# Is there a way to remember the definitions of Type I and Type II Errors?

I'm not a statistician by education, I'm a software engineer. Yet statistics comes up a lot. In fact, questions specifically about Type I and Type II error are coming up a lot in the course of my studying for the Certified Software Development Associate exam (mathematics and statistics are 10% of the exam). I'm having trouble always coming up with the right definitions for Type I and Type II error - although I'm memorizing them now (and can remember them most of the time), I really don't want to freeze up on this exam trying to remember what the difference is.

I know that Type I Error is a false positive, or when you reject the null hypothesis and it's actually true and a Type II error is a false negative, or when you accept the null hypothesis and it's actually false.

Is there an easy way to remember what the difference is, such as a mnemonic? How do professional statisticians do it - is it just something that they know from using or discussing it often?

(Side Note: This question can probably use some better tags. One that I wanted to create was "terminology", but I don't have enough reputation to do it. If someone could add that, it would be great. Thanks.)

• Terminology is a bit vague. I changed error to typeI-errors and typeII-errors. Hope that is fine. Also, your question should be community wiki as there is no correct answer to your question.
– user28
Commented Aug 12, 2010 at 20:00
• @Srikant: in that case, we should make questions like this cw as well: stats.stackexchange.com/questions/22/…. Commented Aug 12, 2010 at 20:01
• Older literature calls H2 the null hypothesis, H1 the alternate hypothesis, then it's natural to call type i error as the error of mistakenly accepting Hi hypothesis Commented Aug 12, 2010 at 20:03
• @Shane: I will abstain from commenting on your point as the present top voted answer is mine (conflict of interest). I will go with what the community feels is appropriate.
– user28
Commented Aug 12, 2010 at 20:04
• Honestly, perhaps the community wikiness of this question should be discussed on meta. I personally feel that there is a singular right answer to this question - the answer that helps me. However, that singular right answer won't apply to everyone (some people might find an alternative answer to be better). Personally, I want to give reputation to the person or people who help me with my problem, but if the community wants this to be community wiki, I can make it happen (but not without a discussion on meta first). Commented Aug 12, 2010 at 20:11

Since type two means "False negative" or sort of "false false", I remember it as the number of falses.

• Type I: "I falsely think the alternate hypothesis is true" (one false)
• Type II: "I falsely think the alternate hypothesis is false" (two falses)
• I kind of like that. I'm thinking this might work for me. Commented Aug 12, 2010 at 21:42
• it's sort of like how in elementary school kids would ask "are you not not cool?" Commented Aug 12, 2010 at 22:10
• yes, now you just need to remember which hypothesis (null or alternate) :P Commented Aug 12, 2010 at 23:17
• Actually it's the alternate hypothesis in both cases Commented Aug 13, 2010 at 0:10
• In null hypothesis testing you're usually rejecting the null, not confirming the alternative, so the answer should read: Type I: "I falsely think the null hypothesis should be rejected", and Type II: "I falsely think the null hypothesis should not be rejected" Commented Mar 20, 2012 at 3:19

When the boy cried wolf ...

The first error the villagers made (when they believed him) was a type 1 error.
The second error the villagers made (when they didn't believe him) was a type 2 error.

The boy's cry was an alternative hypothesis because the null hypothesis is no wolf ;)

• Don't you mean that the null hypothesis is "there is no wolf"? Commented Mar 20, 2012 at 3:21
• Yes ... that's what it means. Commented Mar 24, 2012 at 14:21
• Very nice! I logged in just so I could upvote this! Commented Jan 15, 2013 at 22:13
• This mnemonic has all the characteristics you expect from a great mnemonic! Simple, direct. Great job! Commented May 7, 2015 at 3:35
• We should have an Aesop's Fable for statisticians, not just mnemonics, but the many lessons learned from the wise masters of the past. Commented Jul 8, 2016 at 20:40

I make no apologies for posting such a ridiculous image, because that's exactly why it's easy to remember. Null hypothesis: Patient is not pregnant.

Image source: Ellis, P.D. (2010), “Effect Size FAQs,” website http://www.effectsizefaq.com, accessed on 12/18/2014.

• This is not ridiculous, but very creative graphical/didactic representation of a convoluted topic. Can you please give appropriate credit to the source of the picture ?.I first stumbled on this picture while I was reading this excellent book on effect sizes by Pauld D Ellis and the associated webiste Commented Dec 28, 2014 at 20:20
• @forecaster Its beauty is in its ridiculousness. You're right, it's actually not the image that's ridiculous but the concept of a man being pregnant and a doctor making such an obvious mistake. I Google-image-searched around and it appears that Paul Ellis is indeed the source of the image. Thank you! Credit has been given as Mr. Ellis specifies on his 'about' page.
– mlai
Commented Dec 28, 2014 at 20:49

I was talking to a friend of mine about this and he kicked me a link to the Wikipedia article on type I and type II errors, where they apparently now provide a (somewhat unhelpful, in my opinion) mnemonic. I did, however, want to add it here just for the sake of completion. Although I didn't think it helped me, it might help someone else:

For those experiencing difficulty correctly identifying the two error types, the following mnemonic is based on the fact that (a) an "error" is false, and (b) the Initial letters of "Positive" and "Negative" are written with a different number of vertical lines:

• A Type I error is a false POSITIVE; and P has a single vertical line.
• A Type II error is a false NEGATIVE; and N has two vertical lines.

With this, you need to remember that a false positive means rejecting a true null hypothesis and a false negative is failing to reject a false null hypothesis.

This is by no means the best answer here, but I did want to throw it out there in the event someone finds this question and this can help them.

Here's a handy way that happens to have some truth to it.

Young scientists commit Type-I because they want to find effects and jump the gun while old scientist commit Type-II because they refuse to change their beliefs.

(someone comment in a funnier version of that :) )

• Isn't that agism? :) Commented Aug 12, 2010 at 20:33
• How about "once bitten, twice shy"? No funnier, but commonplace enough to remember. And no ageism required! Commented Aug 12, 2010 at 20:54

You could reject the idea entirely.

Some authors (Andrew Gelman is one) are shifting to discussing Type S (sign) and Type M (magnitude) errors. You can infer the wrong effect direction (e.g., you believe the treatment group does better but actually does worse) or the wrong magnitude (e.g., you find a massive effect where there is only a tiny, or essentially no effect, or vice versa).

See more at Gelman's blog.

• Interesting idea and it makes sense. However, the exam that I'm studying for uses Type I and Type II errors. Commented Aug 13, 2010 at 20:07
• @Thomas Andrew Gelman discussed type I and II errors before introducing S and M errors. I think this response is a valid and interesting one (wtr. other well-founded answers) since it allows to go beyond the traditional decision theory framework. I've upvoted this response.
– chl
Commented Oct 15, 2010 at 20:56

I'll try not to be redundant with other responses (although it seems a little bit what J. M. already suggested), but I generally like showing the following two pictures:

I use the "judicial" approach for remembering the difference between type I and type II: a judge committing a type I error sends an innocent man to jail, while a judge committing a type II error lets a guilty man walk free.

• But you still have to associate type I with an innocent man going to jail and type II with a guilty man walking free. So in the end, it really doesn't get me anywhere. Commented Aug 12, 2010 at 23:07
• +1, I like. @Thomas: Given an "innocent until proven guilty" system, you could think of type I as a primary error to avoid (imprisoning the innocent) and type II as a secondary error (guilty go free).
– ars
Commented Aug 13, 2010 at 3:42
• That's actually quite deep ars, thanks! My way of remembering was admittedly more pedestrian: "innocent" starts with "I". Commented Aug 13, 2010 at 5:32
• @ThomasOwens I see your point about still having to remember the names, but I predict that in practice this mnemonic works (at least for me). The reason is that now the names Type I and Type II are attached to concepts (forms of injustice) we have a strong emotional response to instead of the rather abstract concepts of 'rejecting/not-rejecting the null'. By pure human psychology this already helps rememebering, akin to how you can more easily remember someone's name if you have talked with them more often - even if the name never came up in these conversations again. Commented Jul 6, 2017 at 8:23

Based on the principle of Occam's razor, Type I errors (rejecting the null hypothesis when it is true) are "arguably" worse than Type II errors (not rejecting the null hypothesis when it is false).

If you believe such an argument:

• Type I errors are of primary concern
• Type II errors are of secondary concern

Note: I'm not endorsing this value judgement, but it does help me remember Type I from Type II.

TYPE I ERROR: An alarm without a fire. TYPE II ERROR: A fire without an alarm.

Every cook knows how to avoid Type I Error - just remove the batteries. Unfortunately, this increases the incidences of Type II error. :)

Reducing the chances of Type II error would mean making the alarm hypersensitive, which in turn would increase the chances of Type I error.

Source: A Cartoon Guide to Statistics

Hurrah, a question non-technical enough so as I can answer it!

"Type one is a con" [rhyming]- i.e. fools you into thinking that a difference exists when it doesn't. Always works for me.

• That doesn't rhyme in Australian :D Commented Mar 20, 2012 at 3:25

(a bit joke answer I invented just a minute ago)

1. A first class person thinks he is always right.
2. A second class person thinks he is always wrong.

1. The first class person can only make a type I error (because sometimes he will be wrong).
2. The second class person can only make a type II error (because sometimes he will be right).

I used to think of it in terms of the usual picture of two Normal distributions (or bell curves). Going left to right, distribution 1 is the Null, and the distribution 2 is the Alternative. Type I (erroneously) rejects the first (Null) and Type II "rejects" the second (Alternative).

(Now you just need to remember that you're not actually rejecting the alternative, but erroneously accepting (or failing to reject) the Null -- i.e. restate everything in the form of the Null. Hey, it worked for me!)

• I've never even thought of it pictorially before. Normally, thinking in pictures doesn't work for me, but I'll read that article and maybe this is a special case where it will help me. Commented Aug 12, 2010 at 20:27

I am surprised that noone has suggested the 'art/baf' mnemonic. Basically remember that $\alpha$ is the probability of the type I error and $\beta$ is the probability of a type II error (this is easy to remember because $\alpha$ is the 1st letter in the greek alphabet, so goes with the 1st error, $\beta$ is the 2nd letter and goes with the 2nd error). Now remember the word "art" or "$\alpha$rt" says that $\alpha$ is the probability of Rejecting a True null hypothesis and the psuedo word "baf" or "$\beta$af" says that $\beta$ is the probability of Accepting a False null hypothesis.

The "art" portion is fairly acceptable, the "baf" portion suffers from the fact that 1). it is not a real word, and 2). we are not supposed to accept the null, just fail to reject it. But if you can remember "art/baf" and the idea of Reject True is the R and T in art and the a/$\alpha$ links it to the type I error, then it is a pretty good mnemonic.

• Some texts actually call them the $\alpha$ error and $\beta$ error, rather than Type I and Type II! So rather than remember art/baf (which I have to admit I hadn't heard of before) I find it suffices to remember $\alpha$ and $\beta$. It helps that when I was at school, every time we wrote up a hypothesis test we were nagged to write "$\alpha = ...$" at the start, so I knew what $\alpha$ actually meant (sets the false positive rate), and you start to see $\beta$ once you start doing power calculations (where the error you're concerned about is having insufficient power to reject a false $H_0$). Commented Dec 29, 2014 at 0:53

My friend came up with this and I thought it was rather brilliant. She said that during the last two presidencies Republicans have committed both errors: President ONE was Bush who commited a type ONE error by saying there were weapons of mass destruction in Iraq when in fact..... Under president TWO, Obama, (some) Republicans are comitting a type TWO error arguing that climate change is a myth when in fact....

Whatever your views on politics or climate change, it's a pretty easy way to remember!!

• Is there a separate Type III error going on right now?
– user46481
Commented Aug 3, 2017 at 6:20

RAAR 'like a lion'= first part is *R*eject when we should *A*ccept (type I error) second part is *A*ccept when we should *R*eject (type II error)

This is the easiest way to remember it for me :)

Good LUCK!

Type 1 = Reject : this is a ONE-word expression Type 2 = Do not : this is a TWO-word expression

Here's how I do it: Type I is an Optimistic error. Type II is a Pessimistic error.

O, P: 1, 2. They're alphabetical.

Memorize “It’s Type I not II where the null is true” as it rhymes and figure the rest out while you are looking at the problem

Since you are making an error Type I - the null is true but you say it isn’t (reject it) - False positive Then Type II is where the null is not True but you say it is (Fail to reject it)- False Negative

Also, it helps to state what your Null and Alternative Hypothesis are BEFORE doing anything else

I remember it by thinking: What's the first thing I do when I do a null-hypothesis significance test? I set the criterion for the probability that I will make a false rejection. Thus, type 1 is this criterion and type 2 is the other probability of interest: the probability that I will fail to reject the null when the null is false. So, 1=first probability I set, 2=the other one.

This is how I remember the difference between Type I and Type II errors

Type I is a false POSITIVE

Type II is a false NEGATIVE

Type I is so POSITIVE it jumps out of bed first, runs downstairs and finds a significant breakfast while Type II is so NEGATIVE it stays in bed all day so when it eventually crawls out all the food is gone. It can never find anything!

• I can't figure out what that last paragraph is supposed to mean... Commented Mar 20, 2012 at 3:23

I think that the usual table is confusing because it concatenates negation verbs. I found the following "verdict table" easier to remember an generalize:

                              H0 (fair)
True                False
Positive   False positive      True positive
Decision             Type I error
(Gilty)
Negative   True negative       False negative
Type II error


Note that:

1. the decision (positive/negative) matches the verdict name
2. the verdicts with "false" are the errors

Most of the answers above do not take into consideration what information is available at the time a decision is made. For that reason, $$\alpha$$ and $$\beta$$ are not probabilities of making a decision error, as detailed here, because they are condition on knowledge (the truth about the unknown effect you're trying to estimate) that is unavailable at the decision point. It is thus misleading to attach the word "error" to type I and type II probabilities, which I label as assertion probabilities to keep things straight. Whenever a non-statistician discusses the chance of making an error, it is an unconditional probability, e.g., what is my chance of being wrong if I act as if the effect is present? Note how the person does not say "and if I knew the unknown effect is zero", because if she knew that she would not need to consider the chance of being wrong. The probability of making an error is a Bayesian posterior probability and cannot be derived from $$\alpha$$ and $$\beta$$.

Type One error Reject null hypothesis when it is true

T.O.E.R.N.H.W.I.I.T.

Tiny Overly Eager Raccoons Never Hide When It Is Teatime

Type Two Error Accept null hypothesis when it is false

T.T.E.A.N.H.W.I.I.F.

Twelve Tan Elvis's Ate Nine Hams With Intelligent Irish Farmers

• giggle. Funny mnemonic. Which may make it more memorable Commented Dec 12, 2012 at 11:26

To a software engineer: How about associating Type I error (first of the two) with the term "S"erial "N"umber -- you find something "significant" but it's acutally "not." Type II error is just the opposite once you know what Type I error is.

Sometimes reading really old scientific papers help me to understand some ideas behind statistics.

...they identified "two sources of error", namely:

(a) the error of rejecting a hypothesis that should have been accepted, and

(b) the error of accepting a hypothesis that should have been rejected.

(wiki)

Original source: Neyman, J.; Pearson, E.S. (1967) [1928]. "On the Use and Interpretation of Certain Test Criteria for Purposes of Statistical Inference, Part I". Joint Statistical Papers. Cambridge University Press. pp. 1–66. http://biomet.oxfordjournals.org/content/20A/1-2/175.full.pdf+html

RouTiNe FoR FuN Type I error is RTN: Reject The Null Type II error is FRFN: Fail to Reject a False Null (hypothesis)

My mnemonic for Type II errors is:

TWO: This Was Opposing [our chance of getting published/funding/famous], i.e., the experimental hypothesis was rejected (albeit in error).

Or

TWO: This Was Out-and-out failure (but it's an error so it's not).

Type I is what is left (i.e., false positive).

After reading through all of these I came up with my own to remember about type I (making the opposite apply to type II.)

[A]lpha is first and is an error when you [A]ccept the [A]lternate. AAA.

## RAT denotes type I errors and !RAF is type II.

Type I error - RAT

Rejecting H0 when it's Actually True

Type II - !RAF

!   Rejecting H0 when it's Actually False ≡

not Rejecting H0 when it's Actually False

! denotes the not operator so replace ! with the word "not".

NB: H0 = Null hypothesis

• I beg your pardon? – Reviewer
– Jim
Commented May 14, 2018 at 21:24
• @Jim what's up?
– Mark
Commented May 14, 2018 at 21:32