Critical F Score Calculator

Significance Level (α)

A value between 0 and 1, e.g. 0.05 for a 5% significance level.

Degrees of Freedom (Numerator)

Degrees of Freedom (Denominator)

About This Test

What Is a Critical F-Score?

The critical F-score is the cutoff on the F-distribution that separates "likely due to chance" from "statistically significant." It's built from two degrees-of-freedom values — one for the numerator, one for the denominator — because the F-statistic is a ratio of two variances.

When to Use It

ANOVA, to see if the variation between group means is significant
Comparing the variances of two populations
Testing overall significance in a regression model

The Concept

\[ P(F > F_{\alpha,\,df_1,\,df_2}) = \alpha \]

Worked Example

For an ANOVA with 5 numerator and 10 denominator degrees of freedom at α = 0.05, what's the critical F-value?

\( \alpha = 0.05, \ df_1 = 5, \ df_2 = 10 \)
Right-tailed critical value: \( F_{0.05,\,5,\,10} \approx 3.326 \)
If your calculated F-statistic exceeds 3.326, you reject the null hypothesis at the 5% significance level.

Your Results

Shaded region shows the right-tailed rejection region — the most common case for F-tests. Dashed lines mark the two-tailed critical values.

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