# How to use the F.TEST function

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

The F.TEST function calculates the two-tailed probability from an F-test, the value shows if the variances from two data sets are not significantly different.

This function was introduced in Excel 2010 has replaced the FTEST function which is now outdated.

### Table of Contents

## 1. Introduction

**What is the two-tailed probability from an F-test?**

The two-tailed probability from an F-test refers to testing against the alternative hypothesis that the two population variances are not equal without specifying direction.

The F-test compares two sample variances by forming a ratio that follows an F-distribution. It tests the null hypothesis that the population variances are equal.

If the variances are not equal which can occur in either direction meaning one could be larger or smaller. A two-tailed test checks both flanks of the F distribution for the probability that the ratio is quite large or quite small. The two-tailed p-value is the total area in both tails combined.

**What is a hypothesis in statistics?**

In statistics, a hypothesis is an assumption about some aspect of a population or underlying probability model. Hypotheses are of two main types:

- Null hypothesis (H0) - Represents the status quo. Asserts there is no meaningful effect, relationship, or difference in the parameter of interest between groups.
- Alternative hypothesis (H1) - Asserts there is a statistically significant effect in the parameter. Reflects a potential research finding or relationship.

A statistical hypotheses state an assumption that can be tested to reach conclusions from experimental data using methods like t-tests, ANOVA, or chi-square tests.

**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.TEST Function Syntax

F.TEST(*array1, array2*)

## 3. F.TEST Function Arguments

array1 |
Required. The first data set. |

array2 |
Required. The second data set. |

## 4. F.TEST function Example 1

**Two samples have variances of 1411 and 719, with 8 and 4 degrees of freedom, respectively. Use the F.TEST function to determine if the variances of the two populations are significantly different at a 5% significance level?**

The values for population 1 are in cell range B19:B27, population 2 are in D19:D23. The formula for calculating the variance of population 1 is in cell C29.

The formula for calculating the variance of population 1 is in cell C30.

The F.TEST function calculates the variances for you, however, I have included those calculations here. The following formula calculates the number of degrees of freedom for the first population:

Degrees of freedom of the second population:

The numbers of degrees of freedoms are also not required in the F.TEST function but these calculations allow me to plot the F distribution, shown in the image above.

The F.TEST function calculates the the two-tailed probability from an F-test. This value shows if the variances from two data sets are not significantly different. In this example, if the variances are significantly different at a 5% significance level.

F test formula in cell D34:

The result is 0.5376 which is significantly greater than 0.05 (5% significance level). This means that there is not enough evidence to reject the null hypothesis of equal variances at the 5% significance level.

## 5. F.TEST function Example 2

**A company manufactures two types of batteries, and you want to compare the variability in their lifetimes. Calculate the F-TEST to check if the variances of the two battery types are equal or not using a 10% level of significance?**

The values for population 1 are in cell range B19:B23, population 2 are in D19:D27. The formula for calculating the variance of population 1 is in cell C29.

The formula for calculating the variance of population 1 is in cell C30.

The F.TEST function calculates the variances for you, however, I have included those calculations here. The following formula calculates the number of degrees of freedom for the first population:

Degrees of freedom of the second population:

The numbers of degrees of freedoms are also not required in the F.TEST function but these calculations allow me to plot the F distribution, shown in the image above.

The F.TEST function calculates the the two-tailed probability from an F-test. This value shows if the variances from two data sets are not significantly different. In this example, if the variances are significantly different at a 10% significance level.

F test formula in cell D34:

The result is 0.8196 which is significantly greater than 0.10 (10% significance level). This means that there is not enough evidence to reject the null hypothesis of equal variances at the 10% significance level.

## 6. F.TEST function not working

The F.TEST function returns

- #DIV/0! error value if the number of items in each data set don't match.
- #VALUE! error value if any argument is non-numeric.

The LINEST function calculates the F statistic whereas the F.TEST function calculates the probability.

### Functions in 'Statistical' category

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

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