How to use the F.DIST.RT function

What is the F.DIST.RT function?

The F.DIST.RT function calculates the right-tailed F probability for two tests. This function was introduced in Excel 2010 and has replaced the FDIST function.

1. Introduction

What are the differences between the F.DIST function and the F.DIST.RT function?

The F.DIST function gives the left-tail area under the curve, while the F.DIST.RT function gives the right-tail area under the curve.

The F.DIST function calculates the cumulative distribution function for the F-distribution, which means it returns the probability that a random variable with an F-distribution is less than or equal to the input F-value.

The F.DIST.RT function calculates the right-tailed probability of the F-distribution, which means it returns the probability that a random variable with an F-distribution is greater than the input F-value.

F.DIST.RT(x, deg_freedom1, deg_freedom2)
F.DIST(x, deg_freedom1, deg_freedom2, cumulative)

What is the F probability?

The F-distribution or F-ratio is a continuous probability distribution that compare the variances of two populations.

What is variance?

The variance shows how much a set of numbers are spread out from their average value.

Σ(x- x̄)²/(n-1)

x̄ is the sample mean

n is the sample size.

What is a null distribution?

The null hypothesis in the F-distribution is that two independent normal variances are equal. If the observed ratio is too large or too small, then the null hypothesis is rejected, and we conclude that the variances are not equal.

When is a f-distribution used?

The F-distribution is used in the F-test in analysis of variance comparing two variances, as the distribution of the ratio of sample variances when the null is true of no difference between population variances.

What is a continuous probability distribution?

A continuous probability distribution is defined over an interval and range of continuous values, giving the probability an outcome is exactly equal to any value, and having an area under its probability density curve equal to 1.

2. Syntax

F.DIST.RT(x, deg_freedom1, deg_freedom2)

3. Arguments

x	Required.
deg_freedom1	Required. Degrees of freedom (numerator).
deg_freedom2	Required. Degrees of freedom (denominator).

What are the degrees of freedom?

The degrees of freedom parameters are the numerator and denominator chi-squared distributions. They form the ratio that follows the F-distribution.

The degrees of freedom parameters affect the shape of the F-distribution curve and probability, they relate to the samples and capture the amount of information in the variance estimates.

What is a chi-squared distribution?

A chi-squared distribution is a type of probability distribution that is used in statistical tests that compare the variances of two populations. The chi-squared distribution has one parameter, called degrees of freedom, that determines its shape and location. The degrees of freedom represent the number of independent pieces of information used to estimate the variances.

4. Example 1

A manufacturer wants to test if two production lines have the same variance. The calculated F-statistic is 2.5, with 12 and 18 degrees of freedom. What is the right-tailed probability associated with this F-value?

Here are the arguments for the F.DIST.RT function:

• Cell C18 contains the specified x value, in this case 2.5
• Cell C19 contains the numerator degrees of freedom which is 12
• Cell C20 contain the denominator degrees of freedom which is 18

Formula in cell C22:

The F.DIST.RT function returns 0.0385 which is the area below the blue line from x value 2.5 to infinity. The F.DIST function calculates the area below the blue line from 0 (zero) to x value 2.5.

The relationship between these two functions are: F.DIST.RT = 1 - F.DIST , in other words F.DIST function is the complement to the F.DIST function. To calculate the complement of we F.DIST.RT function subtract 1 - 0.0385 =0.9614

The image above shows a chart displaying three different distributions:

• blue - Probability density function
• orange - Cumulative distribution function
• black - Right-tailed cumulative distribution function

In the image, locate the value 2.5 on the x-axis. From that point, draw an imaginary vertical line upwards until it intersects with the black curve, which represents the right-tailed cumulative distribution function. Then, follow the point of intersection horizontally towards the y-axis. You will find that the corresponding value on the y-axis is approximately 0.04.

5. Example 2

In a two-way ANOVA (analysis of variance) analysis, the F-statistic for the interaction effect is 1.8, with 6 and 20 degrees of freedom. Determine the right-tailed probability for this F-value?

Here are the arguments for the F.DIST.RT function:

• Cell C18 contains the specified x value, in this case 1.8
• Cell C19 contains the numerator degrees of freedom which is 6
• Cell C20 contain the denominator degrees of freedom which is 20

Formula in cell C22:

The F.DIST.RT function returns 0.1502 which is the area below the blue line from x value 1.8 to infinity. The F.DIST function calculates the area below the blue line from 0 (zero) to x value 1.8.

The relationship between these two functions are: F.DIST.RT = 1 - F.DIST , in other words F.DIST function is the complement to the F.DIST function. To calculate the complement of we F.DIST.RT function subtract 1 - 0.1502 =0.8498

The image above shows a chart displaying three different distributions:

• blue - Probability density function
• orange - Cumulative distribution function
• black - Right-tailed cumulative distribution function

In the image, locate the value 1.8 on the x-axis. From that point, draw an imaginary vertical line upwards until it intersects with the black curve, which represents the right-tailed cumulative distribution function. Then, follow the point of intersection horizontally towards the y-axis. You will find that the corresponding value on the y-axis is approximately 0.15.

6. Function not working

The F.DIST.RT function returns

• #VALUE! error value if any argument is non-numeric.
• #NUM! error value if:
  • x < 0 (zero)
  • deg_freedom1 < 1
  • deg_freedom2 < 1

deg_freedom1 and deg_freedom2 will be converted into integers if they are not.

6.1 Troubleshooting the error value

When you encounter an error value in a cell a warning symbol appears, displayed in the image above. Press with mouse on it to see a pop-up menu that lets you get more information about the error.

1. The first line describes the error if you press with left mouse button on it.
2. The second line opens a pane that explains the error in greater detail.
3. The third line takes you to the "Evaluate Formula" tool, a dialog box appears allowing you to examine the formula in greater detail.
4. This line lets you ignore the error value meaning the warning icon disappears, however, the error is still in the cell.
5. The fifth line lets you edit the formula in the Formula bar.
6. The sixth line opens the Excel settings so you can adjust the Error Checking Options.

Here are a few of the most common Excel errors you may encounter.

#NULL error - This error occurs most often if you by mistake use a space character in a formula where it shouldn't be. Excel interprets a space character as an intersection operator. If the ranges don't intersect an #NULL error is returned. The #NULL! error occurs when a formula attempts to calculate the intersection of two ranges that do not actually intersect. This can happen when the wrong range operator is used in the formula, or when the intersection operator (represented by a space character) is used between two ranges that do not overlap. To fix this error double check that the ranges referenced in the formula that use the intersection operator actually have cells in common.

#SPILL error - The #SPILL! error occurs only in version Excel 365 and is caused by a dynamic array being to large, meaning there are cells below and/or to the right that are not empty. This prevents the dynamic array formula expanding into new empty cells.

#DIV/0 error - This error happens if you try to divide a number by 0 (zero) or a value that equates to zero which is not possible mathematically.

#VALUE error - The #VALUE error occurs when a formula has a value that is of the wrong data type. Such as text where a number is expected or when dates are evaluated as text.

#REF error - The #REF error happens when a cell reference is invalid. This can happen if a cell is deleted that is referenced by a formula.

#NAME error - The #NAME error happens if you misspelled a function or a named range.

#NUM error - The #NUM error shows up when you try to use invalid numeric values in formulas, like square root of a negative number.

#N/A error - The #N/A error happens when a value is not available for a formula or found in a given cell range, for example in the VLOOKUP or MATCH functions.

#GETTING_DATA error - The #GETTING_DATA error shows while external sources are loading, this can indicate a delay in fetching the data or that the external source is unavailable right now.

6.2 The formula returns an unexpected value

To understand why a formula returns an unexpected value we need to examine the calculations steps in detail. Luckily, Excel has a tool that is really handy in these situations. Here is how to troubleshoot a formula:

1. Select the cell containing the formula you want to examine in detail.
2. Go to tab “Formulas” on the ribbon.
3. Press with left mouse button on "Evaluate Formula" button. A dialog box appears.
   The formula appears in a white field inside the dialog box. Underlined expressions are calculations being processed in the next step. The italicized expression is the most recent result. The buttons at the bottom of the dialog box allows you to evaluate the formula in smaller calculations which you control.
4. Press with left mouse button on the "Evaluate" button located at the bottom of the dialog box to process the underlined expression.
5. Repeat pressing the "Evaluate" button until you have seen all calculations step by step. This allows you to examine the formula in greater detail and hopefully find the culprit.
6. Press "Close" button to dismiss the dialog box.

There is also another way to debug formulas using the function key F9. F9 is especially useful if you have a feeling that a specific part of the formula is the issue, this makes it faster than the "Evaluate Formula" tool since you don't need to go through all calculations to find the issue..

1. Enter Edit mode: Double-press with left mouse button on the cell or press F2 to enter Edit mode for the formula.
2. Select part of the formula: Highlight the specific part of the formula you want to evaluate. You can select and evaluate any part of the formula that could work as a standalone formula.
3. Press F9: This will calculate and display the result of just that selected portion.
4. Evaluate step-by-step: You can select and evaluate different parts of the formula to see intermediate results.
5. Check for errors: This allows you to pinpoint which part of a complex formula may be causing an error.

The image above shows cell reference C18 converted to hard-coded value using the F9 key. The F.DIST.RT function requires numerical values in the first argument which is not the case in this example. We have found what is wrong with the formula.

Tips!

• View actual values: Selecting a cell reference and pressing F9 will show the actual values in those cells.
• Exit safely: Press Esc to exit Edit mode without changing the formula. Don't press Enter, as that would replace the formula part with the calculated value.
• Full recalculation: Pressing F9 outside of Edit mode will recalculate all formulas in the workbook.

Remember to be careful not to accidentally overwrite parts of your formula when using F9. Always exit with Esc rather than Enter to preserve the original formula. However, if you make a mistake overwriting the formula it is not the end of the world. You can “undo” the action by pressing keyboard shortcut keys CTRL + z or pressing the “Undo” button

6.3 Other errors

Floating-point arithmetic may give inaccurate results in Excel - Article

Floating-point errors are usually very small, often beyond the 15th decimal place, and in most cases don't affect calculations significantly.

Functions in 'Statistical' category

The F.DIST.RT function is one of 73 functions in the 'Statistical' category.

Excel function categories

Excel categories

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