F-Statistic Calculator

The F-statistic is the ratio of two sample variances: F = S₁² / S₂². It is used in hypothesis testing to determine whether two populations have equal variances. Values far from 1 suggest the variances differ significantly.

The F-test compares the variances of two independent, normally distributed populations. The null hypothesis (H₀) states that the two population variances are equal (σ₁² = σ₂²). If the computed F-statistic exceeds the critical value, the null hypothesis is rejected.

A T-test compares the means of one or two groups, testing a single parameter. An F-test compares variances or, in regression, tests whether a linear combination of multiple coefficients is jointly significant. The F-distribution is always non-negative, while the T-distribution is symmetric around zero.

No. Because the F-statistic is a ratio of two variances (both of which are squared quantities and therefore non-negative), the F-statistic is always zero or positive. An F-value of 1 indicates equal variances.

A high F-statistic means the variance in the first sample is much larger than in the second. Whether it is statistically significant depends on the degrees of freedom and the chosen significance level. Compare your F-statistic against the critical F-value to determine significance.

The numerator degrees of freedom is df₁ = n₁ − 1, and the denominator degrees of freedom is df₂ = n₂ − 1, where n₁ and n₂ are the sample sizes. Both values are needed to look up or compute the critical F-value.

No, the F-distribution is not symmetric. It is a right-skewed distribution with all values greater than or equal to zero. Its shape depends on the two degrees-of-freedom parameters (df₁ and df₂).

The main assumptions are: (1) both samples are drawn independently from their populations, (2) both populations follow a normal distribution, and (3) the samples are random. The F-test is sensitive to departures from normality, so it is good practice to verify normality before applying it.