When 95% probability provides 16% certainty.
We hear about statistics almost every day !
This survey says this’n’that with a margin or errors of X % 19 times out of 20 that…..this party will win the election, etc. etc.
This sounds soooooo serious ….and true !
But what if you were diagnosed positive for a rare disease ? Would you question the seriousness of the results or simply go back home and cry your heart out, write your will and wait to die ?
I was inspired by yet another powerful article in Quality Progress about Bayes’ theorem. I am no statistician. I am just starting to realize that I should have studied more deeply this fantastic science instead of attending Iron Maiden concerts….just kidding, no chance in the world that I would have missed this…well maybe a 1% chance in ….oh no stats again !
Let’s go back to the heart of the matter….seriously !
Bayes’s theorem demonstrates that if you are diagnosed positively with a test that is 95% accurate for a rare disease occurring in 1% of the population, you are likely to get the disease with a probability of …er, well… 95% ?
No. Rather 16%.
This shed a completely new light on quality control testing.
I will not go into any details about this (the info is available here) but rather reflects on a few scary facts.
- I recently asked a group of QA experts if they were confortable with statistics. Out of 27 people in the room, two raised their hands. Counting the statistician presenting the data. Although this might not be statistically representative of this region or industry, it was still a scary finding.
- I recently started asking my clients about the presence of a statistician in their midst. Very few had them on staff. Some hired them, once in a while.
- Asking a few specific comprehension question about sampling plans, a statistician presenting some basic statistical analysis was shocked to realize that his audience was pretty much very confused by the results. Well, not so shocked as I was told this was unfortunately the sad truth….being a statistician and not understood…poor guy.
Well, poor us !
As I kept asking questions, I realized that a high proportion of Quality Assurance personal did not know enough about statistics and data analysis to presume to take the right decision with a high level of certainty and accuracy.
Not only Bayes’ theorem is not well understood but even in the best cases, I am not sure if we do 98% or 99% level of accuracy in most tests.
- Human errors for one. Cannot presume to be perfect 100% of the time.
- Methodologies that are not 100% validated in some cases.
- Faulty or non-existent training programs.
- Calibration routines not performed on time on critical equipment.
- System audits not conducted on time.
- Audit findings not covered completely during Quality council reviews.
- Lack of proper data analysis.
- Sampling plans elaborated 20 years ago and never reviewed afterwards although the whole process was modified extensively.
- Abusive and improper use of the ANSI AQL sliding rule.
Not to be perceived as an alarmist however, I know our systems are rock solid.
Are they ?
Are yours rock solid ?
As Einstein once said : “The more I learn, the more I realize I know close to nothing”.
Humility is certainly the way to go to improve.
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