Hypothesis testing is a statistical inferencial procedure in which a statement based on some experimental or observational study is formulated, tested, then put through a decision process. The decision process either accepts or rejects the statement.

More precisely, the hypothesis testing procedure can be broken down into three steps:

1. Formulation of a (hypothetical) statement.

   The hypothetical statement formed is called the null hypothesis, or . For example, in testing whether a coin is “fair”, it is tossed 100 times and the number of heads are counted. could be The number of heads = . Accompanying the null hypothesis is the alternative hypothesis . The statement in is the compliment of the statement in (the universe is the sample space). For example, would be The number of heads .

2. Testing of the statement.

   This is usually the most mathematical part of the procedure. To test , first assume is true. Then apply an appropriate test statistic using values obtained from the study. There are many test statistics, depending on , , and the nature of the study.

   Based on the distributional forms of these test statistics, four major types of tests are of interest. A t test is based on a test statistic that has a t-distribution. An f test and a test are so named for the same reason. A z-test is one that is based on a test statistic having a normal or Gaussian distribution.

   Before calculating the test statistic, a value of the significance level of the test needs to be specified. The significance level, known as , is the probability of rejecting (or accepting ) when in fact, is true: .

3. Deciding whether to accept or reject the statement.

   Once the value of the test statistic is obtained, it is used to find a corresponding probability of obtaining such a statistic given that is true. This probability is called the p-value. This -value is then compared , the significance level of the test. If -value , then the usual next step is to reject the null hypothesis (and accepted). Otherwise, will be accepted.

The concept of statistical hypothesis testing can be found in any standard introductory statistics textbooks, as well as numerous internet websites (for example, click to find the result of a Google search). The purpose of this entry is to give a very brief description of hypothesis testing and to serve as a link reference for other entries.