If you are into risk assessments, you may find yourself evaluating the data
Evaluating the data usually means testing its applicability
with a hypothesis. The process usually cited in project management chapters about
risk is this:
A hypothesis is formed. And then the evidence against the
hypothesis—observable data—is evaluated. If the evidence against is scant, the
hypothesis is assumed valid; otherwise: false.
Guessing?
Is this guessing? The hypothesis is true because no one
seems to object? After all, how much evidence is against? Enough, or have you
taken the time to really look?
Most of us would agree: the evidence-against-the-hypothesis
does not always fit the circumstances in many project situations.
There are
many cases where you've come to the fork in the road; what to do? Famed
baseball player Yogi Berra once posited: "When you come to the fork in
the road, take it!"
In the PM context, Yogi is telling us that with no data to
evaluate, either road is open. In Bayes* terms: it's 50:50 a-priori of there
being an advantage of one road over another.
Weight of
Evidence
Enter: weight-of-evidence**, a methodology for when
there is some data, but yet there is still a fork in the road. In this case, we
consider or evaluate each "road"—in project terms, models or suppositions—and
look at the ratio of probabilities.
- Specifically, the probability of model-1 being the right way
to go, given the data, versus the probability of model-2, given the data.
Each such ratio, given the observable data, conditions, or
circumstances, is denoted by the letter K: K equals the
ratio of probabilities
Strength ratio, aka “K”
|
Implied strength of evidence
favoring one over the other
|
1 - 3
|
Not really worth a mention
|
3 -20
|
Positive
|
20 – 150
|
Strong
|
> 150
|
Very strong
|
Why form a ratio?
It's somewhat like a tug-of-war with a rope:
- Each
team (numerator team and denominator team) pulls for their side.
- The
analogy is that the strength of the pull is the strength or weight of evidence.
Obviously, the weight favors the team the pulls the greatest. Equal weight for
each team is the case for the rope not moving.
- K is representative
of the strength of the pull; K can be greater than 1 (numerator team wins), less
than 1 (denominator team wins), or equal to 1 which is the equal weight case.
More data
The importance and elegance of the methodology is felt when there are
several data sets—perhaps from different sources, conditions, or times—and thus
there are many unique calculations of "K".
You might find you have a
set of K’s: K1 from one pair of teams, but K2 from another, and so on. What to
do with the disparate K’s?
Sum the evidence
The K’s represent the comparative weight of evidence in each
case. Intuitively, we know we should sum up the "evidence" somehow.
But, since "K" is a ratio, we really can't sum the K’s without
handling (carefully) direction.
- That is: how would you sum the odds of 2:1 (K = 2) and 1:2
(K = 2, but an opposite conclusion)? We know that the weights are equal but
pulling in opposite directions. Less obvious, suppose the opposing odds were
2:1 and 1:5?
Add it up
Fortunately, this was all sorted some 70 years ago by
mathematician Alan Turing. His insight:
- What really needs to happen is that the
ratio's be multiplied such that 2:1 * 1:2 = 1.
- To wit: evidence in opposite
direction cancels out and unity results.
But, hello! I thought we were going to sum the evidence. What's with the multiplying thing?
Ah hah! One easy way to multiply—70 years ago to be sure—was to actually sum
the logarithms of K,
It's just like the decibel idea in power: Add 3db to the power is the same as multiplying power by 2
Is it guessing?
You may think of it this way: when you have to guess, and
all you have is some data, you can always wow the audience by intoning: "weight of evidence"!
Appendix:
Geeks beyond this point
Does
everyone remember the log of 2 is 0.3? If you do, then our example of summing
odds of 2:1 and 1:2 becomes: Log(2) + Log(1/2) = 0.3 – 0.3 = 0.
Of
course the anti-Log of 0 is 1, so we are back at the same result we had by
intuitive reasoning.
On first examination, this might seem an unusual
complication, but it's a take-off on the slide rule and the older decibel (dB) measurement
of power. They both multiply by summing: a 3db increase in power (or volume) means
the power has doubled.
An example
What if we had four sets of evidence: odds of {10:1; 2:1; 1:2;
and 1:20}. What’s the weight of evidence?
Using logarithms: log(10) = 1, log(2)
= 0.3, log(1/2) = -0.3; log(20) = log(10) + log(2),
{1 + 0.3 – 0.3 – 1.3} = - 0.3 or odds of
1:2
Not all that obvious
_____________________________________________
*Bayes refers to a protocol of evaluating probabilities,
given some a-priori conditions, with the idea of discovering a-posterior an
underlying probable “truth”. Such discovery depends on an opportunity to gather
more data, perhaps with other conditions attached.
**A practical application of the weight of evidence method
is cryptanalysis. It was first developed into a practical methodology in WWII
by famed mathematician Alan Turing working at storied Bletchley Park. Something
of it is explained in the book "Alan Turing: The Enigma"
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