# One sample variance test in Excel tutorial

This tutorial shows how to test the difference between an observed variance and a theoretical one, using the one sample variance test, in Excel with XLSTAT.

## Dataset to perform a one-sample variance test

A nail factory has acquired a nail production machine. An engineer wants to test if the machine produces nails with nailhead diameter variability lower than a standard of σ = 0.065 (Standard Deviation).

Data are nail diameters measured on 50 nails produced by the machine. They can be downloaded by clicking on the link given at the beginning of this tutorial.

The goal is to check if an observed variance is different from a theoretical one. The test we will manipulate for this purpose can be very useful in Statistical Process Control.

## Setting up a one-sample variance test in XLSTAT

Go over to the menu Parametric tests and select the option One-sample Variance test.

In the General tab, select the data under the Data field.

In the Options tab, enter the theoretical variance in the appropriate field: σ² = 0.065² = 0.004225.

When everything is set, press OK. The results appear in a new spreadsheet.

## Interpreting the results of a one-sample variance test in XLSTAT

The estimated population variance is 0.0024, which is lower than the standard of 0.004225. Furthermore, the observed variance is associated to a chi-square 95% confidence interval of ] 0.0016, 0.0037 [ that does not include the standard. The subsequent p-value (0.0103) is lower than the significance threshold alpha (0.05). Thus, we can say that the machine produces nails with a head diameter variability significantly lower than the standard, with a risk of 1.03% of being wrong.

## What about the mean of nailhead diameter?

The mean of nailhead diameter can also be compared to a standard using the one-sample t-test.