In the field of statistics, there are a few divisions of topics. The most significant division that strikes immediately is the distinction that is there between the descriptive and the inferential statistics. Many other ways are also there by which the separation of the discipline of statistics is possible. Another way is to distinguish the methods as parametric or non-parametric.
Parametric Methods:
This classification is on the basis of what is known about the population that is under study. By Parametric methods we mean those methods for which it is known that the population is normal, or it is possible to use a normal distribution after having invoked the central limit theorem. In the study of statistics the parametric methods are the first ones to be studied. A particular method is also called parametric on the grounds of certain assumptions that we make for the population. The Parametric Methods primarily are:
- The confidence interval for a population mean, when the standard deviation is known
- The confidence interval for a population mean when the standard deviation is not known
- Confidence interval for a population variance
- The confidence interval for the difference of two means, with standard deviation that is not known
Non Parametric Methods:
As the name is suggestive, these methods are contrast to the parametric methods. In these statistical techniques, there is no need to make any specific assumption regarding the normality of the population that is being studied. These methods have no dependence over the population that is being studied. This is why these methods are also called as distribution free methods.
Over the years, there has been a growing popularity of the Non Parametric methods. This has happened for various reasons. The prominent reason is that there is no constrain or compulsion for that matter, to make assumptions about the population, like how it is when one talks of parametric methods. These Non-parametric methods are relatively simpler to administer and apply. Some of the key non parametric methods are:
- Sign test for population mean
- The bootstrapping technique
- U test for independent means
- Spearman Correlation test
The Comparison of Parametric and Non parametric Methods:
There are various alternatives in statistics to figure out the confidence interval about a mean. Where does the need arise for parametric and non-parametric methods to use? Many a times it has been seen that parametric methods are far more efficient than non-parametric methods. The applicability of the method should be considered before actually deciding to apply.