Hypothesis testing

One of the most commonly used methods in statistical decision making is hypothesis testing. In general, a hypothesis test is a process in which you assume an initial claim to be true and then test this claim using sample data. Ordinarily, the initial claim refers to a population parameter of interest such as the population mean (m).

Hypothesis tests include two hypotheses: the null hypothesis (denoted by H0) and the alternative hypothesis (denoted by H1). The null hypothesis is the initial claim and is often specified using previous research or common knowledge. The alternative hypothesis is what you may believe to be true or hope to prove true. The alternative hypothesis is sometimes referred to as the research hypothesis, and can be directional or nondirectional.

The decision-making process for a hypothesis test can be based on the probability value (p-value) for the given test.

·    If the p-value is less than or equal to a predetermined level of significance (a-level), then you reject the null hypothesis and claim support for the alternative hypothesis.

·    If your p-value is greater than the a-level, you fail to reject the null hypothesis and can not claim support for the alternative hypothesis.

When you perform a hypothesis test, there are four possible outcomes. The outcomes depend on whether the null hypothesis is true or false and whether you reject or fail to reject the null hypothesis. These outcomes are summarized in the following table:

When the null hypothesis is true and you reject it, you make a type I error. The probability of making a type I error is called alpha (a) and is sometimes referred to as the level of significance.

When the null hypothesis is false and you fail to reject it, you make a type II error. The probability of making a type II error is called beta (b).

The probability of rejecting the null hypothesis when it is false is equal to 1 - b. This value is also referred to as the power of the test.