Errors in Hypothesis Testing: Fresh Take

  • Recognize Type I and Type II errors and their consequences.

If the null hypothesis is true, the sample should lead us to that conclusion. If the null hypothesis is false, the sample should lead us to that conclusion, too. However, sometimes the data might not lead to the correct conclusion.

errors in hypothesis testing

[latex]α[/latex] = probability of a Type I error = P(Type I error) = probability of rejecting the null hypothesis when the null hypothesis is true.

 

[latex]β[/latex] = probability of a Type II error = P(Type II error) = probability of not rejecting the null hypothesis when the null hypothesis is false.

The four possible outcomes in hypothesis testing:

  1. The decision is not to reject [latex]H_0[/latex] when [latex]H_0[/latex] is true (correct decision).
  2. The decision is to reject [latex]H_0[/latex] when [latex]H_0[/latex] is true (incorrect decision known as a Type I error).
  3. The decision is not to reject [latex]H_0[/latex] when, in fact, [latex]H_0[/latex] is false (incorrect decision known as a Type II error).
  4. The decision is to reject [latex]H_0[/latex] when [latex]H_0[/latex] is false (correct decision whose probability is called the Power of the Test).
Suppose the null hypothesis, [latex]H_0[/latex], is: Frank’s rock climbing equipment is safe.

  • Type I error: Frank thinks that his rock climbing equipment may not be safe when, in fact, it really is safe.
  • Type II error: Frank thinks that his rock climbing equipment may be safe when, in fact, it is not safe.

Notice that, in this case, the error with the greater consequence is the Type II error. (If Frank thinks his rock climbing equipment is safe, he will go ahead and use it.)