Thursday, February 4, 2016

1,2,3 counting or measuring or positioning?


Counting, positioning, or measuring: what's in a number?

Remember pre-school or kindergarten: we all "learned our numbers".
Ah! but did we?

Want to count something? Just use the integers, starting at 0 and going in familiar step: 1, 2, 3 ....
The count takes on the dimension of what you are counting: dollars, inches, meters, liters, etc
You can do arithmetic on count, but because of the dimensioning, the results may or may not be viable: square inches are ok, but square dollars are not.

Want to rank or position something? Again, we fall back to the integers -- 1st or 2nd position is good; position 1.2 in a queue has no meaning or implementation. And, there is no dimension per se in a position. Some arithmetic still applies, but it's tricky. Addition is not commutative: you can add 1 to first position to get second position, but you can't add first position to a 1. Stuff like that.

Want to measure something? You can use any rational number (a number that can be fashioned by the ratio of two numbers). Really, anything on a measurement scale is rational and can be a measurement. And, you can do arithmetic between rational and irrational numbers (like "pi")

For a number to be useful in measuring, every number in between has to be meaningful. That's why you don't do measurements with ranks and positions: the in-between numbers are not meaningful.

Calibration: And, to be meaningful, the scale has to be calibrated.  A ruler with irregular spacings or a warped or bent rule, or guesses without reference to benchmarks or other reference classes are uncalibrated. And, thus, every number in between is not meaningful.

Project management
And so, where does the rubber meet the road in project management?
  • Probability x impact risk tables or matrices
  • Planning poker
What's the first thing you need to do for a risk matrix or planning poker? 
Answer:
  • If for real measurements, you need to normalize the reference class or benchmark to the project. 
  • But, if for ranking or positioning, nothing more is needed
And, you might ask: if I want to work with real measurements, what is the normalization thing?

1-2-4-8
Just about every planning poker game or risk matrix uses some simple scale, like the binary scale, to weight the choices or impacts. Fair enough
But, a "4" in one project may have really no relationship to the value of a "4" in another project. So, are these numbers just ranks, or positions, or are they numbers for measurement?

If just for ranking, then nothing more is needed: 4 ranks over 2 by 2:1. Done
If for measurement, then here's what you do:
  • Find the simplest real thing you've done before that is similar and call it the baseline cost;  divide its cost by its cost. You'll get 1, of course
  • For everything more complicated, divide by the cost of the baseline. Something twice as hard should divide out as a 2; four times harder divides out as 4.
When you're done, you got a set of numbers that are normalized to the baseline; calibrated to the reference baseline; and suitable for measurement (every intervening number is meaningful)

We're done here!






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