Nuts & Volts - May 2004

Amazing Devices

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 with Coliminator

10,000 feet plus - Full 5 mw. A real beauty!!

LAPNGR5 Ready to use...$129.95

Ion Ray Guns

Potential concept for the ultimate weapon of the future. Produces force fields, induces shocks and other weird effects. IOGHP1 Plans .................... $10.00 IOGHP1K Kit .................... $149.95 IOGHP10 Assembled ....... $249.95

Laser Window Bounce

Receiver and laser illuminator modules for 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

F o r

E l e c t r o n i c s

Electrokinetic Guns

Fires an actual projectile using a magnetic pulse. Advanced project must be used with caution. Battery powered.

NUTS & VOLTS E v e r y t h i n g

EML3 Plans ....................... $10.00 EML3K Kit ......................... $69.95

Information Unlimited Box 716, Amherst, NH 03031 USA Orders: 1-800-221-1705 Fax: 1-603-672-5406 Email: riannini@metro2000.net Catalog $2.00

Circle #136 on the Reader Service Card.

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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 10^thplace. 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 groups.

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.

The Normal Distribution

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 valid.

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 particular value.

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 the other.