Setting Up Hypotheses
This section discusses the logic behind hypothesis testing using concrete examples and explains how to set up null and alternative hypothesis. It explains what Type I and II errors are and how they can occur. Finally, it introduces one-tailed and two-tailed tests and explains which one you should use for testing purposes.
Type I and Type II Errors
- In this example, there is really a difference in the population between recognition and recall, but you did not find a significant difference in your sample. Failing to reject a false null hypothesis is a Type II error.
- There is no difference in the population, but you found a difference in your sample. A Type I error occurs when a significance test results in the rejection of a true null hypothesis.
- The Type I error rate is affected by the alpha level; the lower the alpha level is, the lower the Type I error rate gets. Alpha is the probability of a Type I error given that the null hypothesis is true.
- The probability of a Type II error is called beta. The probability of correctly rejecting a false null hypothesis equals 1- beta and is called power.
- A Type I error occurs when a significance test results in the rejection of a TRUE null hypothesis.