Statistics How To

Type I and Type II Errors: Easy Definition, Examples

Statistics Definitions > Type I and Type II Errors

Contents:

  1. Type I Error.
  2. Type II Error.

1. What is a Type I Error?

A Type I error (sometimes called a Type 1 error), is the incorrect rejection of a true null hypothesis. The alpha symbol, α, is usually used to denote a Type I error.

The Null Hypothesis in Type I and Type II Errors.

The null hypothesis, H0 is a commonly accepted hypothesis; it is the opposite of the alternate hypothesis. Researchers come up with an alternate hypothesis, one that they think explains a phenomenon, and then work to reject the null hypothesis. If that sounds a little convoluted, an example might help. Back in the day (way back!) scientists thought that the Earth was at the center of the Universe. That mean everything else — the sun, the planets, the whole shebang, all of those celestial bodies revolved around the Earth.

type i and type II errors 2

An illustration of the Ptolemaic geocentric system by Portuguese cosmographer and cartographer Bartolomeu Velho, 1568 (Bibliothèque Nationale, Paris)

.

This Geocentric model has, of course, since been proven false. So the current, accepted hypothesis (the null) is:
H0: The Earth IS NOT at the center of the Universe
And the alternate hypothesis (the challenge to the null hypothesis) would be:
H1: The Earth IS at the center of the Universe.

Type I Error: Conducting a Test

In our sample test (is the Earth at the center of the Universe?), the null hypothesis is:
H0: The Earth is not at the center of the Universe
Let’s say you’re an amateur astronomer and you’re convinced they’ve all got it wrong. You want to prove that the Earth IS at the center of the Universe. You set out to prove the alternate hypothesis and sit and watch the night sky for a few days, noticing that hey…it looks like all that stuff in the sky is revolving around the Earth! You therefore reject the null hypothesis and proudly announce that the alternate hypothesis is true — the Earth is, in fact, at the center of the Universe!

That’s a very simplified explanation of a Type I Error. Of course, it’s a little more complicated than that in real life (or in this case, in statistics). But basically, when you’re conducting any kind of test, you want to minimize the chance that you could make a Type I error. In the case of the amateur astronaut, you could probably have avoided a Type I error by reading some scientific journals!

2. What is a Type II Error?

A Type II error (sometimes called a Type 2 error) is the failure to reject a false null hypothesis. The probability of a type II error is denoted by the beta symbol β.

Type II Error: The Null Hypothesis in Action

type i and type II errors

Photo credit: Asbjørn E. Enemark|Wikimedia commons


Let’s say you’re an urban legend researcher and you want to research if people believe in urban legends like:

  • Newton was hit by an apple (he wasn’t).
  • Walt Disney drew Mickey mouse (he didn’t — Ub Werks did).
  • Marie Antoinette said “Let them eat cake” (she didn’t).

The accepted fact is, most people probably believe in urban legends (or we wouldn’t need Snopes.com)*. So, your null hypothesis is:
H0Most people do believe in urban legends.

But let’s say that null hypothesis is completely wrong. It might have been true ten years ago, but with the advent of the Smartphone — we have Snopes.com and Google.com at our fingertips. Still, your job as a researcher is to try and disprove the null hypothesis. So you come up with an alternate hypothesis:
H0Most people DO NOT believe in urban legends.

You conduct your research by polling local residents at a retirement community and to your surprise you find out that most people do believe in urban legends. The problem is, you didn’t account for the fact that your sampling method introduced some bias…retired folks are less likely to have access to tools like Smartphones than the general population. So you incorrectly fail to reject the false null hypothesis that most people do believe in urban legends (in other words, most people do not, and you failed to prove that). You’ve committed an egregious Type II error, the penalty for which is banishment from the scientific community.

*I used this simple statement as an example of Type I and Type II errors. I haven’t actually researched this statement, so as well as committing numerous errors myself, I’m probably also guilty of sloppy science!

If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you’re are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.

Type I and Type II Errors: Easy Definition, Examples was last modified: June 25th, 2017 by Andale

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