# What are Type I and Type II Errors?

Posted on April 21, 2017 by Priscilla Wittkopf

When conducting a hypothesis test, we could:

__Reject__the null hypothesis when__there is__a genuine effect in the population;__Fail to reject__the null hypothesis when__there isn’t__a genuine effect in the population.

However, as we are inferring results from samples and using probabilities to do so, we are never working with 100% certainty of the presence or absence of an effect. There are two other possible outcomes of a hypothesis test.

__Reject__the null hypothesis when__there isn’t__a genuine effect – we have a false positive result and this is called__Type I error__.__Fail to reject__the null hypothesis when__there is__a genuine effect – we have a false negative result and this is called__Type II error__.

So in simple terms, a type I error is* erroneously detecting an effect that is not present*, while a type II error is *the failure to detect an effect that is present.*

**Type I error **

This error occurs when we reject the null hypothesis when we should have retained it. That means that we believe we found a genuine effect when in reality there isn’t one. The probability of a type I error occurring is represented by α and as a convention the threshold is set at 0.05 (also known as significance level). When setting a threshold at 0.05 we are accepting that there is a 5% probability of identifying an effect when actually there isn’t one.

**Type II error **

This error occurs when we fail to reject the null hypothesis. In other words, we believe that there isn’t a genuine effect when actually there is one. The probability of a Type II error is represented as β and this is related to the power of the test (power = 1- β). Cohen (1998) proposed that the maximum accepted probability of a Type II error should be 20% (β = 0.2).

When designing and planning a study the researcher should decide the values of α and β, bearing in mind that inferential statistics involve a balance between Type I and Type II errors. If α is set at a very small value the researcher is more rigorous with the standards of rejection of the null hypothesis. For example, if α = 0.01 the researcher is accepting a probability of 1% of erroneously rejecting the null hypothesis, but there is an increase in the probability of a Type II error.

In summary, we can see on the table the possible outcomes of a hypothesis test:

Have this table in mind when designing, analysing and reading studies, it will help when interpreting findings.

**References**

COHEN, J. 1990. Things I have learned (so far). *American psychologist,* 45**,** 1304.

COHEN, J. 1998. *Statistical Power Analysis for the Behavioral Sciences*, Lawrence Erlbaum Associates.

FIELD, A. 2013. *Discovering statistics using IBM SPSS statistics*, Sage.

## 2 Comments on What are Type I and Type II Errors?

ExplainingHypothesisTestingIsHardI’m pretty sure “erroneous” is not the word you’re looking for in the opening sentence!

April 30, 2017 at 4:13 pmSelena Ryan-VigYou’re quite right. This was an editorial issue rather than the fault of the author and has now been amended. Many thanks.

May 2, 2017 at 10:45 am