How to Make a Difference Between Type I and Type II Errors

Type I and Type II errors are commonly encountered in statistics. However, they are also often confused especially by beginner and some intermediate statisticians, the latter most often due to having not been exposed to them in their work for a certain period of time.

A simple search on Google confirms that with blog entries on the topic and comments underneath. Here are some techniques to learn how to make a difference between Type I error and Type II error, also known as false positive (reject a null hypothesis when it is actually true) and false negative (fail to reject a null hypothesis when it is actually false).

In a blog called The Church of Rationality, the author suggests that subscript 0 in the null hypothesis sign (Ho), is a positive number. Therefore, “even numbers go together well [while] even number and odd number do not go together well” as a result of which “the null hypothesis (even) is rejected by Type I error (odd) but accepted by Type II error (even).”

Another suggestion – from a different blog – is “false effect error” and “false no-effect error.” One of the comments suggested the following: Type I error is “what you know that ain’t so” while Type II error is “what you don’t know.”

These techniques are good but I have another suggestion. Read in the next paragraph:

We now know (for the next 10 seconds, I know) that Type I error is a false positive error, while Type II error is a false negative error. As vague as they may seem, try to remember it by the second words – positive and negative. We always tend to say positive before we say negative. The word false is easy to associate with the word error. So step #1 is to remember that positive comes first, thereby Type I error being the false positive error.

Step #2 is to mentally associate the word positive with the word true. In other words, Type I error is false positive, that is, rejecting the null hypothesis when it is actually true. Type II error is false negative, that is failing to reject the null hypothesis when it is actually false.

Bottom line is, there are three words to remember:

  • Error
  • True
  • False
  • Positive
  • Negative

Associate:

  • Error with false (to remember that error always comes with something false)
  • Positive with #1 (to remember that positive (see bullet 1) is first false)
  • True with #1 (to remember that Type I error is about a true null hypothesis)
  • Negative with #2 (to remember that negative (see bullet 1) is the second false)
  • False with #2 (to remember that Type II error is about a false null hypothesis)

What do you think? Read this technique 2-3 times and ask yourself a week from today what Type I error is and what Type II error is.

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