What is F-distribution?

The F-distribution is a probability distribution used in hypothesis testing and analysis of variance.

The F-distribution is a continuous probability distribution that arises in the analysis of variance (ANOVA) and hypothesis testing. It is used to compare the variances of two or more populations. The F-distribution is a ratio of two chi-squared distributions, and its shape depends on the degrees of freedom of the numerator and denominator. The numerator degrees of freedom represent the number of groups being compared, while the denominator degrees of freedom represent the total sample size minus the number of groups.

The F-distribution is commonly used in ANOVA to test whether the means of two or more groups are equal. The test statistic is the F-ratio, which is calculated by dividing the variance between groups by the variance within groups. If the F-ratio is large enough, it indicates that the variance between groups is significantly greater than the variance within groups, and we reject the null hypothesis of equal means.

The F-distribution is also used in hypothesis testing to compare the variances of two populations. The test statistic is again the F-ratio, which is calculated by dividing the sample variances of the two populations. If the F-ratio is large enough, it indicates that the variance of one population is significantly greater than the variance of the other population, and we reject the null hypothesis of equal variances.

In summary, the F-distribution is a probability distribution used in hypothesis testing and ANOVA to compare the variances of two or more populations. Its shape depends on the degrees of freedom of the numerator and denominator, and its test statistic is the F-ratio.