Most people who have taken a research methodology or statistics class will remember the two types of errors that can be made in hypothesis testing – Type I error and a Type II error. They are summarized as:

Type I (false positive) – Incorrectly rejecting the null hypothesis.

Type II (false negative) – Incorrectly accepting the null hypothesis.

These two errors were introduced by Jerzy Neyman and Egon Pearson in a paper published in 1933. These are the two types of errors you will find in most textbooks.

However, did you know that there have been other types of errors proposed? Most popularly are the Type III error proposed by Frederick Mosteller and the Type IV error proposed by Leonard Marascuilo and Joel Levin.

Mosteller (1948) proposed an additional situation to what Neyman and Pearson had already established. He proposed that there were situations in which a statistician would reject the null hypothesis correctly but it would be for the wrong reason. Specifically, Mosteller wrote:

“It is also possible to reject the null hypothesis because some sample O_{i}has too many observations which are greater than all observations in the other samples. But the population from which some other sample say O_{i}is drawn is in fact the rightmost population. In this case we have committed an error of the third kind.”

Schwartz and Carpenter (1999) provided some examples as they relate to homelessness and other public health problems. They point out that often the focus is upon differences among the individuals of a population when the question had nothing to do with those differences. In relationship to homelessness they state:

“We argue that examining causes of interindividual differences in risk for homelessness is not useful for appreciably decreasing the incidence of homelessness, because the causes of interindividual variation in risk for homelessness do not appreciably contribute to the current incidence of homelessness.”

Marascuilo and Levin (1970) proposed their own contribution to the world of errors

when proposing a Type IV error. They define a Type IV error as, “…the incorrect interpretation of a correctly rejected hypothesis”. As an example they state that a Type IV error, “…may be likened to a physician’s correct diagnosis of an ailment followed by the prescription of a wrong medicine.”

So there’s some stats trivia for you. Don’t use all that knowledge in one place…

**References:**

Marascuilo, L. & Levin, J. (1970). Appropriate post hoc comparisons for interaction and nested hypotheses in analysis of variance designs: The elimination of Type IV errors. *American Educational Research Journal, 7*(3), 397-421.

Mosteller, F. (1948). A k-sample slippage test for an extreme population. *Annals of Mathematical Statistics, 19*(1), 58-65.

Neyman, J. & Pearson, E. (1933). The testing of statistical hypotheses in relation to probabilities a priori. *Mathematical Proceedings of the Cambridge Philosophical Society, 29*(4), 492-510.

Schwartz, S. & Carpenter, K. (1999). The right answer for the wrong question: consequences of type III error for public health research. *American Journal of Public Health, 89*(8), 1175-1180.