Parametric vs Non Parametric
Statistics is one branch of studies which allows us to understand population dynamics by using samples drawn from a certain population of interest. It is essential that these samples be random. Many formulae are created with incorporation of mathematics, to take inferences about population parameters. Naturally any population may have a “Normal distribution” where the dispersion of data/samples has a shape of a bell in the frequency graph. In a normal distribution, most of the samples concentrate around mean and 68%, 95%, 99% of data are found within 1, 2, and 3 standard deviations respectively. Parametric and nonparametric statistics depend on whether or not normal distribution is considered.
What is Parametric Statistics?
Parametric statistics is the statistics in which data/samples are considered as drawn from a normal distribution. The definition of parametric statistics is “the statistics that assumes that the data has come from a type of probability distribution and makes inferences about the parameters of the distribution”. Most of the known elementary statistical methods belong to this group. In reality, they may not be normally distributed. Therefore, this statistics type is based on more assumptions. If the data/samples are normally distributed or nearly- normally distributed, the formulae may produce accurate results and inferences. However, if the assumption of being normally distributed is wrong, parametric statistics could be quite misleading.
What is Non-parametric Statistics?
Non parametric statistics is also known as distribution-free statistics. The advantage of this statistic type is that it does not have to make an assumption as previously made with parametrics. Non parametric statistic calculations take medians in to attention than the means. Therefore, if one or two deviates from the mean value, their effect is neglected. Generally parametric statistics are preferred than this because it has more power to reject a false hypothesis than nonparametric method. One of the most known non parametric tests is Chi-square test. There are nonparametric analogues for some parametric tests such as, Wilcoxon T Test for Paired sample t-test, Mann-Whitney U Test for Independent samples t-test, Spearman’s correlation for Pearson’s correlation etc. For one sample t-test, there is no comparable non parametric test.
What is the difference between Parametric and Non-parametric?
• Parametric statistics depend on normal distribution, but Non-parametric statistics does not depend on normal distribution.
• Parametric statistics make more assumptions than Non-Parametric statistics.
• Parametric statistics use simpler formulae in comparison to Non-Parametric statistics.
• When a population is believed to be normally distributed or close to normally distributed, parametric statistics is the best to be used. If not, it is best that a nonparametric method be used.
• Most of the commonly known elementary statistic methods belong to parametric statistics. Non parametric statistics is sparingly used and applied for special cases.