# F test

The F-test is a test for a difference in dispersion (variance) between two independent samples.

The requirements of the test are:

- Two independent samples measured on a continuous scale.
- Samples are from a population with a normal distribution.

## Arranging the dataset

Data in existing Excel worksheets can be used and should be arranged in a List dataset layout or Table dataset layout. The dataset must contain a continuous scale variable and a nominal/ordinal scale variable containing two independent groups.

When entering new data we recommend using New Dataset to create a new** 2 variables (1 categorical) **dataset ready for data entry.

**Using the test**

To start the test:

- Excel 2007:

Select any cell in the range containing the dataset to analyse, then click**Compare Groups**on the**Analyse-it**tab, then click**F test**. - If the dataset is arranged using the table layout

Click**Variable - Group 1**and**Variable - Group 2**and select the samples to compare.If your dataset is arranged using the list layout

Click**Variable**and select the dependent variable, then click**Factor**and select the independent variable containing the two groups to compare. - Click
**Alternative hypothesis**and select the alternative hypothesis to test. - Enter
**Confidence interval**to calculate around the variance ratio. The level should be entered as a percentage between 50 and 100, without the % sign. - Click
**OK**to run the test.

Excel 97, 2000, 2002 & 2003:

Select any cell in the range containing the dataset to analyse, then click **Analyse **on the **Analyse-it **toolbar, click **Compare Groups** then click **F test**.

X ≠ Y to test if the variance(X) is not equal to variance(Y). |

X > Y to test if the variance(X) is greater than variance(Y). |

X < Y to test if the variance(X) is less than variance(Y). |

The report shows the number of observations analysed, and, if applicable, how many missing values were excluded. Summary statistics for each sample are then shown.

The ratio of the variances and confidence interval are shown. A ratio of variances near 1 indicates the variances are similar.

The F statistic and hypothesis test are shown. The *p*-value is the probability of rejecting the null hypothesis, that the samples have the same variance, when it is in fact true. A significant p-value implies that the two samples have different variances.

## Further reading & references

- Handbook of Parametric and Nonparametric Statistical Procedures (3rd edition)

David J. Sheskin, ISBN 1-58488-440-1 2003; 382.

- Welcome
- Getting started
- What's new in this version
- Installing Analyse-it
- Starting Analyse-it
- Defining Datasets
- Setting Variable properties
- Running a statistical test
- Working with analysis reports
- Analyse-it Standard edition
- Describe
- Compare groups
- Summary statistics, Box/Dot/Mean plots
- Test Difference in Location
- Test Difference in Dispersion
- F- test
- Test Difference in Proportion
- Compare pairs
- Correlation
- Agreement
- Regression
- Analyse-it Method Evaluation edition
- Citing Analyse-it
- Contact us
- About us

Version 2.30

Published 9-Jun-2009