Statistics
Activity:
F Distribution
Posted on Apr 17, 2008
Topic: Continuous Distributions and their Properties
In this activity, students study the characteristics of the F distribution and discuss why the distribution is not symmetric (skewed right) and only has positive values. Students then use the Fcdf command to find probabilities and to confirm percentiles.
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Activity Key Steps:
In problem 1, students explore the characteristics of the F Distribution.
Students will notice that, with the chi-square distribution, the values of the F distribution cannot be negative, and the graph is skewed to the right. Unlike the chi-square distribution, the graph does not become more symmetric as the number of degrees of freedom increases.
Students will determine whether the graph changes when the degrees of freedom are interchanged.
Students will see that the distributions are different when the degrees of freedom are interchanged.
Problem 2 explores the variances of two samples if F is near 1.
The variances would be almost the same. When the numerator and denominator of a fraction are the same, the fraction has a value of 1.
The value gets further from 1 as the numerator and denominator have greater differences.
In problem 3, students find the critical values for an F Distribution. They first find the F value for a given area and construct confidence intervals.
Students will check their critical values by changing the x-coordinates and finding the areas under the curve.
At the end of this activity students will be able identify an F Distribution and identify the differences between the F Distribution and a chi-squared distribution.
They will also be able to graph the probability density function of the F distribution of m and n degrees of freedom.