In The Trenches
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
Good Stat, Bad Stat
NUTS & VOLTS
Circle #123 on the Reader Service Card.
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.)
Whenever you see such probabilities associated with a complex
mechanical system, be very skeptical;