There are a few divisions of topics in statistics. One division that quickly comes to mind is the differentiation between descriptive and inferential statistics. There are other ways that we can separate out the discipline of statistics. One of these ways is to classify statistical methods as either parametric or nonparametric. We will find out what the difference is between parametric methods and nonparametric methods.
Methods are classified on the basis of what we know about the population we are studying. Parametric methods are those for which we know that the population is approximately normal, or we can approximate using a normal distribution after we invoke the central limit theorem. Parametric methods are typically the first methods studied in an introductory statistics course.
Ultimately the classification of a method as nonparametric depends upon the assumptions that are made about a population. A few parametric methods include:
- Confidence interval for a population mean, with known standard deviation.
- Confidence interval for a population mean, with unknown standard deviation.
- Confidence interval for a population variance.
- Confidence interval for the difference of two means, with unknown standard deviation.
To contrast with parametric methods we will define nonparametric methods. These are statistical techniques for which we do not have to make any assumption of normality for the population we are studying. Indeed, the methods do not have any dependence on the population of interest. It is for this reason that nonparametric methods are also referred to as distribution free methods.
Nonparametric methods are growing in popularity and influence for a number of reasons. The main reason is that we are not constrained to making as many assumptions about the population that we are working with as what we have to make with a parametric method. Many of these nonparametric methods are easy to apply and to understand.
A few nonparametric methods include:
- Sign test for population mean
- Bootstrapping techniques
- U test for two independent means
- Spearman correlation test
There are multiple ways to use statistics to find a confidence interval about a mean. Why do we need both parametric and nonparametric methods for this type of problem? Many times parametric methods are more efficient than the corresponding nonparametric methods. Although this difference in efficiency is typically not that much of an issue, there are instances where we do need to consider which method is more efficient.