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The p-value is used in the context of null hypothesis testing in order to quantify the statistical significance of a result, the result being the observed value of the chosen statistic . [ note 2 ] The lower the p -value is, the lower the probability of getting that result if the null hypothesis were true.
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 p-value was introduced by Karl Pearson [6] in the Pearson's chi-squared test, where he defined P (original notation) as the probability that the statistic would be at or above a given level. This is a one-tailed definition, and the chi-squared distribution is asymmetric, only assuming positive or zero values, and has only one tail, the ...
The p-value is the probability that a test statistic which is at least as extreme as the one obtained would occur under the null hypothesis. At a significance level of 0.05, a fair coin would be expected to (incorrectly) reject the null hypothesis (that it is fair) in 1 out of 20 tests on average.
Once the t value and degrees of freedom are determined, a p-value can be found using a table of values from Student's t-distribution. If the calculated p-value is below the threshold chosen for statistical significance (usually the 0.10, the 0.05, or 0.01 level), then the null hypothesis is rejected in favor of the alternative hypothesis.
[11] [12] Falling for the temptation to use the statistical analysis of the collected data to estimate the power will result in uninformative and misleading values. In particular, it has been shown that post-hoc "observed power" is a one-to-one function of the p-value attained. [11]
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]
A p-value that satisfies this guarantee is also called a post-hoc p-value. As p ′ {\displaystyle p^{\prime }} is a post-hoc p-value if and only if p ′ = 1 / E {\displaystyle p^{\prime }=1/E} for some e-value E {\displaystyle E} , it is possible to view this as an alternative definition of an e-value.