Wednesday, November 02, 2005

What makes surveys possible?

I want to find the distribution of income in a nation. If it is India, imagine the size and scope of such a project. I will have to find the number of people, ask each person, and then try and arrive at a number. On the contrary you can ask a few people in your neighbourhood (like opinion polls of Times of India) and then state the average income of the nation.

One approach is not possible, the other is not credible!

Surveys use more sophisticated instruments to determine the average or the distribution. You will find them used in social science research; drug evaluation; poll surveys; marketing research and many others. What is interesting is not the sophistication, but what enables the sophistication? Two basic principles. Jargon scares me and it is even rude (in terms of writing etiquette) , so let me relate the concepts. My dear friend, Mark has provided me a correction from the earlier description, and I have incorporated it.

The first principle runs like this. Quite commonsensical, in fact! Imagine you have 10 people in a class. The more the number of people that you involve to find the average age, the closer you are to the average age of the class. This is called the Law of Large Numbers.

The second principle says that as long you take a reasonable sample size (which is the number of people chosen at random in a single instance), and repeatedly plot the obtained averages, you will find that these averages take the shape of a bell curve, usually. So if you take 3 people at random in a class; find their average, and then do this exercise lots of times, you will soon end up with a bell curve (actually a normal distribution because the result of such exercises is normal in nature), which basically allows for a lot more computing, especially of the kind we see done in research and surveys. And makes it easier to understand the nature of the data results.This is called the Central Limit Theorem.

So only a reasonable effort is enough to capture the necessary data hidden in a mass of information. This is the purpose of statistical inference.

This is something...I am learning, a few simple results help scythe through complex problems!

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