Last modified: Monday, May 19, 2008

## What is nonparametric statistics?

Most statistical analyses require certain assumptions, as do most sciences, in order to get anywhere. For example, many physics problems assume that objects are behaving under Newton's laws of motion. Similarly, most statistical problems require the assumption of certain distributions, which are almost always dependent on certain parameters. Hence, much of statistics is "parametric." A good example is the Gaussian, or "normal distribution," which is dependent on two parameters, an average--or mean--and a standard deviation.

Normal distributions are seen when dealing with biological information, like a population's height or weight. Most people will fall towards the mean value, with fewer people at the extreme values. Problems based on parametric assumptions often deal with using data to estimate an unknown parameter, for example, a population's mean.

But special cases do exist. Just like Newton's laws which are not applicable near the speed of light or in situations where quantum mechanics must be used, parametric statistics fall apart when a data set's distribution is unknown or wildly erratic. So theories and methods of nonparametric statistics have evolved to handle data sets such as these.

And because nonparametric statistical techniques are valid under less restrictive assumptions than those of a specified distribution type, they are very versatile, and they have found applications in many new methods of analysis. In general, statisticians use the adjective "nonparametric" to refer to situations in which the usual, parametric assumptions are not valid.

"Nonparametric methods now constitute one of the most successful branches of modern statistics," said Professor Puri. "The theory is elegant, it is widely applicable and it embodies easy as well as very advanced aspects."