Answer to Question #167563 in Statistics and Probability for kmy

Question

Use an analogy to explain a Type I error and a Type II error and discuss its significance in hypothesis testing.

Answer 1

The statistical test requires an unambiguous statement of a null hypothesis (H₀), for example, “this person is healthy”. The result of the test of the null hypothesis may be positive (healthy) or may be negative (not healthy). If the result of the test corresponds with reality, then a correct decision has been made (person is healthy and is tested as healthy, or the person is not healthy and is tested as not healthy). However, if the result of the test does not correspond with reality, then two types of error are distinguished: type I error and type II error.

A type I error occurs when the null hypothesis is true, but is rejected. In our example it's relevant when test determines the person is not healthy, but he is healthy.

A type II error occurs when the null hypothesis is false, but erroneously fails to be rejected. In our example it's relevant when test determines the person is healthy, but he is not healthy.

These two types of errors are used in many spheres of real life. For example, medical testing. It’s probably more accurate to characterize a type I error as a “false signal” and a type II error as a “missed signal.”