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This definition ensures the complementarity of p-values and alpha-levels. In these circumstances (the case of a so-called composite null hypothesis) the p-value is defined by taking the least favourable null-hypothesis case, which is typically on the border between null and alternative. For each possible value of the theoretical mean, the Z-test statistic has a different probability distribution. In the just mentioned example that would be the Z-statistic belonging to the one-sided one-sample Z-test. For example, when testing the null hypothesis that a distribution is normal with a mean less than or equal to zero against the alternative that the mean is greater than zero (variance known), the null hypothesis does not specify the probability distribution of the appropriate test statistic. In contrast, in a composite hypothesis the parameter's value is given by a set of numbers. In parametric hypothesis testing problems, a simple or point hypothesis refers to a hypothesis where the parameter's value is assumed to be a single number. A p-curve can be used to assess the reliability of scientific literature, such as by detecting publication bias or p-hacking.
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The distribution of p-values for a group of studies is sometimes called a p-curve. By contrast, if the alternative hypothesis is true, the distribution is dependent on sample size and the true value of the parameter being studied. In statistics, every conjecture concerning the unknown probability distribution of a collection of random variables representing the observed data X, and the underlying random variable is continuous, then the probability distribution of the p-value is uniform on the interval.