P Value From F Statistic in R Calculator

Calculator

F statistic

Enter this directly, or use mean squares below.

Numerator df

Denominator df

Tail type

Alpha level

Decimal places

Numerator mean square

Denominator mean square

Optional note

Formula Used

The calculator evaluates the F distribution through the regularized incomplete beta function.

x = (df1 × F) / ((df1 × F) + df2)

CDF = I_x(df1 / 2, df2 / 2)

Right tail p = 1 − CDF

Left tail p = CDF

Two tail p = 2 × min(left tail p, right tail p)

For a common ANOVA or regression F test, use the right tail. In R, the matching expression is usually pf(F, df1, df2, lower.tail = FALSE).

How To Use This Calculator

Enter the F statistic from your ANOVA, regression, or variance test.
Enter numerator degrees of freedom as df1.
Enter denominator degrees of freedom as df2.
Select the tail type that matches your hypothesis.
Choose alpha, such as 0.05 or 0.01.
Press Calculate to show the result below the header.
Use CSV or PDF export for records.

Example Data Table

Example	F statistic	df1	df2	Right tail p value	Common reading
ANOVA model	4.26	3	24	0.015119	Significant at 0.05
Regression test	2.75	2	18	0.090749	Not significant at 0.05
Large ratio test	7.90	5	30	0.000076	Strong evidence
Small ratio test	1.35	4	40	0.268443	Weak evidence

Understanding P Values From F Statistics

An F statistic compares two variance estimates. It is common in ANOVA, regression, and variance ratio tests. A large F value usually means the numerator variance is large compared with the denominator variance. The p value tells how unusual that F value is under the null hypothesis.

Why This Calculator Helps

Manual F table lookup can be slow. Tables also give limited probability ranges. This calculator uses the F distribution directly. It accepts the statistic, numerator degrees of freedom, denominator degrees of freedom, and tail choice. It then returns a precise p value and a clear decision against your selected alpha level.

Using R Style Results

Many students and analysts check F tests in R. The common right tail command is pf(F, df1, df2, lower.tail = FALSE). This page shows a matching command beside the result. That makes the answer easier to audit, copy, and explain in reports.

When To Use Each Tail

Most ANOVA and model comparison tests use the right tail. A left tail may be used for a lower variance question. A two tail option is included for special variance ratio work. Always match the tail to your hypothesis before interpreting the answer.

Reading The Output

The calculator reports the transformed beta input, cumulative probability, right tail probability, and final p value. It also compares the result with alpha. If the p value is less than or equal to alpha, the result is statistically significant. Otherwise, the evidence is not strong enough to reject the null hypothesis.

Good Practice

Check that both degrees of freedom are positive. Use the original F statistic from your test output. Do not round too early. Small rounding changes can affect very small p values. Export the result after checking the inputs. The CSV file supports spreadsheets. The PDF button creates a compact result note for records.

Quality Checks

Compare the p value with software output when publishing important work. Confirm whether your F statistic came from ANOVA, regression, or a variance ratio test. Keep df1 and df2 in the correct order. Reversing them changes the distribution. Save exports with the dataset name and date for traceable analysis. This improves later reviews and reduces confusion.

FAQs

What is a p value from an F statistic?

It is the probability of getting an F value at least as extreme as your observed value, assuming the null hypothesis is true.

Which tail should I choose?

Use right tail for most ANOVA, regression, and model comparison F tests. Use left or two tail only when your hypothesis requires it.

What are df1 and df2?

df1 is the numerator degrees of freedom. df2 is the denominator degrees of freedom. Both shape the F distribution.

Does this match R output?

Yes, for standard central F tests. The right tail result matches pf(F, df1, df2, lower.tail = FALSE), within normal rounding limits.

Can I use mean square values?

Yes. Leave the F statistic blank, then enter numerator and denominator mean squares. The calculator uses their ratio as F.

Why is my p value very small?

A very small p value means your F statistic is far into the selected tail. This often shows stronger evidence against the null hypothesis.

What alpha should I use?

Common choices are 0.05, 0.01, and 0.10. Choose alpha before testing, based on your field or reporting standard.

Can an F statistic be negative?

No. An F statistic is based on variance ratios, so it cannot be negative.