F-Test (F₀, F_e & H₀) Calculator

F-Test is the technique using statistical methods to estimate if the test results are statistically significant by analyzing two or more variances. It requires F-statistic F₀ & critical (table) value of F-distribution F_e at a stated level of significance (α = 1%, 2%, 3%, 4%, 5%, 10%, 25%, 5% etc or α = 0.01, 0.02, 0.03, 0.04, 0.05, 0.1, 0.25, 0.5 etc) for the test of hypothesis (H₀) in statistics & probability surveys or experiments to analyze two or more variances simultaneously. Generally, F-test is the ratio between two or more variances to identify the quality of different variances. The estimated value of F or F-statistic (F₀) is compared with the critical value from F-distribution table to check the significance of results. Users may use this below F-test calculator to estimate F-statistic (F₀), critical value (F_e) & hypothesis test (H₀) to test the significance between two or more sample variances.

Inference
The below statements show when to accept or reject null hypothesis H₀ in F-test
For null hypothesis H₀ :
If F₀ < F_e then the null hypothesis H₀ is accepted.
It states that there is no significance difference between F-statistic & expected or critical value of F.
If F₀ > F_e then the null hypothesis H₀ is rejected.
It states that there is significance difference between F-statistic & expected or critical value of F.

Formula :
The below is the mathematical representation for F-test formula to estimate the quality of variances among two or more sample variances to predict the characteristics of population parameters of a unknown distribution.