STATISTICA Blogs

A random factor is a variable of interest for which we selected only a subset of the population levels to test, but which we still want our results to be applicable to all levels possible. For example, suppose that in a factory we sample products from 5 workers, even though we have 100 workers total. Since we want our results to be generalizable to all workers in the factory, not just the 5 we selected, we would treat this variable as a random factor. When a process involves random factors, a common analysis is to calculate the variability in the overall process that is due to these random factors. To quantify this number, we will compute Components of Variance.

Following is a guide on how to compute the Components of Variance in STATISTICA:

1. Above is my data (from www.itl.nist.gov). I have 5 batches of samples (Batch); say each batch came from a different worker on the factory line. I also have some measurements (Resp); we can say that this is the circumference of a blown glass pipe (in mm).

2. On the ribbon bar, select the Statistics tab. In the Advanced/Multivariate group, click Advanced Models and select Variance Components.

2. On the classic menus, select Variance Components from the Statistics > Advanced Linear/Nonlinear Models submenu. 

3. In the Variance Components & Mixed Model ANOVA dialog, click the Variables button.
4. I will pick Resp as my Dependent variable.
5. And Batch as my Random factor.
6. Then click OK to close the variable selection dialog.
7. And click OK again to display the Variance Components and Mixed Model ANOVA/ANCOVA Results dialog.

8. In the Results dialog, click the Summary: Components of variance button.

9. There will be three spreadsheets automatically generated; we will look at the second one, aptly called Components of Variance.

On this sheet, we see that the component of variance for Batch is 11.71, and for random Error is 1.80. If we sum the components, we get 11.71 + 1.80 = 13.51. Now we can calculate the variance in the process due to the workers (11.71/13.51=0.867 or 86.7%) and how much is due to other factors inside the process (1.80/13.51=0.133 or 13.3%). So it seems that we could reduce a good proportion of variance in our responses by focusing on reducing the variance between each worker.

- Shannon L. Dick
  Statistician