## Monday, November 21, 2016

### Understanding project statistics

Chapter 14 from the GAO Cost Estimating Manual on "Cost Risk and Uncertainty" is a good read, easily understood, and very practical in its examples.

Here's one illustration that I particularly like.  When you look at it, it's understood in a moment that the repeated random throw of two dice generates a probability density function [PDF] that has a bell-shape curve.

Statisticians call this phenomenon the Central Limit Theorem: random occurrences over a large population tend to wash out the asymmetry and uniformness of individual events, such that a "central tendency" occurs around the more probable outcomes.  A more 'natural' distribution ensues.  The name for this somewhat natural distribution is the Normal distribution, more commonly: the bell curve.

Here's what it looks like to a project manager.
Regardless of the distribution risks in either cost or schedule as adopted by work package managers for each individual work package, in the bigger picture at the summation will tend to be a bell-shaped distribution of risk.

Consequently,  the project manager's doesn't really need to understand the parameters of variation for each work package. The Central Limit Theorem does all the work. Triangles, Rayleighs, and even Binominal distributions are become bell shaped in the big picture.

This diagram is (again) from Chapter 14 of GAO's manual:

If the risk analyst generates these data from a simulation, like a Monte Carlo simulation, then the numeric statistics like variance and standard deviation are usually reported, along with the cumulative probability more commonly called the "S" curve.  In the diagram, on the right side, we see the cumulative curve plotted and labeled on the vertical axis as the confidence level.  With a little inspection, you will realize that the cumulative curve is just the summation of the probabilities of the bell curve that is adjacent on the left.

The GAO manual, and especially Chapter 14, has a lot more information that is well explained.  Give it a read.

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