Uncertain Totals

Statistically Correct Totals

LiquidPlanner uses some moderately sophisticated statistics to calculate things like ranges of dates and ranges of remaining work.

When adding ranges together you can’t just add up all the best cases, and then add up all the worst cases. Doing that would get you a range that is much larger than what it should be. In effect, if you did that you would be saying, “How much effort if absolutely everything goes right/wrong?”

But it is very unlikely that everything will go right (or even wrong).

In order to get realistic ranges in a project containing multiple tasks you have to do some tricky math. Fortunately we do that math for you. So all you’ve got to do is supply “ballpark” estimates and we’ll turn it into a schedule that reflects the realistic uncertainties you’ve described.

We refer to these things as “Statistically Correct Rollups” because they are a rollup of the contained work that is… well… statistically correct.

Mathematics Warning

The following contains mathematics that may frighten some folks (and may cause excitment of varying degrees among the pocket protector crowd).

LiquidPlanner takes the range you gave us and determines a standard deviation (σ) for the estimate as well as the expected value (also called the population mean). From the standard deviation we calculate the variance (v). These are then the basic values we use for all ensuing calculations.

The variance is a special beast because unlike the end points of the range, the variance of a series of estimates do sum. The expected values also sum. So to calculate the range for two tasks that follow each other we…

1. Calculate the expected value (E) and variance (v) for each task
2. Sum them up E_T = E₁ + E₂ and v_T = v₁ + v₂
3. Back-calculate the standard deviation (σ) of the total from the variance
4. Report the range for the total as E_T – σ to E_T + σ

And bada-bing… you’ve got a statistically correct total.