The F test is used to determine if two sample groups have similar variances.

**Download Practice Workbook**

Download the workbook.

Compare the performance of two different marketing strategies (**Strategy A** and **Strategy B**) based on the number of website visits they generate over a **week**. Test if there is a significant difference in the average website visits for these two strategies (**Ha:**** alternative hypothesis**) or if they are the same (**Ho:****null hypothesis**).

### Method 1 – Using the Data Analysis Toolpak

- Go to the
**Data**tab and select**Data Analysis**. - In the
**Data Analysis**window, select**F-test Two Sample for Variance**and click**OK**.

A new window will be displayed.

- Enter data and it will automatically calculate the result.

Before selecting the **variable range**, calculate the variance for each dataset using **the VAR.S function** (Excel requires the highest variance to be designated as **variable 1 range**).

**For Strategy A**, use the following formula.

`=VAR.S(C5:C11)`

**Strategy A**possesses the highest**variance**. So, input**Strategy A**as**Variable 1****Range**, and**Strategy B**as**Variable 2 Range**.- Check
**Labels**. - Set the significance level (
**alpha**) to**0.05**. - There are three
**output options**. Choose the**output range $C$15**. - Click
**OK**to see the result.

**NOTE:**Set the data range with the

**highest variance**as

**Variable 1 Range**.

The **Analysis ToolPak** will display the outcome.

It provides the** mean**, **variance**,** observation** count, degrees of freedom (**df**), **F value**, **F critical value**, and **P value**.

To determine the **P value** for the F test, you need the **F value** and the** F critical value**. When the calculated** P value** exceeds the chosen significance level (**alpha**), accept the **null hypothesis**: there isn’t a significant difference between the strategies.

If the** P value** is lower than** alpha**, accept the **alternative hypothesis**: there is a distinction between the two strategies.

Since the** P value** is greater than the chosen significance level (**0.05**), you can conclude that the average website visits for the two strategies are statistically considered equal. There is no significant difference in the mean website visits between **Strategy A** and **Strategy B**.

### Method 2 – Using the F.TEST Function

- Select
**C13**and use the following formula.

`=F.TEST(C5:C11,D5:D11)`

The result is **0.21121**.

Since the **p-value** (**0.21121**) exceeds the significance level (**0.05**), the result is not considered statistically significant. Therefore, we cannot reject the **null hypothesis**.

There is no substantial difference in the average number of website visits between **Strategy A** and **Strategy B**.

**NOTE: The F.TEST function**checks if the spreads are different, and

**the Two-Sample Variance F Test**checks which class has wider or narrower spreads.

## How to Activate the Data Analysis Toolpak Add-in in Excel

- Click the
**File**tab. - Select
**Options**. - In the
**Excel Options**window, choose**Add-Ins**. - In
**Manage**, select**Excel Add-ins**. - Click
**Go…**.

- In the
**Add-Ins**window, check**Analysis ToolPak**. - Click
**OK**.

**Data Analysis** is displayed in the **Data** tab on the ribbon.

## Things to Remember

**Set the Significance Level:**Determine your significance level (commonly**0.05**) before interpreting the p-value.

## Frequently Asked Questions

**Q1. What is the formula for the F-test?**

The formula for the F-test depends on the context. To compare two variances (two-sample F-test), the formula is:

**F = Variance1 / Variance2**

In ANOVA, which compares multiple means, the formula involves calculating the ratio of group variance.

**Q2. What is the difference between a one-sample and a two-sample F-test?**

A one-sample F-test assesses the variance in a single sample with a fixed value, whereas a two-sample F-test evaluates the variances in two separate samples.

**<< Go Back to Excel for Statistics | Learn Excel**