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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.
The p-value is not the probability that the observed effects were produced by random chance alone. [2] The p-value is computed under the assumption that a certain model, usually the null hypothesis, is true. This means that the p-value is a statement about the relation of the data to that hypothesis. [2]
To determine whether a result is statistically significant, a researcher calculates a p-value, which is the probability of observing an effect of the same magnitude or more extreme given that the null hypothesis is true. [5] [12] The null hypothesis is rejected if the p-value is less than (or equal to) a predetermined level, .
The weighted harmonic mean of p-values , …, is defined as = = = /, where , …, are weights that must sum to one, i.e. = =.Equal weights may be chosen, in which case = /.. In general, interpreting the HMP directly as a p-value is anti-conservative, meaning that the false positive rate is higher than expected.
In modern terms, he rejected the null hypothesis of equally likely male and female births at the p = 1/2 82 significance level. Laplace considered the statistics of almost half a million births. The statistics showed an excess of boys compared to girls. [5] He concluded by calculation of a p-value that the excess was a real, but unexplained ...
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.
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
This has been extended to show that all post-hoc power analyses suffer from what is called the "power approach paradox" (PAP), in which a study with a null result is thought to show more evidence that the null hypothesis is actually true when the p-value is smaller, since the apparent power to detect an actual effect would be higher. [11]