Statistical significance

In statistics, statistical significance is a "term indicating that the results obtained in an analysis of study data are unlikely to have occurred by chance, and the null hypothesis is rejected. When statistically significant, the probability of the observed results, given the null hypothesis, falls below a specified level of probability (most often P < 0.05)." The P-value, which is used to represent the likelihood the observed results are due to chance, is defined at "the probability, under the assumption of no effect or no difference (the null hypothesis), of obtaining a result equal to or more extreme than what was actually observed."

Hypothesis testing
Usually, the null hypothesis is the there is no difference between two samples in regard to the factor being studied.

Statistics errors
Two errors can occur in assessing the probability that the null hypothesis is true:

Type I error (alpha error)
Type I error, also called alpha error, is the the rejection of a correct null hypothesis. The probability of this is usually expressed by the p-value. Usually the null hypothesis is rejected if the p-value, or the chance of a type I error, is less than 5%. However, this threshold may be adjusted when multiple hypotheses are tested.

Type II error (beta error)
Type II error, also called beta error, is the acceptance of an incorrect null hypothesis. This error may occur when the sample size was insufficient to have power to detect a statistically significant difference.

Frequentist method
This approach uses mathematical formulas to calculate deductive probabilities (p-value) of an experimental result. This approach can generate confidence intervals.

A problem with the frequentist analyses of p-values is that they may overstate "statistical significance".

Likelihood or Bayesian method
Some argue that the P-value should be interpreted in light of how plausible is the hypothesis based on the totality of prior research and physiologic knowledge. This approach can generate Bayesian 95% credibility intervals.