# How to use the F.DIST function

**What is the F.DIST function?**

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

The F.DIST function lets you find out if the means between two given populations are significantly different.

### Table of Contents

## 1. Introduction

**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 Function Syntax

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

## 3. F.DIST function Arguments

x |
Required. |

deg_freedom1 |
Required. Degrees of freedom (numerator). |

deg_freedom2 |
Required. Degrees of freedom (denominator). |

cumulative |
Required. A boolean value. TRUE - Cumulative distribution function. FALSE - Probability density function. |

**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 Function Example 1

**In a statistical experiment, the variances of two independent samples are 25 and 16, with 10 and 12 degrees of freedom, respectively. What is the probability that the ratio of the variances is greater than 2?**

The F-distribution is used to compare the variances of two independent normal populations. The F-statistic is calculated as the ratio of the two variances: F = variance1 / variance2. In this case, F = 25 / 16 = 1.5625.

**How to determine the numerator and denominator degrees of freedom in a F distribution?**

- The numerator degrees of freedom corresponds to the one with the greater variance (25) which is 10.
- The denominator degrees of freedom corresponds to the with the smaller variance (16), which is 12.

Here are the arguments for the F.DIST function:

- Cell C18 contains the specified x value, in this case 2
- Cell C19 contains the numerator degrees of freedom which is 10
- Cell C20 contain the denominator degrees of freedom which is 12
- Cell C21 contains the cumulative argument which is TRUE in this example.

Formula in cell C22:

The F.DIST function returns 0.872 however we want the complement meaning the area below the blue line in the image above from x value 2 to infinity. To calculate the complement we subtract 1 - 0.872 = 0.1275 (12.75%).

In the image, locate the value 2 on the x-axis. From that point, draw an imaginary vertical line upwards until it intersects with the orange curve, which represents the 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 0.87.

## 5. F.DIST Function Example 2

**A researcher wants to compare the means of two populations based on two independent samples. If the F-statistic calculated from the sample data is 3.2 with 8 and 15 degrees of freedom, what is the probability of obtaining an F-value greater than or equal to 3.2?**

**How to determine the numerator and denominator degrees of freedom in a F distribution?**

- The numerator degrees of freedom corresponds to the one with the greater variance which is 8.
- The denominator degrees of freedom corresponds to the with the smaller variance which is 15.

Here are the arguments for the F.DIST function:

- Cell C18 contains the specified x value, in this case 3.2
- Cell C19 contains the numerator degrees of freedom which is 8
- Cell C20 contain the denominator degrees of freedom which is 15
- Cell C21 contains the cumulative argument which is TRUE in this example.

Formula in cell C22:

The F.DIST function returns 0.975 however we want the complement meaning the area below the blue line in the image above from x value 3.2 to infinity. To calculate the complement we subtract 1 - 0.975 = 0.025 (2.5%).

In the image, locate the value 3.2 on the x-axis. From that point, draw an imaginary vertical line upwards until it intersects with the orange curve, which represents the 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 0.97.

## 6. F.DIST function not working

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

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