F Statistic Calculator
Calculate the F-statistic to compare variances of two independent samples. Free online F-test calculator with p-value, degrees of freedom, and variance comparison charts.
About This Calculator
The F Statistic Calculator helps you compare the variances of two independent samples using the F-test. This statistical test determines whether two populations have equal variances, which is a common assumption in many parametric statistical procedures including t-tests and ANOVA.
To use this calculator, enter comma-separated numeric values for two independent groups. The calculator computes the F-statistic as the ratio of the larger sample variance to the smaller sample variance, along with the corresponding degrees of freedom and p-value. A two-tailed F-test is performed at the default 5% significance level. The results also display the mean and variance of each group for comprehensive comparison.
The F-distribution is a continuous probability distribution that arises when the null hypothesis is true. It is skewed to the right and its shape depends on the degrees of freedom of the numerator and denominator. The F-test is widely used in analysis of variance (ANOVA), regression analysis, and quality control applications.
Regional Notes: The F-test is a universal statistical method used the same way worldwide (IN, US, UK, EU). No region-specific parameters are needed. This calculator works with any numeric data set regardless of measurement units or currency.
Frequently Asked Questions
What is an F-statistic?
An F-statistic is a ratio of two variances used in hypothesis testing to determine whether two populations have equal variances. It follows an F-distribution under the null hypothesis and is calculated as F = s1² / s2², where s1² and s2² are the sample variances of two independent groups.
How do you interpret the F-statistic?
A large F-statistic (typically with p-value < 0.05) indicates that the variances of the two populations are significantly different. A small F-statistic (p-value > 0.05) suggests insufficient evidence to conclude the variances differ. The degrees of freedom depend on the sample sizes of each group.
What is the formula for the F-statistic?
The F-statistic formula is F = s1² / s2², where s1² is the variance of the first sample (larger variance placed in numerator) and s2² is the variance of the second sample. The numerator degrees of freedom is df1 = n1 − 1 and denominator degrees of freedom is df2 = n2 − 1.
What is an F-test used for?
An F-test is used to compare the variances of two populations, test the overall significance of a regression model, analyze variance components in ANOVA, and test equality of means across multiple groups. In regression, it tests whether the model explains significant variance in the dependent variable.
Can the F-statistic be negative?
No, the F-statistic can never be negative because it is a ratio of two variances and variances are always positive values. An F-statistic is always greater than or equal to zero. A value close to 1 suggests the two sample variances are similar.
What is the difference between F-test and t-test?
The F-test compares variances of two populations, while the t-test compares means. The F-test uses the F-distribution and is always two-tailed when testing variance equality. The t-test uses the Student t-distribution and can be one-tailed or two-tailed. In ANOVA, the F-test simultaneously tests for differences among multiple group means.
What degrees of freedom does the F-distribution use?
The F-distribution uses two degrees of freedom: numerator degrees of freedom (df1) = n1 − 1 for the first sample, and denominator degrees of freedom (df2) = n2 − 1 for the second sample. The shape of the F-distribution is determined by both degrees of freedom values.
What does a p-value less than 0.05 mean in an F-test?
A p-value less than 0.05 in an F-test means we reject the null hypothesis that the two population variances are equal. This indicates a statistically significant difference between the variances at the 5% significance level. The F-statistic is larger than the critical value from the F-distribution table.