Friday, June 6, 2008

Number Theory

Marketing is pervasive in a capitalist society, as you need to be able to sell your products and services. In the olden days (read your grandparents days) you could fabricate any sort of data and make any claim in order to peddle your wares. Soft drinks because miracle elixirs and colored plastic became xray spectacles. But now there are rules and regulations. People won't put up with being fooled and scammed out of their hard earned money anymore. Now companies are responsible for their claims and must have supporting data. Just this year Airborne settled a lawsuit for claiming that its tablets prevented colds when it clearly did not. We can get into the absurdity of the ruling and penalty in another essay. So what's a business to do? Spin the data, of course! And there are many ways to convey true data to either subconsciously convince or simply scare them into agreeing with you.

If you asked someone what the gross national product of the US is, for example, how many people would know? Not many. But if you followed up the question with, "More or less than $200 million?", a lot of people will give you guesses close to $200 million. If instead you followed up the question with, "More or less than $1 billion?", you would get a lot of guesses close to $1 billion. This clearly does not work with people who already know the answer or have a very good idea of the answer. Thus, it is not usually helpful in negotiating salaries or prices.

How about the old relative instead of absolute comparison? For example, if I told you that taking Pill X increases your death rate two times, would you take Pill X? Probably not. Many of you probably already question that statement, and why wouldn't you? This essay is about the power of suggestion and you should be suspicious. What if I reworded the Pill X statement and said that Pill X increases your annual mortality from 0.01% to 0.02%? Does that make you think any differently about Pill X? What if it increases your annual mortality from 1% to 2%? What if instead of Pill X we talk about controlling blood pressure? If I tell you that a your blood pressure is 20 points higher than normal and thus doubled your risk of having a stroke? Would that get your attention? What if I told you that your risk of stroke went from 0.22% annually to 0.44% annually because your blood pressure was 20 points higher than normal? Would you still be as impressed?

The trick of multiplicity is also common. You see it in the stock market. At an average 7.8% annual return, $100,000 would be $125,272 in just three years! In three years you could have made over $25,000 without doing anything! The sad truth is that the majority of people don't have $100,000 sitting around to just invest in the stock market. They have a couple thousand, and that's only $253 after three years. Granted, it's free money, but it really doesn't make you want to jump into the stock market when you also know it could crash with the next credit crisis. (There are of course, very good reasons to invest in stocks. I just find this argument to be counterproductive.)

One more tricky number tactic is the false idol. It is a form of specious reasoning and incorrect syllogism. Let's consider autism. The prevalence of autism is anywhere from 5 to 30 per 10,000 children. For simplicity in this example (an example, i will remind all readers who are passionate about autism) let's say the prevalence of autism is 0.1%. That means of 1 million children, 1000 will have autism. Let's now say Company Y has developed a breath test for early diagnosis of autism that is 99.9% sensitive and 99.9% specific. That means if you tested 1000 autistic children, 999 of them would test positive. It also means that if you tested 1000 nonautistic children, only 1 of them would test positive. Sounds like a good test, right? Would it be worth $1000 to parents that want to know if they need to make special arrangements for their child months if not years in advance? To me it's worth one penny. Look at the table below.

If we take a million children, 1000 will be autistic, and 999 of those will have a positive breath test. On the other hand, there will be 999,000 children who are nonautistic, but 999 of those will have a positive breath test (0.1% of them given a 99.9% specific breath test). So if you look only at the children who have a positive breath test, there will be 1998 of them, 999 autistic and 999 nonautistic. That means if the breath test is positive, there's a fifty-fifty chance the child will be autistic. You might as well have flipped that penny. The point is that as the disease become less common, the test has to be closer to perfect. If autism were prevalent in 10% of the population, this fictitious breath test would be fabulous.

There are more number plays out there to deceive and scare you, but again, that's another essay.