F.INV

Calculates the inverse of the F probability distribution.

Syntax:

F.INV(probability, deg_freedomOne, deg_freedomTwo)

probability is required, and is the probability associated with the F cumulative distribution (a value between 0 and 1).

deg_freedomOne is required, and is the degrees of freedom for the numerator.

deg_freedomTwo is required, and is the degrees of freedom for the denominator.

Example:

If probability contains 0.05, deg_freedomOne contains 3 and deg_freedomTwo contains 10:

F.INV(0.05, 3, 10)

returns 0.113823594

x:

Deg_freedomOne:

Deg_freedomTwo:

Result:

0.113823594

Application:

Comparing the Consistency of Two Production Lines

Imagine a manufacturing company that has two different production lines (Line A and Line B) for making widgets. The company wants to know if there's a significant difference in the consistency of the widgets produced by each line. They take a sample of widgets from each line and measure their diameter. The variation in the diameter is a measure of the consistency of the production process.

The company sets a significance level (alpha, or α) of 0.05. This means they are willing to accept a 5% chance of incorrectly concluding that the variances are different when they are not.

Here is the data collected from the two production lines:

		Line A	Line B
	A	B	C
1	Sample Size (n)	25	30
2	Sample Variance (s2)	0.045	0.028

1. Calculate Degrees of Freedom:

The degrees of freedom for each sample are calculated as n - 1.

Degrees of Freedom for Line A (Numerator): df1=25−1=24
Degrees of Freedom for Line B (Denominator): df2=30−1=29

2. Determine the Probability:

Since we are performing a two-tailed F-test (we want to know if the variance is different, not just greater or less than), we need to split our significance level (α) between the two tails of the F-distribution. The F.INV function calculates the inverse of the left-tailed cumulative distribution. Therefore, for a two-tailed test with α=0.05, the probability we need to input into the function is 1−(α/2) which is 1−(0.05/2)=0.975.

3. Use the F.INV Function:

To find the critical F-value, you would use the F.INV function with the following arguments:

F.INV(probability, degrees_freedom1, degrees_freedom2)

Using the values from our example:

F.INV(0.975, 24, 29)

The result of this calculation is approximately 2.15. This is the critical F-value.

4. Compare and Conclude:

Calculated F-statistic: The F-statistic is calculated as the ratio of the two sample variances: $F_{calculated} = \frac{s _{1}^{2}}{s _{2}^{2}} = \frac{0.045}{0.028} \approx 1.61$
Critical F-value: 2.15

Since the calculated F-statistic (1.61) is less than the critical F-value (2.15), the company does not have enough evidence to reject the null hypothesis. In plain terms, there is no statistically significant difference in the consistency (variance) of the widgets produced by the two production lines at the 0.05 significance level.

Result for F.INV(0.975, 24, 29):

2.15