## Monday, May 13, 2019

### "Absolute Confidence" # Statistics #Analytics

Tim Healy writes in The Irish Independent that a US laboratory confirms it will appeal landmark judgement in Ruth Morrissey cervical cancer case. I have no argument with the results of the case or the award made by the court - my comment here is based on statistical probability. However, an intriguing aspect of the judgement is that the Judge ruled that laboratories should have "absolute confidence" in their results.

Is there such a thing as "absolute confidence"? Well - yes, there is. We will all die, night follows day, and so on. But could there be "absolute confidence" in smear or any other tests? The answer is theoretically "Yes", but practically "No". The reason is that in statistics, we make inferences about populations using samples (think of a poll before an election). For example, we accept that Paracetamol is an effective cure for pain in humans - but does it work in all cases for all humans? We can't know that unless we test every single person in the world - an expensive and impractical idea. All we can do is conduct clinical trials on a sample of the population and make inferences about the population using the results. Because it is a sample, we cannot be certain of the result - hence there is always uncertainty in experiments that do not involve the entire population. What we can say is that we are confident of the result - 95% or 99% confidence is often an acceptable level of confidence in statistics.

Without wishing to diminish the awful cases that some people have endured due to misread results, there is uncertainty in almost everything that we do. In 2018, 149  people lost their lives on Ireland's roads - there is a risk that you will die every time you use our roads. Thankfully, this is a small risk - 149 deaths from a population of 4,857,000 (Estimate: April 2018, CSO) - this translates into a 0.003% chance of being killed on our roads. While this is a tiny risk, it does mean that our roads are not safe for everyone. A 0.003% of being killed also means that you have a 99.997% of not being killed.

Is 99% confidence enough? Would you get on a plane if you were 99% certain that it would not crash? According to FlightAware, there is an average of "9,728 planes, carrying 1,270,406 people, in the sky at any given time". If 99% of these were safe, this means that 9,631 would be safe - but 97 would not be safe. That's a lot! What about 99.9% safety? 9,718 would be safe, but 10 would be unsafe. Only at 99.9999% would you get an acceptable safety level - 9,727.99 out of 9,728 flights would be safe. Still a tiny chance, but enough for us to get on a plane. Crucially, even at 99.9999% we cannot have "absolute confidence".