An F-test p-value calculator is a statistical tool that is used to test the degree of variability or diversity between two datasets. It calculates the p-value of the F-statistic. After that, the calculator then uses the degrees of freedom for the numerator and denominator, and the computed F-statistic to generate the probability of obtaining a result like the sample result given the null hypothesis.
If the p-value is small (typically less than 0.05), the calculator reject the null hypothesis, and conclude there is a difference. This tool is useful in use cases as biology, economics, engineering, social sciences for comparing data sets, testing regression models or performing ANOVA analysis.
How to Calculate the F-Test and p-Value?
Generally, the F-test is done to compare the two independent variances samples. This is used to determine whether they come from populations with equal variances or not. Keep in mind that this is commonly applied before conducting a t-test or in ANOVA.
1. F-Test Statistic
The formula for the F-statistic is:
F = \frac{s_1^2}{s_2^2}
Where:
- s_1^2 = variance of sample 1
- s_2^2 = variance of sample 2
⚠️ Don’t forget to keep the larger variance in the numerator to ensure F ≥ 1 (especially for two-tailed tests).
2. Degrees of Freedom
You’ll need the degrees of freedom for each sample:
- \text{df}_1 = n_1 - 1
- \text{df}_2 = n_2 - 1
Where n_1 and n_2 are the sample sizes.
3. Calculating the p-value
Here, the p-value is the
The p-value is the probability of getting an F-statistic as extreme as, or more extreme than, the one you observed from taking F under the null hypothesis (equal variances).
Two approaches:
Using the F-distribution CDF:
For a two-tailed test: \text{p-value} = 2 \times \min\left( P(F \leq f), \; P(F \geq f) \right)
Where:
- fff = calculated F-statistic
- P(F \geq f) is the survival function (1 – CDF) of the F-distribution
- Use statistical libraries (e.g., Python’s
scipy.stats.f.cdfor JavaScript approximations)
Using statistical tables:
You could also look at where the F-statistic stands relative to the threshold from an F-table at your significance level (say 0.05) and the degrees of freedom.
Interpretation
- If p-value ≤ α (usually 0.05), null hypothesis is rejected → variances are considered to be different
- If p-value > α, then do not reject (fail to reject) the null hypothesis → no significant difference among variances
F-Test P-Value Calculator
What is an F-test?
The F-test is a technique used to determine whether the variances of two populations are equal.
When to use it:
Use the F-test if you would like to determine that if two samples have significantly different variances.
What does the p-value tell us?
The p-value is a measure of the probability that the observed result (or something far away from that) would have occurred by chance when the null hypothesis (equal variances) is true. A p-value that is small (typically < 0.05) indicates evidence against the null hypothesis.