Type 1 Errors - (or type I errors) return false positive results for alternative hypotheses, leading researchers to disregard and reject true null hypotheses. In other words, they might cause you to incorrectly believe your statistical experiment was a success. According to statisticians, type 1 errors happen at the alpha level (or statistical significance level) of your results.
Type 2 Errors - (or type II errors) mean you’ve accepted a false null hypothesis and prematurely disregarded your alternative hypothesis. Type 2 errors convey whether or not the statistical power of the test was high or low enough in your initial examination of a dataset. Keep in mind this might not mean you have a true positive when it comes to your alternative, just that you’ve returned a false negative result for the null. You likely thought your alternative hypothesis did not return a statistically significant result when it actually did, at least to the point at which you can question the null hypothesis.
Type 1 vs. Type 2 Errors
A type 1 error is a false positive,
while a type 2 error is a false negative.
In both situations, the researcher arrives at an incorrect conclusion.
In a type 1 error situation, the researcher rejects an actually true null hypothesis.
In a type 2 situation, the researcher accepts an actually false null hypothesis.
A null hypothesis is a statistical theory that there is no statistically significant relationship or difference when you look at the same variable between two discrete data sets.
While both type I and type II errors can skew datasets, they do so in different ways. Some significant differences between these types of errors:
Ability to correct: When you attempt to reduce a type 1 error rate—by lowering the statistical significance level—it comes with the trade-off of increasing your type 2 error rate. The opposite is also true—raising your statistical significance level to stave off a type 2 error makes it more probable you’ll fall into the trap of a type 1 error. By increasing the sample size instead, you can make it easier to correct for the possibility of both errors at the same time.
Potential impact: If you have to choose between avoiding a type 1 or type 2 error, aim to avoid the former in most cases. This is because type 1 errors might lead to mistaken further experimentation or harmful real-world policies due to the acceptance of a false positive. A type 2 error, by contrast, cuts off research preliminarily but has little real-world effect otherwise. Still, tailor your own decision-making to the specifics of your unique statistical experiment to make the correct decision. Always do your best to avoid both types of errors if possible.
Source of the problem: A type 1 error means your statistical significance level is too high, while a type 2 error often means it’s too low. Of course, in either case, the source of the problem might arise from something different, but the significance level remains one of the most probable causes. To check this, see how your p-value (or the results of your test) measures up against the significance level and whether those findings seem incoherent.
As the number of false conclusions about statistics rise, data skews further and further into unreality.
A high type 1 error rate in your studies leads people to make wrong conclusions about hypotheses that might influence later research.
Vice versa, the same is true with a high type 2 error rate.
Many of the things you can do to mitigate the likelihood of one type of error increases the risk of the other; however, increasing sample size calculations mitigates the likelihood of either occurring.
Example: Type 1 Error
This type of error can ruin the validity and credibility of statistical tests, but it can also have an impact on real life beyond the lab or academy.
As an example of a type 1 error with a real world impact, suppose you have a null hypothesis stating a specific drug does not effectively treat heart disease and an alternative hypothesis where you state that it does. If you state the drug can treat heart disease, you run the risk of people taking the drug while, in actuality, leaving their heart condition untreated.
In other examples of type 1 errors, you might give rise to a false alarm about a certain hypothesis—for example, perhaps you run a study wherein you wrongly conclude kale causes cancer—when there’s no actual reason for concern.
Example: Type 2 Error
Suppose a drug company hopes to prove its new medication can lower cholesterol and reduce heart disease. When the results come in, the results fall short of the usual 0.05 alpha or significance level.
In some cases, this might mean the drug did prove ineffective. In others, it might be a sign to rerun the test with both a larger sample size and an increased alpha level to avoid accepting a null hypothesis as still relevant. With better inputs and parameters, your alternative hypothesis might still overturn the null.
How to Reduce the Risk of a Type 1 Error
Reducing your type 1 error rate is an important aspect of statistical analysis and calculation. Keep these tips in mind as you strive to prevent this type of error from occurring:
Check for influential extenuating factors. False positive and negative results can both arise from ignoring or missing additional factors influencing your data. Think about whether something besides your independent variable might influence possible outcomes. You’re less likely to cause a type 1 error if you can root out any issues like this early on in your research.
Ensure your data is accurate. Make sure all the data you use is as ironclad and accurate as possible. If you use bad inputs, you’ll get bad outputs. The statistical power of a hypothesis test revolves around ensuring the information you gather is reliable. Make sure your confidence level is as high as possible for every individual element that goes into your research.
Give yourself a high burden of proof. You’re far less likely to come to incorrect conclusions if you set high standards for yourself. To overturn a null hypothesis, you should be able to point to a large and statistically significant difference between the result of the test you ran and current established research. Use t-tests and other well-received metrics to verify your data.
Increase random sample size. If you use a larger sample, you help mitigate your risk of causing a Type 1 error. The more information you use to fill out the parameters of your test, the more confidence you will have you represented as thorough a breadth of data as possible. This also has the benefit of decreasing the probability of a type 2 error.
Set a lower significance level. In general, the level of significance for a test of this ilk is around 5 percent or .05. When your p-value (the results of your statistical analysis) are lower than your significance level, you’re within your rights to reject a null hypothesis in favor of your alternative. Still, this can sometimes lead to false positives. The lower your level of significance, the greater the burden of proof necessary to prove your findings are what they appear to be.
How to Reduce Type 2 Errors
It’s possible to reduce the probability of a type 2 error in your statistical hypothesis testing. Keep these tips in mind as you strive for greater accuracy:
Enlarge the sample size. If you use a larger random sample, you help mitigate your risk of causing a type 2 error. The more information you use to fill out the parameters of your test, the more positive you can be you’ve represented as thorough a breadth of data as possible. This also has the added benefit of decreasing the probability of a Type 1 error.
Increase the significance level. In general, you set your statistical level of significance to 0.05 to test whether or not you should reject a null hypothesis. To mitigate the likelihood of a type 2 error, you can raise this significance level to around 0.10 or higher. This raises the bar for whether or not you’ve obtained a statistically significant result. This does, unfortunately, come with the negative side effect of increasing the likelihood of a type 1 error.
Reevaluate your data. Your statistical results will be only as good as the information you use at the start of your experiment. Try to remain vigilant about this process so you don’t have to go back and start again. Type 2 errors often result from people getting too lackadaisical about recording accurate data. Still, if something seems off about the results of the test as you conclude your initial research, rerun the test rather than accept potentially inaccurate results.
I am spectacularly offended by this Matt Levine reader email about using astrology in consumer finance prediction.
This was a machine learning model – the job of the data scientist was, put everything in, see what's significant, of that discard everything that's discriminatory, the rest is your model. Ultimately with twelve astrological signs it's over 50/50 that one will come out significant at 95%.
I thought it was elegant. "Astrological signs? Do you believe that?" my boss said. I said it wasn't a question of belief, I was a statistician and was going to follow the numbers rather than letting anyone's preexisting theories about the stars and planets influence the data science. I think he believed that meant I'd agreed to take it out.
Like, the guy literally said "We're very likely to have a false positive here by chance, but since we got one we have to take it seriously. I'm a statistician."
He's fully aware that he's p-hacking and garden-pathing. He's fully aware of the multiple comparisons problem. And then he endorses the conclusion anyway!
(And, as a side note, it's not over 50/50; If you do twelve tests the chance of one coming out significant by chance is about 46%. So he fucked up the arithmetic too!)
One of the 3 people I’ve told I’m aroace definitely cannot understand how it’s possible to not have these attractions. Surely I must eventually be attracted to someone. I can give her plenty of grace because I still don’t understand how allo people behave the way they do—I just had to accept that it must be a horribly powerful feeling (which is how I know I’ve never felt it). But she sent me an article about Paris Hilton saying she thought she was asexual until she met her husband & was like, “you’re gonna meet the right person and BOOM!” This is a great example of a failure of analogical reasoning, since Case A (Paris Hilton) and Case B (me) could not have less in common if we tried (both on the surface & in the abuse & betrayal she’s experienced), so her experiences are in no way transferable. While I appreciate what my friend believes she’s doing (cheering me up), I would think she’d know me better than to assume mine & Paris’s journeys are the same. Of course I would never exclude Paris as asexual simply because of her trauma or because she found someone she’s attracted to (maybe she’s demi, maybe she’s using asexual to describe something else entirely, idk), and it’s great that she can talk about these things. But it becomes an issue for aroaces like me, since it’s hard (impossible?) to prove a negative. To test a hypothesis scientifically, you have to try to prove the negative (null hypothesis) of what you’re actually interested in finding so you can find proof against it to disprove the null. If my hypothesis is already the lack of existence of something (allo attractions), then the null hypothesis is that something, some event, some ONE out there must be lurking to prove it wrong. But I already know myself & my experience, and now that I’ve tested my own null hypothesis, I shouldn’t have to bother with anyone else’s testing. My friend means well, and Paris’s experiences are valid, but this is why I don’t tell people I’m aroace—they suddenly become scientists & want to prove me wrong.
The replication crisis is a major problem in medicine and social science; we know that a huge fraction of the published literature is outrig
I have a new blog post up, about the replication crisis. Why don't we have a replication crisis within mathematics? And what can this tell us about the fields that do have a replication crisis?
