The beauty of Statistics is that any data you visualize you would find a particular pattern in which the data is distributed. From being a bell-shaped curve to being uniformly distributed, the data can attain any form. These data can then be classified and analyzed based on their distribution. Parametric tests are statistical tests used for such type of distribution-reliable data. With these Parametric tests, we can test our hypotheses and confirm them.
Just like there are always a few students in a class who do not mend with the crowd, who do not come under any particular category, there are a few data that are distribution-free. They do not follow any assumptions of normality or the assumptions required to perform a parametric test. These data do not have any particular pattern and are very difficult to be tested. Mostly categorical data such as the satisfaction score, Likert scale, Ranks, or grades are few examples of distribution-free data. Weird! Isn't it? Well, anything is possible in this weird unpredictable world.
In order to perform statistical tests on these distribution-free data, there is a group of tests that does not require the data to follow any kind of distribution or fulfill the needs of normality. Those are the non-parametric tests. They are analogous to the parametric tests in a way, yet they do not require the data to have any of those assumptions.
Let us have a look at the various types of non-parametric tests and when and how we could use them.
When would I use the Non-Parametric test?
When the data are nominal or ordinal rather than interval or ratio
When the data are not normally distributed or have heterogeneous variance.
When one or more rules of a parametric test are violated.
When you have outliers in your data and they cannot be removed.
When your sample size is very low.
When you want to perform the test for the median instead of the mean. This usually happens when your data is skewed.
Types of Non-parametric tests
There are so many non-parametric tests available that can be used as an alternative to the parametric tests.
1-sample sign test
1-sample Wilcoxon signed-rank test
Friedman test
Goodman's Kruska's Gamma
Kruskal-Wallis test
The Mann-Kendall Trend Test
Mann-Whitney test
Mood's median test
Spearman Rank Correlation test
The Alternatives
Advantages of Non-Parametric Tests
1. It is readily comprehensible.
2. There is no assumption about the parent population.
3. It is the only method that is used for the analysis of Classification data.
4. It is suitable for Socio-economic data.
5. It is suitable for data in the form of ranks or grades.
6. It is suitable for datasets with small sample size.
Disadvantages of Non-Parametric Tests
Although the non-parametric tests have the said advantages, several reputed journals do not accept papers with non-parametric tests. In addition to that, there are the below-mentioned advantages as well.
1. It is less powerful than parametric tests.
2. It is used only for hypothesis testing and not for parameter estimation.
3. So far, no non-parametric test is developed for testing interactions in ANOVA.
Now that you have learned an overview of what a non-parametric test is and when you can use them, stay tuned for more posts in this series explaining each of the types of non-parametric tests in-depth, along with examples in R, SAS, SPSS, and Python of how to perform each one of them.
Sources
1. Kotz, S.; et al., eds. (2006), Encyclopedia of Statistical Sciences, Wiley.
2. Lindstrom, D. (2010). Schaum’s Easy Outline of Statistics, Second Edition (Schaum’s Easy Outlines) 2nd Edition. McGraw-Hill Education.
Very good Arthi, it seems tremendous