This tutorial will help you test the difference between an observed variance and a theoretical one, using the one sample variance test, in Excel with XLSTAT.
Not sure this is the statistical test you are looking for? Check out this guide.
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Goal of this tutorial
The goal of this tutorial 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.
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 here.
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.