Lesson 13.3 Facts About the F Distribution
- The curve is not symmetrical but skewed to
the right.
- There is a different curve for each set of
dfs.
- The F statistic is greater than or equal
to zero.
- As the degrees of freedom for the
numerator and for the denominator get
larger, the curve approximates the
normal.
- Other uses for the F distribution include
comparing two variances and two-way Analysis
of Variance.
![](data:image/png;base64,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)
This
example shows a One-Way ANOVA to
determine if the average number of goals
scored per game are the same for 4 different
teams.
This is the last section to be
covered for this course.