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# How to Get Your Way with Statistics

By Ali Hyder Mulji

“If you are a heavy French fry eater, your risk of dying doubles!”

Haven’t we all heard sentences like this, one too many times and are always left dumbstruck by the claims they make? Sometimes they’re too awful to be believable but at most others, its simply a smart statistician slyly fooling laymen using mathematical jargon. It is not that sentences like these are erroneous per se but they tend to bend the truth in a manner that still keeps the statistician “honest”

Let’s look at 3 ways in which statisticians use their confusing jargon to fool people.

1. The Well-Chosen Average

Imagine your broker convinces you to shift to a locality by saying that the average income of people there, is 20,00,000 Rupees and naturally you would expect to meet several upstanding and educated people there. However, after shifting you, you’re told that the average income of people is actually only 7,00,000. You’d assume at first that your broker fudged the numbers but actually he was technically correct.

The concept used here is actually that of choosing the correct average to suit your needs. As we all know there are three different kinds of averages: mean, median and mode. In several cases like the average height of people in a country or the average attendance of people in a class, the three averages will fall at roughly the same place. In financial terms however, such is not the case.

The following graph explains it clearly.

This is called a skewed distribution where the data is not symmetrical. In these cases, the extreme values do not cancel out each other as would have been in the case of a bell-shaped curve as shown here:

2) The Real Risk

“If you are a heavy French fry eater, your risk of dying doubles!”

Let’s analyse the above statement thoroughly. The statement makes a bold claim but does not go far enough to explain how many or how often do we have to eat French fries before we actually double our risk of dying.

The study was conducted by the American Journal of Clinical Nutrition and concluded that eating French fries does double your risk of death. However, it also said that the result only applies if a person eats fried potatoes more than 3 times a week So let’s take an average person in this study: a 60-year-old man. What is his risk of death, regardless of how many French fries he eats? One percent. That means that if you line up 100 60-year-old men, at least one of them will die in the next year simply because he is a 60-year-old man. Now if a 60-year-old man actually eats fried potatoes more than 3 times a week, his chances of dying double. But what’s the double of 1%? 2! And that man also gets to eat fried potatoes more than 3 times a week for his ENTIRE LIFE! Sounds like a win-win to me.

This is called Relative Risk. If your chances of winning the lottery are 1 in a billion and someone offers you a special ticket that increase your chance of winning by ten times, the probability that you will win the lottery will still be only 10 in 1 billion.

3) Small Sample Sizes

“Users report 23% fewer cavities by the use of Colgate!”

In the world we live in, it is hard to believe that any one toothpaste can show better results than any other. After all, 9 out of 10 dentists are always in support of any random toothpaste. The fallacy behind this study lies in the sample size chosen. On several occasions the companies silently omit such important information from detailed study reports. This is how you could conduct a similar study that works in your favour and still get it approved by every authority out there.

Step 1: Get a small number of people to join a random college association, say, their college Math Club.

Step 2: One of three things could happen. Their attendance falls, remains the same or increases.

Step 3: Repeat the above steps until, by the principle of operation, you arrive at a situation where the attendance of students increased substantially. (The principle of operation basically says that if repeated enough number of times all possibilities will occur sooner or later.)

There you have it! A headline that goes by the lines “Students say joining the Math Club has resulted in increased attendance by n% !”

Another example would be:

Step 1: Toss a coin 10 times

Step 2: Note down the results. You can have 1024 possible outcomes ranging from HHHHHHHHHH to TTTTTTTTTT

Step 3: Choose an arbitrary outcome, say, HHHHTTHHHH

Step 4: Here the number of times you got a head is 8 which is 80% instead of 50%. You can now conclude that you have proven that tossed coins have an 80% chance of showing heads. Although do mention the exact details of the study… somewhere in the corner… in small font.

(If repeated enough times the Law of Averages will eventually result in a 50% probability of Heads and Tails)

Note: Some concepts in this article are from the book How to Lie with Statistics by Darrell Huff.