Parametric versus Nonparametric

Parametric statistics is the branch of statistics that assumes that the population from where the sample data was taken has an underlying probability distribution. It was mentioned as a distinctive branch of statistics by Robert Fisher in his foundational book Statistical Methods for Research Workers, originally published in 1925. A typical parametric method is the confidence interval for a population mean.

On the other hand, nonparametric statistics makes no assumptions about the sample data or the population. This term has been used to classify two different cases. First, to describe techniques that do not rely on any specific parametric distribution. Second, to include methods that don’t assume a fixed model structure. Although in this case models consider an underlying parametric distribution, they usually change to adapt to data complexity.

There are many well-known nonparametric models and methods. Perhaps the best known is the histogram. Other widely used models are the kernel density estimation, support vector machines, and nonparametric regression methods.

Why are Parametric and Nonparametric Statistics Important?

Both, parametric and nonparametric statistics have an important role in science and engineering. Parametric methods are widely used as they present the advantage of considering a known distribution. This knowledge allows for an easier and accurate description of the sample and population.

However, nonparametric methods are becoming increasingly used, particularly for studying populations that can be ordered (ranked) but have no defined numerical interpretation. An example is preference analysis, where data is sometimes ranked according to a certain criterion.

Nonparametric methods have the advantage over their parametric counterparts of being more robust because they rely on fewer assumptions. However, the implicit simplicity of nonparametric methods has a downside, as they may require larger samples to conclude with the same level of confidence as parametric procedures.

Parametric and Nonparametric Statistics + LogicPlum

Deciding what statistical technique to use is not always easy and usually requires a sound background in statistics and mathematics.

LogicPlum eliminates the need for such knowledge by providing its clients with a tool that does all operations in an automated manner. From sample handling to model creation to reporting, all tasks are done by LogicPlum’s platform without the need for user intervention.

Guide to Further Reading

For those interested in Robert Fisher’s seminal book:

Fisher, R. Statistical Methods for Research Workers. Online version available at http://psychclassics.yorku.ca/Fisher/Methods/