Homework SourseWhat is the most critical condition which can affect the val
What is the most critical condition which can affect the validity of a test using the F distribution? Why does this condition have such a great effect on the validity of the test?
Solution
he f statistic, also known as an f value, is a random variable that has an F distribution. (We discuss the F distribution in the next section.)
Here are the steps required to compute an f statistic:
The following equivalent equations are commonly used to compute an f statistic:
f = [ s12/12 ] / [ s22/22 ]
f = [ s12 * 22 ] / [ s22 * 12 ]
f = [ 21 / v1 ] / [ 22 / v2 ]
f = [ 21 * v2 ] / [ 22 * v1 ]
The distribution of all possible values of the f statistic is called an F distribution, with v1 = n1 - 1 andv2 = n2 - 1 degrees of freedom.
The curve of the F distribution depends on the degrees of freedom, v1 and v2. When describing an F distribution, the number of degrees of freedom associated with the standard deviation in the numerator of the f statistic is always stated first. Thus, f(5, 9) would refer to an F distribution with v1 = 5 and v2 = 9 degrees of freedom; whereas f(9, 5) would refer to an F distribution with v1 = 9 and v2 = 5 degrees of freedom. Note that the curve represented by f(5, 9) would differ from the curve represented by f(9, 5).
The F distribution has the following properties:
