In statistics, statistical significance (or statistically significant result) is attained when a p-value is less than the significance level. The p-value is the probability of observing an effect given that the null hypothesis is true whereas the significance or alpha (α) level is the probability of rejecting the null hypothesis given that it is true (type I error). As a matter of logic, the significance level is always set ahead of time, usually at a threshold value of 0.05 (5%). Other alpha values (e.g., 0.01) are also used, depending on the field of study.
Statistical significance is fundamental to statistical hypothesis testing as it allows investigators to reject null hypotheses. 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 is less than the significance level (e.g., p < 0.05), then an investigator can conclude that the observed effect actually reflects the characteristics of the population rather than just sampling error. An investigator may then report that the result attains statistical significance, thereby rejecting the null hypothesis.
The present-day concept of statistical significance originated with Ronald Fisher when he developed statistical hypothesis testing based on p-values in the early 20th century. It was Jerzy Neyman and Egon Pearson who later recommended that the significance level be set ahead of time, prior to any data collection.
Statistical significance is not the same as research, theoretical, or practical significance.
The concept of statistical significance was originated by Ronald Fisher when he developed statistical hypothesis testing, which he described as "tests of significance", in his 1925 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 their 1933 paper, Jerzy Neyman and Egon Pearson recommended that the significance level (e.g. 0.05), which they called 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, and in his 1956 publication Statistical methods and scientific inference he recommended that significant levels be set according to specific circumstances.
Statistical significance plays a pivotal role in statistical hypothesis testing, where it is used to determine if a null hypothesis should be rejected or retained. A null hypothesis is the general or default statement that nothing happened or changed. For a null hypothesis to be rejected as false, the result has to be identified as being statistically significant, i.e. unlikely to have occurred due to sampling error alone.
To determine if a result is statistically significant, a researcher would have to calculate a p-value, which is the probability of observing an effect given that the null hypothesis is true. The null hypothesis is rejected if the p-value is less than the significance or α level. The α level is the probability of rejecting the null hypothesis given that it is true (type I error) and is most often set at 0.05 (5%). If the α level is 0.05, then the conditional probability of a type I error, given that the null hypothesis is true, is 5%. Then a statistically significant result is one in which the observed p-value is less than 5%, which is formally written as p < 0.05.
If an observed p-value is not lower than the significance level, then rather than simply accepting the null hypothesis, where feasible it would often be appropriate to increase the sample size of the study, and see if the significance level is reached.
If the α level is set at 0.05, it means that the rejection region comprises 5% of the sampling distribution. This 5% can be allocated to one side of the sampling distribution as in a one-tailed test or partitioned to both sides of the distribution as in a two-tailed test, with each tail (or rejection region) containing 2.5% of the distribution. One-tailed tests are more powerful than two-tailed tests, as a null hypothesis can be rejected with a less extreme result.
Researchers focusing solely on whether their results are statistically significant might report findings that are not necessarily substantive. To gauge the research significance of their result, researchers are also encouraged to report the effect size along with p-values (in cases where the effect being tested for is defined in terms of an effect size): the effect size quantifies the strength of an effect, such as the distance between two means or the correlation between two variables.
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