# F-Tests Determine if Variances are the Same or Different

## You Don't Have to be a Statistician to do an F-Test

### F-Test Example

If you're producing rubber made with two different recipes, you might want to know if the variances in tensile strengths are the same or different (Juran's QC Handbook 4th pg 23.74):

### The QI Macros for Excel Makes F-Tests as Easy as 1-2-3

- Enter your data in Excel, then click and drag over the data to select it. Next click on the QI Macros Menu, Statistical Tools and then select the F-Test:
- The QI Macros will prompt for a significance level (default = 0.05):

The QI Macros will perform the F-Test calculations and interpret the results for you.

**What's Cool about the QI Macros F-Test?**

Unlike other statistical software, the QI Macros is the only SPC software that interprets the results for you. It compares the p-value (0.152) to the significance level (0.05) tells you: "Cannot Reject the Null Hypothesis because p>0.05" and that the "Variances are the same." Based on the F-test results we now know which t-Test to run.

### Interpreting F-Test results

- The null hypotheis (H0) - variances are the same
- The alternate hypothesis (Ha) - variances are different

Hypothesis Test |
Compare |
Result |

Classical Method | test statistic > critical value (i.e. F > F crit) |
Reject the null hypothesis |

Classical Method | test statistic < critical value (i.e. F < F crit) |
Cannot Reject the null hypothesis |

p value Method | p value < a | Reject the null hypothesis |

p value Method | p value > a | Cannot Reject the null hypothesis |

Since F < Fcrit (.33 < 6.39) and p value > a ( .152 > 0.05), we cannot reject the null hypothesi - the Variances are the Same.

**Excel Note:**

If you run the test using, Excel's Data Analysis toolpak, Excel requires that the recipe with the largest variance be first to ensure correct calculations. The QI Macros does not have this requirement to perform the calculations correctly.