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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.
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
In order to calculate the significance of the observed data, i.e. the total probability of observing data as extreme or more extreme if the null hypothesis is true, we have to calculate the values of p for both these tables, and add them together. This gives a one-tailed test, with p approximately 0
This fact is the basis of a hypothesis test, a "proportion z-test", for the value of p using x/n, the sample proportion and estimator of p, in a common test statistic. [ 35 ] For example, suppose one randomly samples n people out of a large population and ask them whether they agree with a certain statement.
The p-value of the test statistic is computed either numerically or by looking it up in a table. If the p-value is small enough (usually p < 0.05 by convention), then the null hypothesis is rejected, and we conclude that the observed data does not follow the multinomial distribution.
The Bonferroni correction can also be applied as a p-value adjustment: Using that approach, instead of adjusting the alpha level, each p-value is multiplied by the number of tests (with adjusted p-values that exceed 1 then being reduced to 1), and the alpha level is left unchanged.
The Šidák correction is derived by assuming that the individual tests are independent.Let the significance threshold for each test be ; then the probability that at least one of the tests is significant under this threshold is (1 - the probability that none of them are significant).
The maximum variance of this distribution is 0.25, which occurs when the true parameter is p = 0.5. In practical applications, where the true parameter p is unknown, the maximum variance is often employed for sample size assessments. If a reasonable estimate for p is known the quantity () may be used in place of 0.25.