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In statistics, alpha (α) is the significance level of a hypothesis test: the probability of rejecting the null hypothesis when the null hypothesis is actually true. You choose it before you look at the data, and it sets the line your p-value must fall below for a result to count as statistically significant. The most common choices are 0.10, 0.05 and 0.01.
What does alpha mean in statistics?
Alpha is an error rate that you decide to tolerate. The NIST/SEMATECH e-Handbook of Statistical Methods puts it this way: “A value of α = 0.05 implies that the null hypothesis is rejected 5 % of the time when it is in fact true.” That kind of mistake, rejecting a true null hypothesis, is the Type I error, so alpha is the Type I error rate you accept. The NIST handbook also states that the significance level “defines the sensitivity of the test”: a smaller alpha makes the test harder to pass.
The handbook notes that “the choice of α is somewhat arbitrary, although in practice values of 0.1, 0.05, and 0.01 are common.” Nothing in the mathematics makes 0.05 special; it is a convention. For the companion idea, the Type II error (failing to reject a false null, written β), see the comparison of Type I and Type II errors.
Alpha in one rule
Alpha turns a p-value into a decision. Compare the two numbers:
- If p ≤ alpha (many texts use the strict form, p < alpha), reject the null hypothesis and call the result statistically significant at that level.
- If p > alpha, do not reject the null hypothesis.
The NIST handbook advises: “It is good practice to decide in advance of the test how small a p-value is required to reject the test.” Fixing alpha first matters because choosing it after seeing the p-value lets the answer decide the threshold. For what the p-value itself measures, read what a p-value is.
Formula and symbols
Alpha is a probability you choose, so there is no data formula for it. It is defined as:
α = P(reject H0 | H0 is true)
- α: the significance level, a number between 0 and 1.
- P( ): probability.
- H0: the null hypothesis.
- |: “given that”; the probability is calculated assuming the null hypothesis is true.
Alpha also fixes the critical value. For a two-sided test you split alpha into two tails of α/2 each, and the critical value is the point that cuts off α/2 in each tail. Tables and lookups are covered in how to find a critical value.
Worked example: the same data at α = 0.05 and α = 0.01
A researcher tests whether a mean differs from 50 using a two-sided one-sample t test. The sample has n = 25, mean = 54 and standard deviation s = 8. The numbers are invented for illustration.
- Standard error: s / √n = 8 / √25 = 8 / 5 = 1.6.
- Test statistic: t = (54 − 50) / 1.6 = 2.5.
- Degrees of freedom: n − 1 = 24.
- Two-sided p-value for t = 2.5 with 24 degrees of freedom: p ≈ 0.0197.
Now apply two different alphas to the same result:
| Alpha | Critical value (two-sided, df = 24) | Compare | Decision |
|---|---|---|---|
| 0.05 | ±2.064 | 2.5 exceeds 2.064; p = 0.0197 is below 0.05 | Reject the null |
| 0.01 | ±2.797 | 2.5 is below 2.797; p = 0.0197 is above 0.01 | Do not reject the null |
The data did not change; only the threshold did. This is why alpha has to be declared in advance.
Alpha is also linked to confidence intervals: confidence level = 1 − alpha. The NIST handbook states that a null hypothesis is rejected if and only if the hypothesised value is not in the confidence interval. Here the 95% interval is 54 ± 2.064 × 1.6 = 50.70 to 57.30, which excludes 50 (rejected at 0.05). The 99% interval is 54 ± 2.797 × 1.6 = 49.52 to 58.48, which includes 50 (not rejected at 0.01). The two views agree. A related comparison is p-value vs confidence interval.
Interpretation: how to read a choice of alpha
| Alpha | What it means |
|---|---|
| 0.10 | You accept rejecting a true null hypothesis 10% of the time; the least strict of the common values. |
| 0.05 | You accept rejecting a true null hypothesis 5% of the time (the NIST wording above). |
| 0.01 | You accept rejecting a true null hypothesis 1% of the time; a stricter bar for significance. |
Lowering alpha reduces the Type I error rate you allow. It does not come free: for a fixed sample size, a stricter alpha makes it harder to detect a real effect, which raises the Type II error probability β. Which alpha is appropriate depends on how costly a false rejection is in your field and is set by the study protocol, not by the data.
Alpha vs p-value
Alpha is chosen before the study and does not depend on the data. The p-value is computed from the data after the study. Alpha is the threshold; the p-value is the number compared against it. A p-value of 0.0197 is not “an alpha of 0.0197”; it is the result you hold against whatever alpha you declared. See also the dictionary entry for the p-value.
Assumptions and common mistakes
- Choosing alpha after seeing the result. This undermines the stated error rate. Decide in advance, as NIST advises.
- Treating 0.05 as a law. It is a convention; 0.1 and 0.01 are equally standard options.
- Reading alpha as the probability the null is true. Alpha is calculated assuming the null is true; it is not the probability that the null is true given your data.
- Running many tests at one alpha. Each test carries its own Type I risk. A simple correction (Bonferroni) divides alpha by the number of tests m: with five tests and an overall alpha of 0.05, each test uses 0.05 / 5 = 0.01. Sequential trial designs spend alpha across interim looks.
- Confusing it with Cronbach’s alpha. The same Greek letter names a different quantity in measurement work: Cronbach’s alpha is a reliability coefficient for a scale, not a significance level. See Cronbach’s alpha in SPSS. Krippendorff’s alpha, an agreement coefficient, is a third unrelated use.
How to report alpha
State the alpha level in your methods before the results, then give the test statistic, degrees of freedom and exact p-value. A plain-language template:
“A two-sided one-sample t test was used with a significance level of α = 0.05. The mean (M = 54, SD = 8, n = 25) differed from 50, t(24) = 2.50, p = .020.”
Check your target journal’s author guidelines for its exact formatting of statistics and for whether it expects an alpha stated for each test.
How to get critical values from alpha in Excel, R or Python
Each snippet returns the two-sided critical value for α = 0.05 with 24 degrees of freedom (2.064) and the two-sided p-value for t = 2.5 (0.0197).
Excel
=T.INV.2T(0.05, 24) =T.DIST.2T(2.5, 24)
R
qt(1 - 0.05/2, df = 24) 2 * pt(-2.5, df = 24)
Python
from scipy import stats stats.t.ppf(1 - 0.05/2, 24) 2 * stats.t.sf(2.5, 24)
For a one-sided test, put all of alpha in one tail: use 1 − 0.05 in the first argument (for df = 24 this gives 1.711).
FAQ
What does alpha mean in statistics?
Alpha is the significance level: the probability you accept of rejecting a true null hypothesis (a Type I error). Common values are 0.10, 0.05 and 0.01.
What is the difference between alpha and the p-value?
Alpha is the threshold set in advance; the p-value is calculated from the data. You reject the null hypothesis when the p-value is below alpha.
Is alpha the same as the confidence level?
They are linked, not identical: confidence level = 1 − alpha. An alpha of 0.05 corresponds to a 95% confidence interval.
Why is alpha usually 0.05?
It is a widely used convention. NIST describes the choice as somewhat arbitrary, with 0.1, 0.05 and 0.01 all common in practice.
Sources
- NIST/SEMATECH e-Handbook of Statistical Methods, hypothesis tests and p-values: itl.nist.gov/div898/handbook/prc/section1/prc131.htm (checked 2026-10-29).
- NIST/SEMATECH e-Handbook, Exploratory Data Analysis, significance level and Type I/II error: itl.nist.gov/div898/handbook/eda/section3/eda35.htm (checked 2026-10-29).
- NIST/SEMATECH e-Handbook, tests and confidence intervals: itl.nist.gov/div898/handbook/prc/section1/prc15.htm (checked 2026-10-29).
