the alternative hypothesis when it is true). [a]
Note that data dredging is a valid way of finding a possible hypothesis but that hypothesis must then be tested with data not used in the original dredging. The misuse comes in when that hypothesis is stated as fact without further validation. "You cannot legitimately test a hypothesis on the same data that first suggested that hypothesis.
From a Neyman–Pearson hypothesis testing approach to statistical inferences, the data obtained by comparing the p-value to a significance level will yield one of two results: either the null hypothesis is rejected (which however does not prove that the null hypothesis is false), or the null hypothesis cannot be rejected at that significance ...
The consistent application by statisticians of Neyman and Pearson's convention of representing "the hypothesis to be tested" (or "the hypothesis to be nullified") with the expression H 0 has led to circumstances where many understand the term "the null hypothesis" as meaning "the nil hypothesis" – a statement that the results in question have ...
Proving too much – an argument that results in an overly generalized conclusion (e.g.: arguing that drinking alcohol is bad because in some instances it has led to spousal or child abuse). Psychologist's fallacy – an observer presupposes the objectivity of their own perspective when analyzing a behavioral event.
This is the problem of induction. Suppose we want to put the hypothesis that all swans are white to the test. We come across a white swan. We cannot validly argue (or induce) from "here is a white swan" to "all swans are white"; doing so would require a logical fallacy such as, for example, affirming the consequent. [3]
In 1970, L. A. Marascuilo and J. R. Levin proposed a "fourth kind of error" – a "type IV error" – which they defined in a Mosteller-like manner as being the mistake of "the incorrect interpretation of a correctly rejected hypothesis"; which, they suggested, was the equivalent of "a physician's correct diagnosis of an ailment followed by the ...