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F-Test

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QXL Stat Tools Tab > Hypothesis Tests > Tests for Variance > F-Test

Test type: Variance
Data: Quantitative
Number of Variables: 2
Number of Groups: 2
Assumptions: Two normally distributed samples

The F-Test is a hypothesis test used for testing variance equality between two populations. It assumes that two samples come from independent populations and that they are normally distributed. If samples are not normally distributed, use Levene's test.

Hypothesis tested:

H0 : σ1 = σ2
H1 : σ1 ≠ σ2

where σ1 and σ2 are the populations variances.

Step #1: Select data source for F-Test.

Data for the F-Test can come from an Excel spreadsheet, SQL data source, or it can be entered manually.

See source data formats and example data for the F-Test.

Step #2: Options.

  • Standard options

    • 'Not equal to' option. Select this option to run a two tailed test. The null hypothesis is that the variances are equal.
    • 'Less Than' option. Select this option to run a lower tailed test. The alternative hypothesis is that the variance of the first dataset is smaller than the variance of the second dataset.
    • 'Greater Than' option. Select this option to run an upper tailed test. The alternative hypothesis is that the variance of the first dataset is greater than the variance of the second dataset.

  • Advanced options

    • 'Decision Criteria' option (default = 0.05). The value of the decision criteria (significance or α level).
    • 'Box Plot' option. Display box plot results.
    • 'Display mode' option. When the 'Verbose (long)' option is on, Quantum XL will display additional text that explains the hypothesis test results.

Example

  • Open F-Test worksheet.

  • Run Quantum XL > Hypothesis Tests > Tests for Variance > F-Test.

  • In the Standard Options dialog, select 'Not equal to' test.

F-Test Results

Quantum XL will display test statistic (F), p Value, 95% Bonferroni CI for StDevs, and dataset statistics.

In this example, p-Value of 0.9469 is greater than the decision criteria (0.05) so there is not enough evidence to reject the null hypothesis. We cannot conclude that the variances are different.

Update

The F-Test is updatable. After you create the analysis, you can change its data source or add new data to the data source and simply update the analysis.

  • Update: Quantum XL > Statistical Tools > Update Sheet

  • Change settings: Quantum XL > Statistical Tools > Modify Chart/Analysis