Nuts & Volts - May 2004

In The Trenches

Basic Tests

It's useful to be familiar with common statistical tests. We've seen how different distributions have different characteristics. You can compare distributions with "Analysis of Variance" tests. There are several, ranging from the fairly simple "F" test to complicated multi-variate forms. Truthfully, there is rarely a need for engineers to use this.

A more common test is one of averages used to determine if one group is significantly different from another group. For example, you have version A and version B of a receiver and you test 10 pieces of each and find that version A has an average sensitivity of -110 dB with values ranging from - 106 to -120. Version B has an average sensitivity of -113 dB, with values ranging from - 100 to -119. (Note that all statistics also apply to groups. Statistical procedures cannot be applied to a single piece or single measurement.)

Is version B really more sensitive than version A or is it just random variation? Since version B costs more, is the performance worth the extra price? You would use the "T" test for means (averages) in this

example. It would tell you how different the two groups were in terms of a probability. That is, the answer would be something like 25%. This means that, 25% of the time, there is no measurable difference between versions A and B. You would then have to decide if the extra costs were worth investing into a product where 75% of the customers would see an improvement and 25% wouldn't.

It's interesting to note that most basic statistical calculations are as follows: sum the squares of the differences from the average and then take the square root. This is the same method used to find the Root-Mean-Square — or RMS value — of a signal.

Correlation compares two (or more) groups against some common factor. There is a clear correlation between drinking alcohol and car accidents and, in this case, there is a clear and direct link between them.

However, did you know that there is also a clear correlation between ice cream sales and boating accidents? Does this mean that we should restrict sales of ice cream to those over 18 or, perhaps, not allow open ice cream containers while boating? Obviously, there is only an indirect relationship here; the indirect relation-

ship is one of warm weather activities. It's very important to realize that, while things may be highly correlated, they may have no direct relationship.

Correlation (and its related statistic — regression) is useful in engineering. In particular, a special type of correlation, called "auto-corre-lation," is used in signal processing. This procedure compares one part of a signal to another part of the same signal. This is a search for similar patterns. Telephone equipment uses this technique to eliminate echoes. It's a very powerful and useful tool.

One simple statistical test that I recommend for all engineers is the Chi Square test. (Chi is pronounced like "cry" without the "r.") This is a test for an expected result. If you roll a die, you expect six to come up once every six rolls, on the average, but, of course, six won't come up every sixth roll. There will always be some variation. The Chi Square test will tell you if the variation is normal or if the dice are loaded. It will also tell you if your system is failing more than you expected.

Good Stat, Bad Stat

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Many areas of engineering rely on statistics. It is extremely important for any engineer to have some familiarity with them because, without that familiarity, engineers lose their ability to determine what is reasonable and what is not. Statistics is a tool. It can be used well and it can be used poorly. Do you know enough to be able to tell the difference?

In 1975, the Atomic Energy Commission published a study, headed by Dr. Norman Rasmussen, which placed the probability of a total nuclear meltdown at less than one chance per 10,000,000 per year. NASA had statistics that said the chance of a catastrophic Space Shuttle failure was one in 100,000. (Work it out. That's a launch every day for 275 years per failure.)