The probability of making a Type 1 error is equal to the significance level you set before running a statistical test, known as alpha (α). In most research, alpha is set at 0.05, meaning there is a 5% chance of concluding that an effect or relationship exists when it actually does not. You choose this probability before collecting data, and it acts as a cap on how often you’re willing to be wrong in that specific way.
What a Type 1 Error Actually Is
A Type 1 error is a false positive. It happens when you reject a null hypothesis that is actually true. In practical terms, you conclude something is real when it isn’t. If a clinical trial compares two drugs and declares the new one superior when it performs no differently, that’s a Type 1 error. The researchers “found” a difference that doesn’t exist in the real population.
The consequences can be serious. Imagine a study concludes that a new, more expensive drug reduces symptoms better than the current standard, but the difference was just statistical noise. Patients get switched to a costlier medication with potentially more side effects, healthcare spending goes up, and clinical outcomes don’t actually improve. That chain of events starts with a single false positive.
Alpha: The Number You Pick
Alpha is the maximum probability of a Type 1 error that a researcher is willing to accept. It’s chosen before the study begins, not calculated afterward. Setting alpha at 0.05 means you’re accepting a 5% risk that you’ll incorrectly reject the null hypothesis. Setting it at 0.01 lowers that risk to 1%.
The most common alpha levels in published research are 0.05, 0.01, and 0.10. A review of published papers found that 9 out of 10 used 0.05, with one using 0.01. The 5% threshold dominates scientific publishing, though it’s worth understanding that this number is a convention, not a law of nature. Some statisticians have proposed moving the standard threshold to 0.005 for new discoveries, arguing that the traditional 0.05 cutoff contributes to a high rate of false positives in the literature and poor research reproducibility.
Alpha vs. the P-Value
One common point of confusion is the difference between alpha and a p-value. The simplest way to think about it: you pick alpha, and you calculate the p-value. Alpha is your predetermined threshold for how much false-positive risk you’ll tolerate. The p-value is what your data actually produces. It represents the probability of getting a result as extreme as (or more extreme than) what you observed, assuming the null hypothesis is true.
If the p-value falls below alpha, you reject the null hypothesis. If it doesn’t, you fail to reject it. But the p-value itself is not the probability of a Type 1 error. Alpha is. The p-value tells you how surprising your data would be under the null hypothesis. Alpha tells you where you drew the line for “surprising enough to act on.”
The Trade-Off With Type 2 Errors
Lowering alpha to reduce your Type 1 error risk doesn’t come free. It increases the probability of making a Type 2 error, which is a false negative: failing to detect a real effect. If you set an extremely strict alpha of 0.001, you’ll almost never declare a false positive, but you’ll miss genuine effects more often because your bar for “convincing evidence” is so high.
This is why researchers don’t simply set alpha at 0.001 for every study. The choice depends on context. In a drug safety trial where a false positive could lead to an ineffective treatment being approved, a lower alpha makes sense. In an exploratory study where missing a real finding is the bigger concern, a more lenient alpha might be appropriate. The balance between these two types of errors is one of the core decisions in study design.
Why Multiple Tests Change the Odds
The 5% false-positive rate applies to a single test. When you run multiple tests on the same dataset, the overall probability of making at least one Type 1 error rises quickly. This overall rate is called the familywise error rate.
If you test 20 different hypotheses at alpha = 0.05, you’d expect about one false positive even if none of the effects are real. Run 100 tests, and you’d expect roughly five. The math is straightforward: each individual test carries a 5% chance of a false alarm, and those chances accumulate across tests.
Researchers use correction methods to keep the overall Type 1 error rate in check. The most well-known is the Bonferroni correction, which divides the desired overall error rate by the number of tests. If you want a 5% familywise error rate across 10 tests, each individual test uses an alpha of 0.005 (0.05 divided by 10). This is simple but conservative, meaning it can make it harder to detect real effects.
More sophisticated approaches offer a better balance. Holm’s method, for instance, orders p-values from smallest to largest and applies progressively less strict thresholds as it moves through them. The Simes-Hochberg method works in the opposite direction, starting with the largest p-values first and is more powerful than Holm’s, though it requires that the tests be independent of each other. These sequential methods control the false-positive rate while preserving more statistical power than a blanket Bonferroni correction.
Choosing the Right Alpha for Your Situation
There’s no universal “correct” alpha. The 0.05 standard is a default, not an optimization. The right choice depends on what’s at stake. Fields where false positives are expensive or dangerous, like pharmaceutical development or genomics, often use stricter thresholds. Genome-wide association studies, for example, routinely use alpha levels of 0.00000005 because they’re testing millions of genetic variants simultaneously.
If you’re evaluating a study or running your own analysis, the key question is: what happens if this result is a false positive? If the downstream cost is high, a stricter alpha protects you. If the cost of missing a true effect is higher, a more lenient alpha paired with a larger sample size is the better strategy. Either way, the probability of a Type 1 error is the number you set it to be. It’s one of the few things in statistics that’s entirely under your control.