Statistical significance

In statistical hypothesis testing, a result has statistical significance when it is very unlikely to have occurred given the null hypothesis. More precisely, a study's defined significance level, denoted α, is the probability of the study rejecting the null hypothesis, given that the null hypothesis were true; and the p-value of a result, p, is the probability of obtaining a result at least as extreme, given that the null hypothesis were true. The result is statistically significant, by the standards of the study, when p < α. The significance level for a study is chosen before data collection, and typically set to 5% or much lower, depending on the field of study. In statistical hypothesis testing, a result has statistical significance when it is very unlikely to have occurred given the null hypothesis. More precisely, a study's defined significance level, denoted α, is the probability of the study rejecting the null hypothesis, given that the null hypothesis were true; and the p-value of a result, p, is the probability of obtaining a result at least as extreme, given that the null hypothesis were true. The result is statistically significant, by the standards of the study, when p < α. The significance level for a study is chosen before data collection, and typically set to 5% or much lower, depending on the field of study. In any experiment or observation that involves drawing a sample from a population, there is always the possibility that an observed effect would have occurred due to sampling error alone. But if the p-value of an observed effect is less than the significance level, an investigator may conclude that the effect reflects the characteristics of the whole population, thereby rejecting the null hypothesis. This technique for testing the statistical significance of results was developed in the early 20th century. The term significance does not imply importance here, and the term statistical significance is not the same as research, theoretical, or practical significance. For example, the term clinical significance refers to the practical importance of a treatment effect. Statistical significance dates to the 1700s, in the work of John Arbuthnot and Pierre-Simon Laplace, who computed the p-value for the human sex ratio at birth, assuming a null hypothesis of equal probability of male and female births; see p-value § History for details. In 1925, Ronald Fisher advanced the idea of statistical hypothesis testing, which he called 'tests of significance', in his publication Statistical Methods for Research Workers. Fisher suggested a probability of one in twenty (0.05) as a convenient cutoff level to reject the null hypothesis. In a 1933 paper, Jerzy Neyman and Egon Pearson called this cutoff the significance level, which they named α. They recommended that α be set ahead of time, prior to any data collection. Despite his initial suggestion of 0.05 as a significance level, Fisher did not intend this cutoff value to be fixed. In his 1956 publication Statistical Methods and Scientific Inference, he recommended that significance levels be set according to specific circumstances. The significance level α is the threshold for p below which the null hypothesis is rejected even though by assumption it were true, and something else is going on. This means α is also the probability of mistakenly rejecting the null hypothesis, if the null hypothesis is true. Sometimes researchers talk about the confidence level γ = (1 − α) instead. This is the probability of not rejecting the null hypothesis given that it is true. Confidence levels and confidence intervals were introduced by Neyman in 1937. Statistical significance plays a pivotal role in statistical hypothesis testing. It is used to determine whether the null hypothesis should be rejected or retained. The null hypothesis is the default assumption that nothing happened or changed. For the null hypothesis to be rejected, an observed result has to be statistically significant, i.e. the observed p-value is less than the pre-specified significance level.