F.DIST.RT

Calculates the right-tailed probability of the F-distribution.

Syntax:

F.DIST.RT(x, deg_freedomOne, deg_freedomTwo)

x is required, and is the value you want to use to evaluate the function.

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 x contains 3.8, deg_freedomOne contains 3 and deg_freedomTwo contains 15:

F.DIST.RT(3.8, 3, 15)

returns 0.032932086

x:

Deg_freedomOne:

Deg_freedomTwo:

Result:

0.032932086

Application:

A company has two manufacturing plants, Plant A and Plant B, that produce identical parts. The company wants to know if there's a significant difference in the consistency (variability) of the parts produced by each plant. A quality control team takes a sample of parts from each plant and measures a critical dimension.

The null hypothesis (H0) is that the variances of the two populations (Plant A and Plant B) are equal. The alternative hypothesis (Ha) is that the variances are not equal. The F-test helps us determine if the difference in sample variances is large enough to reject the null hypothesis.

Data

The following table shows the summary statistics for the samples taken from each plant.

	Plant	Sample Size (n)	Sample Variance (s2)	Degrees of Freedom (df)
	A	B	C	D
1	Plant A	25	3.5	24
2	Plant B	30	2	29

Degrees of Freedom (df): The degrees of freedom for each sample is calculated as n−1.
F-statistic: The F-statistic is the ratio of the two sample variances. We always place the larger variance in the numerator.

$F = \frac{s _{1}^{2}}{s _{2}^{2}} = \frac{3.5}{2.0} = 1.75$

Using F.DIST.RT in a Spreadsheet

The F.DIST.RT function takes three arguments:

x: The F-statistic value (1.75).
degrees_freedom1: The degrees of freedom for the numerator's variance (24).
degrees_freedom2: The degrees of freedom for the denominator's variance (29).

You would enter the formula as:

F.DIST.RT(1.75, 24, 29)

Table

Imagine a table with the following layout:


	A	B	C
1	Description	Value	Formula
2	Plant A Sample Size	25
3	Plant B Sample Size	30
4	Plant A Sample Variance	3.5
5	Plant B Sample Variance	2
6
7	Calculations
8	Number df (Plant A)	24	B2 - 1
9	Denominator df (Plant B)	29	B3 - 1
10	F-statistic	1.75	B4 / B5
11	F.DIST.RT p-value	0.075484713	F.DIST.RT(B10, B8, B9)

Interpretation of the Result

The result from the F.DIST.RT function is the p-value. In this case, F.DIST.RT(1.75, 24, 29) returns 0.075484713.

The p-value represents the probability of observing an F-statistic as extreme as, or more extreme than, the one calculated from our samples, assuming the null hypothesis is true.

To make a conclusion, we compare the p-value to a predetermined significance level (alpha or α), which is typically 0.05.

If p-value < α, we reject the null hypothesis. This means there is a statistically significant difference in variances.
If p-value ≥ α, we fail to reject the null hypothesis. This means there is not enough evidence to conclude a significant difference in variances.

In this example, our p-value (0.075484713) is greater than our significance level (0.05). Therefore, we fail to reject the null hypothesis.

Conclusion: Based on the sample data, there is not enough statistical evidence to conclude that the variability in the parts produced by Plant A is significantly different from the variability of parts produced by Plant B. The observed difference in sample variances is likely due to random chance.