Statistics Definitions > Type III error and Type IV Error

## What is a Type III error?

A type III error is where you correctly reject the null hypothesis, but it’s rejected for the wrong reason. This compares to a Type I error (incorrectly rejecting the null hypothesis) and a Type II error (not rejecting the null when you should). Type III errors are **not considered serious**, as they do mean you arrive at the correct decision. They usually happen because of random chance and are a rare occurrence.

You can also think of a Type III error as giving the right answer (i.e. *correctly *rejecting the null) to the wrong question. Either way, you’re still **arriving at the correct conclusion for the wrong reason**. When we say the “wrong question”, that normally means you’ve formulated your hypotheses incorrectly. In other words, both your null and alternate hypotheses may be poorly worded or completely incorrect.

**Type III errors can generally be avoided by running a two-tailed test instead of a one-tailed test.**A one-tailed test has a higher power if your hypothesized direction is correct. However, if your direction is wrong, the one-tailed test will return the probability of a Type III error (only you won’t realize this!). For example, let’s say you hypothesize that there is a difference between the means of two samples, and that the mean difference is lower. You test this theory by running a left-tailed test. The test returns a small p-value and you (correctly) reject the null hypothesis that the means are the same. However, unknown to you, the means

*are*different: it’s just that one set is

*higher*(i.e. you should have run a right-tailed test), not lower.

Type III errors aren’t limited to differences between means. The can happen in every type of statistical test (e.g., correlations, proportions, variances etc.).

## What is a Type IV error?

A Type III error is directly related to a Type IV error; it’s actually a specific type of Type III error. When you correctly reject the null hypothesis, but make a mistake interpreting the results, you have committed a Type IV error. Some common reasons that Type IV errors happen include:

- Aggregation bias (the wrong assumption that “what is true for the group is true for the individual”).
- Running the wrong test for your data.
- Collinearity among predictors.

## References

Dodge, Y. (2008). The Concise Encyclopedia of Statistics. Springer.

Kotz, S.; et al., eds. (2006), Encyclopedia of Statistical Sciences, Wiley.

Levine, D. (2014). Even You Can Learn Statistics and Analytics: An Easy to Understand Guide to Statistics and Analytics 3rd Edition. Pearson FT Press