Type I and Type II Errors

A Type I error is one which occurs when a true null hypothesis H₀ is rejected by a statistical test.

A Type II error is one which occurs if a statistical test fails to reject the null hypothesis H₀ when the alternative hypothesis H₁ is true.

Notes:

• As an example, suppose you are trying to compare a new treatment with a standard treatment for a certain illness. In this case, you might wish to test
  
  

  H₀: New treatment is not better than the standard one

  versus

  H₁: New treatment is better than the standard one

  
  Here, a Type I error occurs if you conclude on the basis of a statistical test that the new treatment is better than the standard one when in fact it is not. On the other hand, if the new treatment is better than the standard one and performance of your statistical test results in a failure to conclude accordingly, then you would have committed a Type II error.
• The critical region of a statistical test is usually determined in way that ensures a small chance of Type I erorr occurring (see the notes on level of significance). Subject to this condition, we are usually interested in a statistical test which gives the smallest chance of Type II error occurring.