In The Trenches
Anti Gravity Projects
All new mini 35 kv 1.5
ma adjustable output
power supply with
instructions on making
a simple craft.
GRA1K Kit ......................... $69.95
GRA10 Assembled .......... $119.95
Green Lasers Pointers
10,000 feet plus - Full 5 mw. A real
LAPNGR5 Ready to use...$129.95
Ion Ray Guns
the ultimate weapon of the
future. Produces force fields,
induces shocks and other weird
IOGHP1 Plans .................... $10.00
IOGHP1K Kit .................... $149.95
IOGHP10 Assembled ....... $249.95
Laser Window Bounce
building a listening device.
LWB9 Plans complete system..$20.00
Infra Red Laser Module
CWL1K Kit ...................... $199.95
C WL10 Assembled .......... $299.95
Optical Receiver with Voice Filter
LLR4K Kit ........................ $149.95
LLR40 Assembled ........... $199.95
Fires an actual
projectile using a
magnetic pulse. Advanced
project must be used with
caution. Battery powered.
NUTS & VOLTS
EML3 Plans ....................... $10.00
EML3K Kit ......................... $69.95
Box 716, Amherst, NH 03031 USA
Circle #136 on the Reader Service Card.
have no actual value associated
with the number. In gym class, you
counted off by fours to get four
groups. It didn't mean that group one
was better than group two. It's easy to
identify a nominal class. Just change
the number to a letter (group one to
group A). If there is no meaningful
change, then the class is nominal.
You cannot apply any statistical
measure to nominal numbers.
The ordinal class puts things in
order — high to low, large to small,
slow to fast. There is a difference
between these numbers, but it is not
directly linked to the numerical value.
Consider a race. There is a first place
through a 10th place. The first place
runner wasn't twice as fast as the
second place runner; all you can say
is that the first place runner was
faster. Only specialized statistical
procedures can be applied to ordinal
The interval class uses incremental
steps for its members. A good
example of this is temperature
measured in Fahrenheit or Celsius.
Each degree is an equal step. The key
limiting point of an interval class is
that there is no true zero. You can't
say that 1° C is infinitely hotter than
freezing or that 100° F is 10 times
hotter than 10° F. You can use some
statistical procedures with this class,
but you have to be careful.
The ratio class has incremental
steps and a true zero. The Kelvin
temperature scale has a true zero —
it's called absolute zero. You can't get
any colder than that. This class is the
truly mathematical class. There are
no mathematical limitations with
these measurements. All statistical
procedures can be applied.
Except for special procedures, all
of statistics is based on the "Normal
Distribution." (As we saw earlier, this
is also a Gaussian distribution.) What
this means is that the average value
of a group is the most likely value and
that the farther a value deviates from
the average, the less likely it
becomes. It is critical to understand
that, if this distribution does not hold,
then common statistical procedures
cannot be applied and the results are
not valid. However, it is a rare case
when the normal distribution is not
Let's look at some resistors to
illustrate this. If I take 200 loose
packed, 1K Ω resistors and measure
them, I expect that the average
resistance will be very nearly 1,000
Ω. I also expect to find most of the
values close to 1,000 Ω and fewer
that deviate farther from 1,000 Ω.
This is just common sense.
Notice, however, that I did not
specify the tolerance of the resistors.
Are they 1%, 5%, or 10%? The surprising fact is that it doesn't make any
difference. The average — also called
"mean" — for any tolerance is the
same. When you stop to think about
it, this is also common sense. While
an individual 10% resistor may vary
farther from 1,000 than a 1% resistor,
the average of any large group of 1K
resistors is, by definition, 1,000 Ω.
Of course there is a difference
between the 1% and 10% distributions.
If you were to graph the number of
resistors and their resistance in 1 Ω
increments, you would find that the
1% resistors were all within 10 Ω of
1,000 Ω. The 10% resistors had a
different distribution. It would be
more spread out and less peaked.
Again, this is just common sense.
Since the values are more spread
out, there are fewer resistors at any
What may not be common sense
is that these curves, while clearly
different, have the same shape. The
only thing that changed was the
scale. A common analogy is looking
at a sine wave on an oscilloscope. If
you change the horizontal or vertical
gain, the trace looks different, but, of
course, it's still the same sine wave.
The same is true for the resistor
distributions. Both distributions are
"normal," but one varies more than
This brings up an important