Fstatistika

Fstatistika is a statistical concept used to assess whether a set of explanatory variables significantly improves the fit of a model compared with a baseline. It is most closely associated with analysis of variance (ANOVA) and linear regression, providing a formal test for whether group means differ or whether coefficients of predictors are different from zero.

The F-statistic is the ratio of the model mean square to the error mean square: F = MS_model / MS_error, with MS_model = SS_model/df_model and MS_error = SS_error/df_error. Under the null hypothesis and typical assumptions, this statistic follows an F-distribution with df_model and df_error degrees of freedom. A large observed F indicates that the model explains more variance than expected by chance, and the corresponding p-value is used to decide significance.

Applications include one-way and multi-way ANOVA, multiple regression, and ANCOVA. F-tests can compare nested models to determine whether adding predictors improves fit. Assumptions include independence of observations, normally distributed residuals, and homoscedasticity; violations can affect the accuracy of the F-test, and alternative methods may be chosen in such cases.

Historically, the F-statistic was developed by Ronald A. Fisher in the context of agricultural experiments and ANOVA in the early 20th century. Today it remains a standard tool in statistical inference and is implemented in most statistical software.