Hypothesis Testing

Statistical inference is the science of making conclusions, decisions, or inferences about a population based on information obtained in a sample. The procedure that leads to rejecting or not rejecting specific statements about a population is called hypothesis testing. If there is only one population under investigation, researchers conduct a one-sample test. If they are comparing two populations, they conduct a twosample test. Additionally, there are multisample tests (also known as k-sample tests) to consider more than two populations.

A statistical hypothesis is an assumption or statement or inference regarding one or more parameters of a population distribution, or the type or nature of a population. Both the following are examples of statistical hypotheses: (1) The specificities of two diagnostic tests are the same and (2) the average score on the ABC test is 70. Statistical hypotheses are always about population parameters, while a decision to accept or reject a hypothesis is based on a test statistic derived from a sample.

Hypothesis testing is a decision-making process for evaluating claims about a population. A hypothesis test determines if an observed value of a statistic (from a sample) differs enough from a hypothesized value of a parameter (from a population) to draw the inference that the hypothesized value is not the true value. ‘Enough’ difference is measured by using subjective judgment and statistical conventions to set a predetermined acceptable probability of making an inference error due to sampling error.

The most commonly used current method for hypothesis testing is formally called ‘null hypothesis significance testing.’ Most people today simply refer to this method as significance testing or hypothesis testing and often use the terms interchangeably. However, this method combines the two historical procedures that are known separately as ‘significance testing’ and ‘hypothesis testing.’ In this article, unless a distinction is necessary, the term hypothesis test will refer to the current method of the ‘null hypothesis significance test.’