# 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.

### Table of Contents

## 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. F.DIST.RT Function Syntax

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

## 3. F.DIST.RT Function 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. F.DIST.RT function 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. F.DIST.RT function 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. F.DIST.RT 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.

### Functions in 'Statistical' category

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

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