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
Analysis
The output from this program reports the sample variance/covariance matrix.
| S | GENVAR | ||||
|---|---|---|---|---|---|
|
157829.44 |
940.08944 | 6075.8163 |
102411.13 |
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:
\[|S| = 2.83 \times 10^{19}\]
Interpretation
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.