Difference Between Parametric and Non-Parametric Test: Explanation

Parametric and non-parametric tests both are important branches of Statistics. Parametric tests take value for assumptions whereas non-parametric tests don’t. Both are efficient and possess unique characteristics. If we have to choose between the two tests, we must see what kind of normal distribution our data follows. If our sample size is larger, we may take the help of a parametric test. Here the mean is the central tendency. On the other hand, if the median is better, non-parametric tests are devised. Some of the examples of Non-parametric tests are Kruskal-Wallis, Mann-Whitney, and so forth. Now, let us get more insight regarding the nature of these two tests, their advantages, disadvantages, and differences.

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Key Takeaways: Parametric test, Pearson correlation, Non-parametric tests, Distribution, Data, Statistics, Hypothesis test, Population

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What is a Parametric Test?

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Parametric test is an important branch of Statistics. It creates and provides us with generalizations about the mean of an original parent population. It assumes sample data consisting of a fixed set of parameters. It can also be called a hypothesis test. 

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In a parametric test, the mean value is assumed or known. A test called t-test is performed. It is based on factors like the t-test of individual students which is generally used. These tests strictly follow the Pearson correlation and distribution of normal probabilistic nature. They are assisted in helping find the interval data and are confined to variables only. 

Advantages of a Parametric Test

Using parametric tests in Statistics has many upsides about it. Let us take a look at the many advantages they provide us with, 

• Not much data is required to be converted to a rank format in the case of parametric tests.
• They have more statistical power that is the capability of easily detecting any effect.
• Parametric tests are easy to calculate and have a time-saving nature. You can spot the software and make calculations quicker.
• These tests offer real and genuine information regarding the data of the population. This inspires great confidence in performing parametric tests.
• Parametric tests work best when they are spread over different types of groups. It increases the flexibility of the values taken as assumptions in contrast to non-parametric tests where assumptions are zero or less.

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Disadvantages of a Parametric Test

The following points should be remembered as the disadvantages of a parametric test, 

• Parametric tests often suffer from the results being invalid in the case of small data sets
• The sample size is very big so it makes the calculations numerous, time taking, and difficult
• These tests are used only for interval data and ratio data
• It can be observed at the end of the parametric tests, certain values are missing and we can not just omit them. Data is not continuous

The video below explains this:

Derivatives of Function in Parametric Form Detailed Video Explanation:

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What is a Non- Parametric Test?

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Non-parametric tests are those tests that don't depend on any data for the assumption. At the time of modeling data, it doesn't restrict itself to finite parameters. This too, is a kind of hypothesis test that is based on the difference of the medians, as median acts as the central tendency here. This test assumes the variables at a nominal level and also goes by the name “distribution-free test”. Non-parametric statistics are classified into three types known as non-inferential statistical measures, inferential estimation techniques, and the most important, hypothesis testing. 

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Mood’s median test, Mann-Whitney test, Kruskal-Wallis test, Friedman test are well-known examples of non-parametric kind of tests. They assume the Spearman rank of correlation and help find the nominal data. 

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Advantages of a Non- Parametric Test

Performing a nonparametric test has its own perks. These are mentioned below, 

• Non-parametric tests are very flexible and can be used with different varieties of data 
• These tests are much simpler to understand and are applicable to a large number of situations 
• Sample sizes which are small are suitable for non-parametric tests
• They need very few or zero assumptions about the population data and are not affected by extreme values
• In some cases, they are considered to be more efficient than parametric tests
• They also offer many alternative tests for the parametric tests

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Disadvantages of a Non- Parametric Test

Non-parametric tests also suffer from major drawbacks. Some of these are as follows, 

• Non-parametric tests don't provide effective results like that of parametric tests
• They possess less statistical power as compared to parametric tests
• The results or values may not be very reliable and therefore accurate in some cases and may make insufficient use of the data while performing the test
• As there is no accuracy or precision, the result may lead to ultimately rejecting the null hypothesis
• The sample distribution of a nonparametric test suffers from the drawback of being constricted to small sample sizes
• Distribution tables are too large and calculation gets difficult 
• With the advent of technology, the usage of non-parametric tests have become negligent

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Difference between Parametric and Non- Parametric 

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Things to Remember 

• Parametric and nonparametric tests are both important branches of Statistics. Parametric tests are a kind of hypothesis test that assumes data about the mean population. 
• It is adhered to following a fixed set of parameters within the normal probabilistic distribution. T-tests, ANOVA, and z-tests are common examples of such parametric tests. 
• Parametric tests give a real sense of information regarding the population while being confined to specific parameters. The calculations are very easy and extremely time-saving. However, on the downside, they are not very reliable when it comes to small data sets. They also face the disadvantage of the sample size is very big. 
• Non-parametric tests on the other hand are completely opposite in nature as compared to parametric tests. However here, parameters are not restricted and these tests either may or may not take any values for the assumption.
•  It is based on differences of the medians and is applicable to both variables and attributes. Kruskal-Wallis and Mann-Whitney are considered good examples of non-parametric tests.
• The advantage is that almost zero or very few assumptions have to be made about the data and work smoothly with outlying observations. They are simple and applicable to small samples. 
• But they suffer from disadvantages like they may not be as effective as parametric tests are. The values may not be very accurate and the test uses data inadequately. Sample distribution can get too big at times and may cause trouble in calculations. 

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