Statistical

F.DIST Formula

Returns the F probability distribution, used in analysis of variance (ANOVA) and comparing two sample variances. The F-distribution is the ratio of two chi-squared distributions divided by their degrees of freedom. It appears in F-tests, regression analysis, and ANOVA tables.

Syntax

F.DIST(x, deg_freedom1, deg_freedom2, cumulative)
ParameterDescription
x Parameter of the F.DIST function.
deg_freedom1 Parameter of the F.DIST function.
deg_freedom2 Parameter of the F.DIST function.
cumulative Parameter of the F.DIST function.
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Examples

Left-tail probability for ANOVA

Formula
=F.DIST(3.5, 3, 20, TRUE)
Returns ~0.9655. About 96.6% of the F-distribution with 3 and 20 df falls at or below F=3.5.

P-value for F-statistic

Formula
=1-F.DIST(4.2, 2, 15, TRUE)
Returns ~0.0352. The right-tail p-value for an F-statistic of 4.2 with 2 and 15 df indicates significance at the 5% level.

PDF for visualization

Formula
=F.DIST(2, 5, 10, FALSE)
Returns ~0.1209. The density value at F=2 with 5 and 10 df, useful for plotting the F-distribution curve.

Common Errors

#NUM!

x must be non-negative, and both degrees of freedom must be at least 1.

#VALUE!

Occurs when arguments are non-numeric.

Tips

Left-tail CDF

F.DIST with cumulative=TRUE returns the left-tail probability. For the right-tail p-value used in ANOVA, use F.DIST.RT or =1 - F.DIST(x, df1, df2, TRUE).

Two sets of degrees of freedom

df1 is the numerator (between-group) degrees of freedom and df2 is the denominator (within-group). The order matters — swapping them gives a different result.

Only right-skewed

The F-distribution only takes positive values and is right-skewed, especially with small df. At large df values, it becomes more symmetric.

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