Reality is not what it seems: probability in practice
By David Towlson
I have been refreshing my memory recently on Bayes’ theorem. It’s named after the Reverend Bayes. He built on the work of earlier mathematicians and, like any self-respecting Victorian, took the glory for himself.
The theorem is really just a conditional probability equation or rule. Conditional probability is all about how the probability of an event changes depending on what you know. So, basically, what’s the probability of event X happening, given that I already know that event Y has happened? That can be rather different from the isolated probability of event X happening. Knowledge changes expectations (just think about the liberal democrats for a minute). Indeed there is an old adage – it is better to be thought a fool than to open your mouth and remove all doubt.
Bayes’ theorem is actually very widely used – it’s even used to detect email spam. It does this by predicting whether an email is spam, given that it contains certain key words. As you’d expect the naked (forgive the pun) probability that an email is spam, is quite different from the probability that an email is spam, given that you have already detected some likely, spammy, key words in the body text, like say, the words ‘viagra’, ‘enlargement’ and ‘satisfy’. But, it might be just the email for you, and not spam. Prediction is not perfect. Such predictions give false positives and false negatives.
Taking a safety professional example, you might like to consider the pure probabilities of whether a safety advisor has a specific safety qualification (like a NEBOSH Diploma or an NVQ) and whether they are actually any good. One conditional probability of interest might be given that if they have a safety qualification, what’s the likelihood they are any good?
Now, some may simply assume a list of qualifications and associations as long as your arm would automatically mean they were good (so probability close to 1 (or 100 per cent if you like it expressed that way)). But, it will be less. We have all met false positives (good at exams, but no good at their job or life for that matter) and false negatives (fails exams, but good at their job).
I have no idea what the true picture is, but I am assuming that the false negatives (good but fail exams) don’t greatly outnumber the real positives (good and pass exams). It would be rather a failing if the false positives were the largest group. That would question whether the nature of such assessment reflects accurately what people are required to do in practice, something that education has always struggled with. It doesn’t do to think about things too much…
David Towlson is director of training and quality at RRC International