Question

Types of errors and power of study.

Hint:

Increasing the sample size or effect size can help improve the power of a study and reduce the likelihood of Type II errors.

Answer 1

Understanding the types of errors and the power of a study is essential in the design and interpretation of scientific research.
Step 1: Types of Errors:
1. Type I Error (False Positive):
- Occurs when the null hypothesis is rejected when it is actually true. It is denoted by \(\alpha\) (level of significance). - Example: Concluding a treatment is effective when it actually isn't. 2. Type II Error (False Negative):
- Occurs when the null hypothesis is not rejected when it is actually false. It is denoted by \(\beta\) (probability of Type II error). - Example: Failing to detect a true treatment effect when one exists.
Step 2: Power of Study:
- The power of a study is the probability of correctly rejecting the null hypothesis when it is false. - Power is calculated as \(1 - \beta\), and it depends on factors such as sample size, effect size, and significance level. - A study with high power (typically 80% or greater) is more likely to detect a true effect.