Introduction to Hypothesis Testing
Basic Terms
The first step in hypothesis testing is to set up two competing hypotheses. The hypotheses are the most important aspect. If the hypotheses are incorrect, your conclusion will also be incorrect.
The two hypotheses are named the null hypothesis and the alternative hypothesis.
- Null hypothesis
- The null hypothesis is typically denoted as H0. The null hypothesis states the “status quo”. This hypothesis is assumed to be true until there is evidence to suggest otherwise.
- Alternative hypothesis
- The alternative hypothesis is typically denoted as Ha or H1. This is the statement that one wants to conclude. It is also called the research hypothesis.
The goal of hypothesis testing is to see if there is enough evidence against the null hypothesis. In other words, to see if there is enough evidence to reject the null hypothesis. If there is not enough evidence, then we fail to reject the null hypothesis.
Consider the following example where we set up these hypotheses.
Example 6-1
A man, Mr. Orangejuice, goes to trial and is tried for the murder of his ex-wife. He is either guilty or innocent. Set up the null and alternative hypotheses for this example.
Putting this in a hypothesis testing framework, the hypotheses being tested are:
- The man is guilty
- The man is innocent
Let’s set up the null and alternative hypotheses.
H0: Mr. Orangejuice is innocent
Ha: Mr. Orangejuice is guilty
Remember that we assume the null hypothesis is true and try to see if we have evidence against the null. Therefore, it makes sense in this example to assume the man is innocent and test to see if there is evidence that he is guilty.
