The F-test is a statistical test used primarily in regression analysis and ANOVA (Analysis of Variance) to compare two competing models and assess their ability to explain the variance in a dependent variable. In the context of regression analysis, the F-test helps determine whether a more complex model (with additional variables) significantly improves the explanation of the variance compared to a simpler model, often referred to as the restricted model. The simpler model typically includes only an intercept, while the complex model includes additional predictors ¹.

The F-test operates under the null hypothesis that the additional variables in the complex model do not provide a significant improvement in fit compared to the simpler model. If the F-statistic calculated from the data exceeds a critical value from the F-distribution, the null hypothesis can be rejected, indicating that the complex model is statistically better at explaining the variance in the dependent variable ².

However, the F-test has limitations, particularly when sample sizes are large or when the number of explanatory variables increases. In such cases, it may yield misleading results regarding the goodness-of-fit of the model ². Modifications to the F-test can enhance its utility in these situations ².