# F-test

We’ve already seen what F-score is. Now let’s see what
F-test. Side note: I came across it when I was writing
Elbow Method and my thoughts were, cool another F-word for my readers, so

## Here you go:

• F-test is any stats test that uses F-distribution

• It is often used when comparing stats models that have been fitted to a data set.. Ahh.. That
sounds no different from F-score then.. May be just different
fields(Statistics and Machine Learning) have different naming conventions?? Anyway two different
F-words.. So let’s just say what F-score/test?? Why two names for samething and move on…

## Examples:

• Null Hypothesis: Means of a given set of normally distributed populations all having same standard deviation being equal.(used in ANOVA)

• The hypothesis that a proposed regression model fits the data well.

• The hypothesis that a data set in a regression analysis follows the simpler of two proposed linear models that are nested within each other.

• It(non-regression type) is also a test of homoskedasticity

## Formula

• Formula: $explained variance/un-explained variance$ or $between-group-variability/within-group-variability$ Ok. That doesn’t sound like the F-score

• Formula(for regression models): $((RSS\_1 - RSS\_2) / (p_2 - p_1)/(RSS_2/(n-p_2)))$