## Scale types example

### Nominal scale

Assume a litter of kittens. {-Stop climbing the furniture. -Meow?} They can be sorted by coat patterns. {tabby; orange & white; calico; Siamese points; solid; black & white; Where'd the other one go? tortoiseshell.} There is no inherent ordering for these patterns, and no sense of distances between them. We could attempt ordering solid colors, then bicolors, but different patterns of the same number of colors don't have an order. {Meow? yawn}

### Ordinal scale

Okay, next we can order them by size. Grab the smallest, {mew!} gently, and the largest, and place them as the endpoints of a continuum. Then arrange the rest, in order, between those endpoints. {work fast} The kittens can then be numbered in increasing order. The simplest labels to use are 1-7, but A-G would work, as would 4, 9, 12, 17, 34, 78, 99, as long as it is understood that only the _order_ of the numbers matters.

### Interval scale

Next, {the kittens are thoroughly out of order by now}, we can take their temperatures. We will use the Celsius scale because it covers a convenient range. We don't expect much of a difference among the kittens, but we know that a difference of one degree is always the same difference in energy, wherever in the scale that one-degree difference is located. However, a reading of 10 degrees does not mean twice the energy of a reading of 5 degrees.

### Ratio scale

We could instead use the Kelvin scale, which uses degree differences of the same size as Celsius degrees, but has a zero point defined as an absence of molecular motion (it's not actually possible to reach zero, in real life). Therefore, the famous PV=nRT equation relating (P)ressure, (V)olume, and (T)emperature of a particular (n)umber of molecules of a gas (where R is a constant) uses the Kelvin scale, because the volume of a gas doubles for every doubling of Kelvin degrees (at a given pressure).

Back to the kittens for another example, measuring lengths (including tail). We know that a length of four cm is twice a length of two cm, so now we can say that the calico is 95% as long as the tabby, etc. Again, nothing can actually be measured to be 0 cm, but the theoretical construction of the scale includes it.