<Dd> Pr (R e j e c t H H) = Pr (p ≤ α H) = α (\ displaystyle \ Pr (\ mathrm (Reject) \; H H) = \ Pr (p \ leq \ alpha H) = \ alpha). </Dd> <P> This also means that if we fix an instantiation of p - value and allow α (\ displaystyle \ alpha) to vary over (0, 1) (\ displaystyle (0, 1)), we can obtain an equivalent interpretation of p - value in terms of α (\ displaystyle \ alpha) level as the lowest value of α (\ displaystyle \ alpha) that can be assumed for which the null hypothesis can be rejected for a given set of observations . </P> <P> The p - value is widely used in statistical hypothesis testing, specifically in null hypothesis significance testing . In this method, as part of experimental design, before performing the experiment, one first chooses a model (the null hypothesis) and a threshold value for p, called the significance level of the test, traditionally 5% or 1% and denoted as α . If the p - value is less than the chosen significance level (α), that suggests that the observed data is sufficiently inconsistent with the null hypothesis that the null hypothesis may be rejected . However, that does not prove that the tested hypothesis is true . When the p - value is calculated correctly, this test guarantees that the Type I error rate is at most α . For typical analysis, using the standard α = 0.05 cutoff, the null hypothesis is rejected when p <. 05 and not rejected when p>. 05 . The p - value does not, in itself, support reasoning about the probabilities of hypotheses but is only a tool for deciding whether to reject the null hypothesis . </P> <P> Usually, X (\ displaystyle X) is a test statistic, rather than any of the actual observations . A test statistic is the output of a scalar function of all the observations . This statistic provides a single number, such as the average or the correlation coefficient, that summarizes the characteristics of the data, in a way relevant to a particular inquiry . As such, the test statistic follows a distribution determined by the function used to define that test statistic and the distribution of the input observational data . </P>

What is the meaning of a p value of 0.05
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