In the earlier note, we have seen the primary drawbacks of parametric statistical analysis and understand the need for nonparametric statistical analysis. In this note, we will learn furthermore about nonparametric statistical analysis properties and methods.
Nonparametric statistical Analysis
A statistical method is nonparametric if it does not assume the population distribution or the sample size. It is in contrast with Distribution free methods, which are not synonymous.
It means it is quite correct to say that in nonparametric statistics also, we may have a very general assumption about distribution. These concepts we will see in the later sections of this nonparametric statistical inference notes. For example, in statistical tests on nonparametric way where sample size may be two or three, but still we can work with that small size data.
Nonparametric and Distribution free Methods
In the nonparametric methods, there are very little or no assumptions required about the distribution of the population. For example, it might be assumed that the data are from a population with a continuous distribution. Here our assumption is that data comes continuous distribution.
In the distribution-free procedures, we do not make any assumptions about the sampled population. However, it is devised primarily for nonparametric problems. Hence, after these terms are used synonymously, but there is a subtle difference between the two.
Use of Nonparametric Procedures
The following are some situations where the use of a nonparametric procedure is appropriate.
- The hypothesis to be tested involves no population parameter. Actually, when we are talking about a mean of a distribution, this can be found from the parameters of the underlying distribution or underlying Probability Density Function (PDF) or Probability Mass Function (PMF) like, say normal distribution function, binomial distribution function, or Poisson distribution function, etc.
- The data have been measured on a weaker scale so that assumption necessary for the valid use of a parametric procedure are not met. There are different types of data with different measurement scales. For example, we have nominal, ordinal, interval and ratio measurement scale and nominal is considered as the weaker scale as compare to others.
- In a class of 100, the CGPA distribution is not typically normal. There may be a more significant number of students in the passing boundary, that is, D grade and more number of students belong to A grade, and the remaining students would be in-between. Thus, it does not form a normal or symmetric distribution.
- The distribution of SGPA given CGPA is not homoscedastic. It means variance in SGPA and CGPA would not be the same.
- With the smaller data set, such as 20 students, no assumption hold.
Advantages of Nonparametric Methods
- It makes fewer assumptions as compared to parametric statistics.
- It need not involve population parameters and is not bothered about the distribution parameters or distribution from where data comes.
- There is a slight chance of improper use of methods as these methods are developed for particular purposes. So it is implausible that it is going to use in the wrong way.
- It is very applicable to data measured on a weaker scale. For example, marks (Quantitative) are a much stronger scale than grades (Qualitative and Ordinal) because it merges several marks into the same grade. Therefore that is a weaker scale.
- It is easy to understand and involves less intricate mathematical or statistical knowledge. However, solving problem using nonparametric is laborious but straightforward.
- It does not require much computation power and can be quickly performed. It is designed for small numbers of data, including counts, classifications, and ratings.
- The procedures depend on a minimum set of assumptions; thus, it has a broader range of applicability.
Disadvantages of Nonparametric Methods
- Using this method, we may waste information as often actual values are not considered. For example, given the marks we have converted into grades, and that way, we lose lots of information.
- Manual computation is difficult for large samples as calculations are laborious.
- Tables are not widely available as compared to parametric methods, such as normal distribution tables, etc.
- It is less efficient as compared to parametric approaches.
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