Non-parametric analysis

When to perform non-parametric analysis

To achieve the best results from a non-parametric test, we should know the kind of situations in which such tests are appropriate. Here are the most common:
If the data being tested does not meet parametric assumptions: Basically, parametric analysis requires that the data being studied meets a given set of assumptions. For instance, the data should be normally distributed and the variance of the population should be homogenous. But some data samples may display skewness, rendering parametric tests less powerful. On the other hand, non-parametric tests work perfectly with skewed distributions and will come in handy in this situation.

• The size of the population sample is too small: The size of the sample is an essential aspect when it comes to selecting the most suitable statistical method. If the sample size is relatively large, a parametric test can be applied. If the size is too small, however, validating the distribution of data can be difficult, and the only way around it is to use non-parametric analysis.
• The data being analyzed is nominal or ordinal: Unlike parametric analysis that only works with continuous data, non-parametric analysis can be performed on other data types like nominal or ordinal data. For such data types, a non-parametric test is the only suitable solution.

Types of non-parametric tests

When we come across the word “parametric analysis” the first thing that we think of is an analysis of variance or t-test. These two tests assume that the data being observed is distributed normally. The non-parametric analysis does not assume that the data has a normal distribution and the only non-parametric analysis you are likely to perform in a statistics class is the chi-square test. But there are many other tests that can be carried out when performing non-parametric analysis and these include:

• 1 sample sign test: Used to determine the median of a data set and comparing it to a target value or a reference value.
• Wilcoxon signed-rank test: Like 1 sample sign test, the Wilcoxon test allows you to make an approximation of a data set’s median and compare it to a target or reference value. Nevertheless, the test makes an assumption that the data has been obtained from a symmetric distribution like a uniform distribution or Cauchy distribution.
• Friedman test: Used to determine the difference between various groups with ordinal dependent variables. The Friedman test can also be performed on continuous data if some assumptions have been violated, for instance, if one-way analysis of variance is inappropriate.
• Goodman Kruska’s Gamma: Used to test the relationship between ranked variables
• Kruskal Wallis test: Used in place of a one-way analysis of variance to determine whether multiple medians are different. In this test, the calculations use the ranks of data points instead of the data points themselves.
• Mann Kendall trend test: Used to identify trends in time series data
• Mann Whitney test: Used to check the differences between two independent groups of data sets when the dependent variables are either continuous or ordinal.
• Mood’s median test: Used in place of the 1 sample sign test when the data being analyzed has two independent variables
• Spearman rank correlation: Used to determine a correlation between two data sets

Advantages and disadvantages of non-parametric analysis

Non-parametric tests have a number of advantages over their parametric counterparts. These include:

• Fewer assumptions
• Acceptance of smaller sample sizes
• More powerful when the parametric test assumptions have been violated
• Can be used on almost all types of data including interval variables, nominal variables, or data that has been measured inaccurately or that has outliers

• More labor-intensive and time consuming when calculated manually
• Essential value tables for many tests are not incorporated into many statistical software packages