F-score to p-value calculator
Enter your F-statistic, the F value your ANOVA or regression table reports, with its numerator and denominator degrees of freedom for an exact right-tailed p-value. F-tests are always right-tailed.
Enter a test statistic to begin
Your p-value, a plain-English reading, and a shaded distribution chart appear here instantly.
Results
P-value
What this means
What it does not mean
Report it (APA)
Where this statistic comes from
You will typically be holding one of these:
- One-way, two-way, or repeated-measures ANOVA
- The overall F-test of a regression model
- Comparing two nested models
- Levene's test for equality of variances
F-value or F-statistic? Same number
Both names point at the same quantity: the ratio of two variance estimates that your
ANOVA or regression output reports. R's anova() table calls the column
F value, SPSS and Stata print a bare F, and textbooks say
F-statistic. Type whichever one you are holding into the box above.
Where the wording does matter is telling F apart from the numbers next to it. An ANOVA table hands you the F, a df for the effect row, and a df for the residual row, and this calculator needs all three. Feed it an F with the wrong pair of df and you get a confident, wrong p-value rather than an error — nothing about F alone reveals which distribution it should be compared against.
The two degrees of freedom
An F-statistic is a ratio of two variances, so it carries two df values and both change
the answer. They are conventionally written F(df₁, df₂), numerator first.
- One-way ANOVA: df₁ = number of groups − 1; df₂ = total observations − number of groups.
- Regression overall F: df₁ = number of predictors; df₂ = n − predictors − 1.
- Model comparison: df₁ = difference in parameters; df₂ = residual df of the fuller model.
Order matters. F(3, 16) and F(16, 3) are different
distributions and give different p-values for the same statistic — reversing them is one
of the easiest mistakes to make here.
What a significant F actually tells you
In ANOVA, a significant F says that at least one group mean differs from the others. It does not say which, and it does not say how many. That is a genuine limitation, not a detail — an F-test is an omnibus test by construction.
To find out where the difference lies you need post-hoc comparisons (Tukey's HSD, Bonferroni-corrected t-tests, and so on). Running unadjusted pairwise t-tests instead inflates your false-positive rate quickly: with five groups there are ten comparisons, and at α = 0.05 the chance of at least one false positive rises to about 40%.
The relationship between F and t
For a comparison of exactly two groups, an F-test and a two-tailed t-test are the same
test: F(1, df) = t(df)², and both give an identical p-value. You can verify
it here — a t of 2.3 with df = 15 gives p = 0.0364, and an F of 5.29 with df₁ = 1,
df₂ = 15 gives the same.
This identity is one of the checks in our validation suite, because any error in either implementation breaks it.
Frequently asked questions
Is the F-value the same as the F-statistic?
Yes — they are the same number under two names. Statistical software usually labels the column "F value" or simply "F", while textbooks and write-ups say F-statistic. Either way it is the ratio of explained to unexplained variance from your ANOVA or regression, and either way it goes in the box above.
How do you find the p-value from an F-statistic?
Take the F together with both of its degrees of freedom — numerator (the effect row of your ANOVA table) and denominator (the residual row) — and read the area of the F distribution to the right of your F. That right-tail area is the p-value. An F of 4.10 with df₁ = 2 and df₂ = 27 gives p = 0.0279. Enter all three numbers above and the exact area is computed for you.
What F-value is significant?
It depends on both degrees of freedom. At α = 0.05, F(1, 10) needs 4.965, F(3, 20) needs 3.098, and F(5, 50) needs 2.400. Larger denominator df lowers the critical value, because more residual data makes the variance estimate more reliable.
Is an F-test one-tailed or two-tailed?
Always right-tailed. F is a ratio of explained to unexplained variance, so evidence against the null only ever pushes it upward. A small F means the groups look alike, which is exactly what the null hypothesis predicts.
Which degrees of freedom goes first?
The numerator, written F(df₁, df₂). In a one-way ANOVA df₁ is the number of groups minus 1 — usually the smaller number — and df₂ is the residual degrees of freedom. Swapping them gives a different and incorrect p-value.
Why can a significant F-test not say which groups differ?
Because F is a single ratio of between-group to within-group variance, computed across every group at once. It asks whether the group means are more spread out than the scatter inside the groups can account for — a question about the set as a whole, with no term in it specific to any one group. That is what makes it an omnibus test, and it is why post-hoc procedures such as Tukey's HSD exist: they run the group-by-group comparisons F cannot, while controlling the error rate across the whole family.