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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.
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 ...
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 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.
The procedures of Bonferroni and Holm control the FWER under any dependence structure of the p-values (or equivalently the individual test statistics).Essentially, this is achieved by accommodating a `worst-case' dependence structure (which is close to independence for most practical purposes).
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.
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]
Illustration of the power of a statistical test, for a two sided test, through the probability distribution of the test statistic under the null and alternative hypothesis. α is shown as the blue area , the probability of rejection under null, while the red area shows power, 1 − β , the probability of correctly rejecting under the alternative.