## How to compare variation of paired parameters between groups?

Community Trekker

Joined:

Nov 9, 2016

In semicondutor industry, VMIN and IDDQ (leakage) are very critical parameters for mobile CPU power and performance. For each device, there will be a pair of VMIN and IDDQ for each power domain, such as logic and memory. There is certain degree of correlation between VMIN and IDDQ (device with higher VMIN tends to have smaller IDDQ) as shown below (gree circles represent 95% of the population):

Let us assume the left bivariat chat corresponds to logic IDDQ (X-axis) vs VMIN (Y-axis) while the right one corresponds to memory. If someone were to compare VMIN vs IDDQ variation between logic and memory, how would you go about and do so?

Thanks!

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Accepted Solutions

Staff

Joined:

Jun 23, 2011

Solution

I don't think this is an easy question, since I believe an appropriate answer will depend on what such a 'comparison' would actually be used for. I assume you are looking for one or more figures of merit that make sense in your situation.

In many ways, the fairest comparison is provided by the displays that you have above, except for the fact that you don't have common x and y scales. Generally, using the same scale is seen as an important part of any comparison (and that's why GraphBuilder forces this when making trellis plots). Additionally, I would be wary of the green elipses, since it seems that your data is not normally distributed, either in a univariate or bivariate sense. The y variable also seems to be quantised, which may or may not matter.

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Staff

Joined:

Jun 23, 2011

Solution

I don't think this is an easy question, since I believe an appropriate answer will depend on what such a 'comparison' would actually be used for. I assume you are looking for one or more figures of merit that make sense in your situation.

In many ways, the fairest comparison is provided by the displays that you have above, except for the fact that you don't have common x and y scales. Generally, using the same scale is seen as an important part of any comparison (and that's why GraphBuilder forces this when making trellis plots). Additionally, I would be wary of the green elipses, since it seems that your data is not normally distributed, either in a univariate or bivariate sense. The y variable also seems to be quantised, which may or may not matter.

Community Trekker

Joined:

Nov 9, 2016

Thanks much for the feedback and suggestions, Ian! BTW, IDDQ is log normally distributed.

Staff

Joined:

Jun 23, 2011

If you are prepared to believe that the bivariate Gaussian is a useful model for all groups you want to compare, then you could exploit that (having transformed IDDQ appropraitely).

If the complexity arises because you have so many groups that the raw data would be overwhelming, you could, for instance, plot an elipse (probably at the 95% fitted value) that would show the location, spread and correlation of each group. Additionally, if you count the number of points in each group that fall outside the 95% elipse, you could increase the transparency of the elipse so that the eye is not drawn to groups for which the assumed model is suspect.