Peter Donnelly’s Fooled by statistics

Donnelly is a statistician, please keep reading it’s more interesting than it sounds, in his talk discussing errors that people use when they apply statistics it shows a real example of rational understanding. He goes onto talk about disease tests being right 99%, why this does not mean the chance of the test being right being 99% and then about how statistics can be used to fool juries. The example that I want to present is the part about coin tossing, watch the video for this wonderful talk. It is important to understand what he is saying because we must in order to judge the things we come across in life that we think to be logical and reasonable. The coin tossing is a random event, it can either be presented with a head (H) or a tails (T) and is generally agreed that it is a fair representation of random.

The experiment is to toss a coin until we can see a pattern of HTH, for example HTTTHTTHTH or the pattern HTT such as THTHTHTHTT. We do this 100 times for HTH and another 100 times for HTT writing down the results each time so you can create the mean (average) number of toss before each pattern occurs. If you understand the process then pick a following statement based on what you think is true.

A. It will take longer (more tosses) for HTH to occur in random coin tosses than for HTT to occur.
B. They will take the same number of tosses for either HTH or HTT to occur.
C. It will be sooner (less tosses) for HTH to occur in a random coin tosses than for HTT to occur.

Come up with your answer before you read on!

We assume that because the coin toss is random that everything that comes from it is also random. This ignores the fact that both HTT and HTH are not random; they are non-random patterns that have been created. Most people think that B is the correct answer, although it is actually A which is correct. The average number of tosses for HTH is 10 before the pattern occurs and 8 tosses before the pattern HTT occurs. To explain why A is correct; it has to do with the third toss in the patterns. When we are looking for the pattern HTH, and we have the HT the next toss could result in H in which case we complete the pattern or T where we have to start over again. When we are looking for the pattern HTT, and we have HT the next toss could result in a T in which case we complete the pattern or a H which would not complete the pattern but it is then possible to use that H in the start of the next HTT. It’s weighted for the benefit of HTT and that is why we need fewer coin tosses to get the pattern HTT. If you still don’t understand please watch the video.

Why does this matter? Well a lot of people make decisions and accept things on the bases that they seem to be logical and rational, see my earlier post about the event in ghost hunters, when they are in fact not logical or rational at all. If we can explain to people why they are wrong with such powerful logic, perhaps we could start to break down irrational belief. How much time, money and control is given over to things that don’t stand up to logic, how many laws or social no go areas exist because they are seen as right. The logic in the real world is of course much larger, the simple example by Peter Donnelly is wonderful and compact which can be applied to it.

We and our minds are not very good at understanding statistics, since we never really live in a statistical world and our minds are programmed to understand just a few objects rather than thousands. Statistically very few people have ever died in an elevator still this does not remove the notion that a lot of people feel really scared and trapped in one. Statistically you are more likely to die in a car accident than a plane accident still a lot more people are scared of flying than driving. Even if we understand that we are 99.99% safe while travelling in an elevator or plane, we tend to focus on the 0.01% chance of what could happen. The possibility is that even with 99.99% chance of a positive event it is as likely to occur as the negative; somehow they are equally liable to happen in our minds. The perception of the mind is why this tends to happen, since the confines of our brain is set at a certain limit in our thinking. We cannot remember thousands of names just 30 or so; we cannot attend to everything that comes through our senses so we ignore most and only focus on a few. With these limits when we prepare to get onto a plane the imagination of possible outcomes is limited to just a few, we cannot imagine millions of successful journeys so then more weight is given to the negative ones, perhaps one successful journey and one unsuccessful one. This is of course only part of the process; needless to say that the imaginational crash presents a much more dramatic picture so we attend to them with greater detail.

Ok right now you are possibly thinking that I am just making stuff up, so let me put it in another way! Around 20,000 Americans join the Muslim religion each year, that seems quite a lot and if you have read some of my blog then most likely this seems like a worrying trend that is going on. Will America soon be overrun with Muslims? Well, no! The 20,000 is only about half a percent and is nothing compared to the 3% or so that become atheists each year in America. Living in middle earth with relative few world objects limits our understanding of statistics. There is another problem, a much greater hitch with statistics they are often collected for a certain reason. It is only when someone or groups want to show something do they go out and find the information. Going back to the religion statistics, is could be argued that at certain times in history perhaps the turn of either the atheist or Muslim right now, people tend not to want to tell the truth when people ask them questions. I am not saying everyone is a liar but it is easy to do when you don’t want to enter the discussion. Statistics are not often true reflections of what is going on rather perhaps a loose indication of the truth.

Always use statistics with a pinch of salt!