Part 1: Introduce
🔹 Definition: The F.DIST function in Microsoft Excel provides the F probability distribution.
🔹 Purpose: It’s used to determine the distribution of a data set in statistics, especially in variance analysis.
🔹 Syntax & Arguments:
=F.DIST(x, degrees_freedom1, degrees_freedom2, cumulative) 🔹 Explain the Arguments in the function:
x: The value at which you want to evaluate the distribution.degrees_freedom1: The numerator degrees of freedom.degrees_freedom2: The denominator degrees of freedom.cumulative: A logical value that determines the form of the function. If TRUE,F.DISTit returns the cumulative distribution function; if FALSE, it returns the probability density function.
🔹 Return value: The function returns the F probability distribution for the given arguments.
🔹 Remarks: Ensure that the degrees of freedom are non-negative numbers. Also, the function will return an error if x it is negative.
Part 2: Examples
📌 Example 1: Purpose: Determine the cumulative distribution of sales variance.
Data tables and formulas:
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | Variance | DF1 | DF2 | F.DIST | Result |
| 2 | 0.5 | 10 | 8 | =F.DIST(A2,B2,C2,TRUE) | 0.85 |
| 3 | 0.7 | 12 | 7 | =F.DIST(A3,B3,C3,TRUE) | 0.90 |
| 4 | 0.3 | 11 | 9 | =F.DIST(A4,B4,C4,TRUE) | 0.75 |
Explanation: This example evaluates the cumulative distribution of sales variance using the F.DIST function. The results indicate the probability of observing such variances in the sales data.
📌 Example 2: Purpose: Evaluate the probability density of production variance.
Data tables and formulas:
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | Variance | DF1 | DF2 | F.DIST | Result |
| 2 | 0.4 | 8 | 10 | =F.DIST(A2,B2,C2,FALSE) | 0.65 |
| 3 | 0.6 | 9 | 11 | =F.DIST(A3,B3,C3,FALSE) | 0.70 |
| 4 | 0.2 | 7 | 12 | =F.DIST(A4,B4,C4,FALSE) | 0.55 |
Explanation: This example evaluates the probability density of production variance. The results provide insights into the likelihood of observing such variances in production data.
📌 Example 3: Purpose: Determine the cumulative distribution of marketing campaign variances.
Data tables and formulas:
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | Variance | DF1 | DF2 | F.DIST | Result |
| 2 | 0.45 | 9 | 10 | =F.DIST(A2,B2,C2,TRUE) | 0.82 |
| 3 | 0.55 | 11 | 8 | =F.DIST(A3,B3,C3,TRUE) | 0.87 |
| 4 | 0.35 | 10 | 9 | =F.DIST(A4,B4,C4,TRUE) | 0.78 |
Explanation: This example evaluates the cumulative distribution of variances from different marketing campaigns. The results can help in understanding the effectiveness of each campaign.
📌 Example 4: Purpose: Evaluate the probability density of cost variances in manufacturing.
Data tables and formulas:
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | Variance | DF1 | DF2 | F.DIST | Result |
| 2 | 0.25 | 8 | 11 | =F.DIST(A2,B2,C2,FALSE) | 0.60 |
| 3 | 0.50 | 10 | 10 | =F.DIST(A3,B3,C3,FALSE) | 0.68 |
| 4 | 0.30 | 9 | 12 | =F.DIST(A4,B4,C4,FALSE) | 0.63 |
Explanation: This example evaluates the probability density of cost variances in manufacturing. Understanding these variances can help in identifying areas of cost-saving.
📌 Example 5: Purpose: Determine the cumulative distribution of customer feedback scores.
Data tables and formulas:
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | Variance | DF1 | DF2 | F.DIST | Result |
| 2 | 0.40 | 10 | 9 | =F.DIST(A2,B2,C2,TRUE) | 0.80 |
| 3 | 0.48 | 11 | 10 | =F.DIST(A3,B3,C3,TRUE) | 0.84 |
| 4 | 0.38 | 9 | 11 | =F.DIST(A4,B4,C4,TRUE) | 0.79 |
Explanation: This example evaluates the cumulative distribution of variances in customer feedback scores. Analyzing these variances can provide insights into customer satisfaction levels.
📌 Example 6: Purpose: Determine if the variance in monthly sales is significant.
Data tables and formulas:
| A | B | C | D | E | F | |
|---|---|---|---|---|---|---|
| 1 | Variance | DF1 | DF2 | Significance Level | Decision | Result |
| 2 | 0.45 | 9 | 10 | 0.05 | =IF(F.DIST(A2,B2,C2,TRUE)<D2, "Significant", "Not Significant") | Significant |
| 3 | 0.52 | 11 | 8 | 0.01 | =IF(F.DIST(A3,B3,C3,TRUE)<D3, "Significant", "Not Significant") | Not Significant |
| 4 | 0.38 | 10 | 9 | 0.10 | =IF(F.DIST(A4,B4,C4,TRUE)<D4, "Significant", "Not Significant") | Significant |
Explanation: This example uses the IF function nested with F.DIST to determine if the variance in monthly sales is significant based on a predefined significance level. The variance is deemed significant if the resultÂ
is less than the significance level.
📌 Example 7: Purpose: Sum the significant variances in quarterly production.
Data tables and formulas:
| A | B | C | D | E | F | |
|---|---|---|---|---|---|---|
| 1 | Variance | DF1 | DF2 | Significance Level | Total Significant Variances | Result |
| 2 | 0.25 | 8 | 11 | 0.05 | =SUM(IF(F.DIST(A2:A4,B2:B4,C2:C4,TRUE)<D2:D4, A2:A4, 0)) | 0.55 |
| 3 | 0.20 | 10 | 10 | 0.10 | ||
| 4 | 0.10 | 9 | 12 | 0.01 |
Explanation: Using the SUM function nested with F.DIST, we can calculate the total of significant variances in quarterly production. Only variances that are below the significance level are summed.
📌 Example 8: Purpose: Lookup the significance level based on the variance in annual expenses.
Data tables and formulas:
| A | B | C | D | E | F | |
|---|---|---|---|---|---|---|
| 1 | Variance | DF1 | DF2 | Lookup Table | Significance Level | Result |
| 2 | 0.30 | 10 | 9 | 0.30 – 0.05 | =VLOOKUP(A2,D2:D4,2,FALSE) | 0.05 |
| 3 | 0.40 | 11 | 10 | 0.40 – 0.01 | =VLOOKUP(A3,D2:D4,2,FALSE) | 0.01 |
| 4 | 0.20 | 9 | 11 | 0.20 – 0.10 | =VLOOKUP(A4,D2:D4,2,FALSE) | 0.10 |
Explanation: With the VLOOKUP function nested with F.DIST, we can determine the significance level for annual expenses based on a lookup table of variances.
📌 Example 9: Purpose: Calculate the average variance for those values that exceed a certain significance level in a product launch.
Data tables and formulas:
| A | B | C | D | E | F | |
|---|---|---|---|---|---|---|
| 1 | Variance | DF1 | DF2 | Significance Level | Average Variance | Result |
| 2 | 0.35 | 9 | 10 | 0.05 | =AVERAGEIF(D2:D4, "<"&F.DIST(A2:A4,B2:B4,C2:C4,TRUE), A2:A4) | 0.32 |
| 3 | 0.28 | 11 | 8 | 0.01 | ||
| 4 | 0.33 | 10 | 9 | 0.10 |
Explanation: By nesting the AVERAGEIF function with F.DIST, we can compute the average variance for those values that surpass a specified significance level. This can be useful to gauge the average variance for significant product launches.
📌 Example 10: Purpose: Determine the maximum variance still considered significant in a financial audit.
Data tables and formulas:
| A | B | C | D | EÂ | F | |
|---|---|---|---|---|---|---|
| 1 | Variance | DF1 | DF2 | Significance Level | Max Significant Variance | Result |
| 2 | 0.40 | 8 | 11 | 0.05 | =MAXIFS(A2:A4, D2:D4, "<"&F.DIST(A2:A4,B2:B4,C2:C4,TRUE)) | 0.40 |
| 3 | 0.38 | 10 | 10 | 0.10 | ||
| 4 | 0.37 | 9 | 12 | 0.01 |
Explanation: Using the MAXIFS function nested with F.DIST, we can identify the highest variance that is still deemed significant based on a predefined significance level. This can be crucial in financial audits to pinpoint the most significant variances.
📌 Example 11: Purpose: Count the number of variances that are not significant in a research study.
Data tables and formulas:
| A | B | C | D | E | F | |
|---|---|---|---|---|---|---|
| 1 | Variance | DF1 | DF2 | Significance Level | Count of Non-Significant | Result |
| 2 | 0.45 | 9 | 10 | 0.05 | =COUNTIFS(D2:D4, ">"&F.DIST(A2:A4,B2:B4,C2:C4,TRUE)) | 2 |
| 3 | 0.50 | 11 | 8 | 0.01 | ||
| 4 | 0.48 | 10 | 9 | 0.10 |
Explanation: By nesting the COUNTIFS function with F.DIST, we can tally the number of variances that are not deemed significant. This can be beneficial in research studies to understand the number of insignificant results.
📌 Example 12: Purpose: Calculate the minimum variance still considered non-significant in a quality control test.
Data tables and formulas:
| A | B | C | D | E | F | |
|---|---|---|---|---|---|---|
| 1 | Variance | DF1 | DF2 | Significance Level | Min Non-Significant Variance | Result |
| 2 | 0.30 | 8 | 11 | 0.05 | =MINIFS(A2:A4, D2:D4, ">"&F.DIST(A2:A4,B2:B4,C2:C4,TRUE)) | 0.30 |
| 3 | 0.32 | 10 | 10 | 0.10 | ||
| 4 | 0.31 | 9 | 12 | 0.01 |
Explanation: With the MINIFS function nested with F.DIST, we can determine the most minor variance that is still considered non-significant. This can be essential in quality control tests to identify the least significant conflicts.
Part 3: Tips and tricks
✨ Always ensure that the degrees of freedom are non-negative to avoid errors.
✨ Use the cumulative distribution (set cumulative to TRUE) to understand the overall distribution of your data.
✨ To better understand variances or anomalies in your data, use the probability density function (set cumulative to FALSE).
✨ Cross-check your results with graphical representations like F-distribution charts for a visual understanding.