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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.
An important property of a test statistic is that its sampling distribution under the null hypothesis must be calculable, either exactly or approximately, which allows p-values to be calculated. A test statistic shares some of the same qualities of a descriptive statistic, and many statistics can be used as both test statistics and descriptive ...
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.
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 chi-squared statistic can then be used to calculate a p-value by comparing the value of the statistic to a chi-squared distribution. The number of degrees of freedom is equal to the number of cells , minus the reduction in degrees of freedom, . The chi-squared statistic can be also calculated as
The t-test p-value for the difference in means, and the regression p-value for the slope, are both 0.00805. The methods give identical results. The methods give identical results. This example shows that, for the special case of a simple linear regression where there is a single x-variable that has values 0 and 1, the t -test gives the same ...
A two-tailed test applied to the normal distribution. 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.
Fisher's exact test is a statistical significance test used in the analysis of contingency tables. [ 1 ] [ 2 ] [ 3 ] Although in practice it is employed when sample sizes are small, it is valid for all sample sizes.