1.6 - Example: Generalized Variance

Example 1-7: Woman's Health Survey (Generalized Variance) Section

Find and interpret the generalized variance for the Women's Health Survey data.

Download the data file here: nutrient.txt

Using Technology

Using SAS

The generalized variance for the Women's Health Survey data can be calculated using the SAS program below.

Download the SAS file: nutrient3.sas

The lines of this program are saved in a simple text file with a .sas file extension. If you have SAS installed on the machine on which you have download this file, it should launch SAS and open the program within the SAS application. Use the "Inspect" button below to work your way through the lines of programming. Marking up a print out of the SAS program is also a good strategy for learning how this program is put together.


Using Minitab

Click on the arrow in the window below to find the generalized variance for the Women's Nutrition Data using Minitab.

To do this you will need to download the macro file: MATRXDET.mac

Video: Generalized Variance using Minitab


The output from this program reports the sample variance/covariance matrix.

Example: Nutrient Intake Data - Generalized variance

S         GENVAR


940.08944 6075.8163


6701.616 2.83E19
940.08944 35.810536 114.05803 2383.1534 137.67199  
6075.8163 114.05803 934.87688 7330.0515 477.19978  
102411.13 2383.1543 7330.0515 2668452.4 22063.249  
6701.616 137.67199 477.19978 22063.249 5416.2641  

You should compare this output with the sample variance/covariance matrix output obtained from the corr procedure from our last program, nutrient2. You will see that we have the exact same numbers that were presented before. The generalized variance is that single entry in the far upper right-hand corner. Here we see that the generalized variance is:

\[|S| = 2.83 \times 10^{19}\]


In terms of interpreting the generalized variance, the larger the generalized variance the more dispersed the data are. Note that the volume of space occupied by the cloud of data points is going to be proportional to the square root of the generalized variance.

In this example...

\[\sqrt{|S|} = 5.37 \times 10^9\]

This represents a very large volume of space. Again, the interpretation of this particular number depends largely on subject matter knowledge. In this case, we can not say if this is a particularly large number or not unless we know more about women's nutrition.