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In null-hypothesis significance testing, the p-value [note 1] is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. [2] [3] A very small p-value means that such an extreme observed outcome would be very unlikely under the null hypothesis.
A one-tailed test, showing the p-value as the size of one tail. In statistical significance testing, a one-tailed test and a two-tailed test are alternative ways of computing the statistical significance of a parameter inferred from a data set, in terms of a test statistic. A two-tailed test is appropriate if the estimated value is greater or ...
As an example, if the two distributions do not overlap, say F is below G, then the P–P plot will move from left to right along the bottom of the square – as z moves through the support of F, the cdf of F goes from 0 to 1, while the cdf of G stays at 0 – and then moves up the right side of the square – the cdf of F is now 1, as all points of F lie below all points of G, and now the cdf ...
Under Fisher's method, two small p-values P 1 and P 2 combine to form a smaller p-value.The darkest boundary defines the region where the meta-analysis p-value is below 0.05.. For example, if both p-values are around 0.10, or if one is around 0.04 and one is around 0.25, the meta-analysis p-value is around 0
Most of the tests in DIEHARD return a p-value, which should be uniform on [0,1) if the input file contains truly independent random bits. Those p -values are obtained by p = F ( X ), where F is the assumed distribution of the sample random variable X – often normal.
Note that a p-value of 0.01 suggests that 1% of the time a result at least that extreme would be obtained by chance; if hundreds or thousands of hypotheses (with mutually relatively uncorrelated independent variables) are tested, then one is likely to obtain a p-value less than 0.01 for many null hypotheses.
The probability is sometimes written to distinguish it from other functions and measure P to avoid having to define "P is a probability" and () is short for ({: ()}), where is the event space, is a random variable that is a function of (i.e., it depends upon ), and is some outcome of interest within the domain specified by (say, a particular ...
In hypothesis testing, the primary objective of statistical calculations is to obtain a p-value, the probability of seeing an obtained result, or a more extreme result, when assuming the null hypothesis is true. If the p-value is low (usually < 0.05), the statistical practitioner is then encouraged to reject the null hypothesis.