I was overdue with the blog for two weeks and struggling with finding inspiration for it when I routinely called my dad to chat about this and that. Not very proud I mentioned my struggle and in return I was told:
“You should read more” and he asked me to call him back in a bit. When I called back I started being told the following story: “When usually problems look simple to you, you might have a problem understanding why others have a problem. We might have a chance to understand it though if we thoroughly start comparing our ways of thinking.” He said, till now he remembers when a student asked him how it is possible that something has 1/7 chance to occur when the case involved 5 people. My dad told me that at first he did not understand the student’s question and the problem. Until he heard that the student intuitively was only allowing answers of 1/5, 2/5, and so on. But not 1/7…
He then sent me the book of Leonard Mlodinow “The Drunkard’s Walk: How Randomness Rules Our Lives” – and suggested that since QUICS is largely about calculating probabilities I may find inspiration for my blog in this book.
The above example with the student may appear trivial, but it is not. Leonard Mlodinow in his book shows a different example of how our intuition may complicate our life. Of course, you have already been forewarned with the student’s example, but before you read further, imagine a situation where someone you know got their health check results and (according to these results) has a virus of an incurable disease causing death within the next 10 years. You also have information that the accuracy of the detection method is 999/1000. Now close your eyes and imagine above again. What is that person’s chance to survive the next 10 years? Will you start supporting that person as if they were going to die? Or perhaps there is no need?
Now imagine a community of 10000 people in a place where this disease does not occur. If everyone undergoes the health check, the chance of 1/1000 that the detection method gives wrong result will effect in that about 10 people receives a positive result. But the chance that any of these people is sick is exactly ZERO!
That’s why it is so important to understand the additional information of the accuracy of the detection method – finding the virus becomes a correct result in 999 on 1000 cases, but only if the person IS sick. If you do the check on a healthy person, the detection of the virus means INCORRECT result in EVERY case. So, if like in your case, a person you know gets the result of having the virus – always ask them first what risk group they belong to.
Now quoting Leonard Mlodinow: “To not account for this is a common mistake in the medical profession. For instance, in studies in Germany and the United States, researchers asked physicians to estimate the probability that an asymptomatic woman between the ages of 40 and 50 who has a positive mammogram actually has breast cancer if 7 percent of mammograms show cancer when there is none. In addition, the doctors were told that the actual incidence was about 0.8 percent and that the false-negative rate about 10 percent. Putting that all together, one can use Bayes’s methods to determine that a positive mammogram is due to cancer in only about 9 percent of the cases. In the German group, however, one-third of the physicians concluded that the probability was about 90 percent, and the median estimate was 70 percent. In the American group, 95 out of 100 physicians estimated the probability to be around 75 percent.”
Many of us apply Bayes’ law in our research. But how much do we think of it in our day-to-day life?
PS. Apparently, a similar mathematical question to the ones described above my dad asked a number of people, all with a higher education degree, some in maths, but only one (!) replied that the answer is not obvious and needs more information to calculate conditional probability (Bayes’). That person was my sister!
I don’t remember being asked that question, but she often happens to be ahead of me on various tracks:
PPS. Now I hope that the above post won’t be like Leonard Mlodinow describes: “that sometimes lands me on the do-not-invite list for my neighbors’ parties”