Non-parametric inferential statistics refer to a set of statistical techniques used when data do not meet the assumptions required for traditional parametric tests, such as normal distribution or equal variances. These methods are especially useful when dealing with ordinal data, ranked outcomes, or small sample sizes where the distribution of data is unknown or skewed.
Unlike parametric tests, which rely on specific parameters (like the mean and standard deviation), non-parametric methods are more flexible and make fewer assumptions about the underlying data. They are often used in situations where data are not continuous, where outliers are present, or when the scale of measurement is not interval or ratio.
Common Non-parametric Tests #
Some widely used non-parametric tests include the Mann-Whitney U test (for comparing two independent groups), the Wilcoxon signed-rank test (for paired data), the Kruskal-Wallis test (an alternative to one-way ANOVA), and the Chi-square test (for categorical data).
Advantages of Non-parametric Inferential Statistics: #
- They are useful for small or skewed samples.
- They can handle ordinal or ranked data.
- They are less affected by outliers.
- They do not require normal distribution.
Limitations of Non-parametric Inferential Statistics: #
- They are generally less powerful than parametric tests.
- The results may be harder to interpret in terms of effect size.
- They may not make full use of detailed data information.
Non-parametric inferential statistics provide a valuable alternative for analyzing data that don’t fit traditional parametric assumptions, ensuring robust insights in a wide range of real-world research settings.
List of recommended resources #
For a broad overview #
Inferential Statistics | An Easy Introduction & Examples
This article by Pritha Bhandari for Scribbr provides an easily accessible introduction to inferential statistics and its various types. It helps in understanding the background for nonparametric inferential statistics and its uses.
Nonparametric Statistics: Overview, Types, and Examples
This article by Mitchell Grant for Investopedia gives an overview of nonparametric statistics, its examples, and some special considerations of the field. Grant also gives a brief about how nonparametric statistics work and how it is applied to data.
For in-depth understanding #
Non-parametric Statistical Inference
This lecture series by NPTEL IIT Delhi gives an in-depth understanding of non-parametric statistical inference. Over the course of 10 lectures, learners are familiarised with all there is to know about non-parametric statistical inference.
Performance Evaluation: Proven Approaches for Improving Program and Organizational Performance
Chapter 12 of this book, ‘Analysis of Evaluation Data’ by Ingrid Guerra-López, talks about parametric and non-parametric inferential statistics. Guerra-López deals in detail with statistical inference and how it is crucial to the analysis and evaluation of data.
Case study #
This paper by Ignacio Rodríguez-Iturbe and Juam B. Valdes provides examples and case studies of water resource projects, particularly dealing with flood hydrology. One of the tests used in the studies includes the Mann-Kendall test, which is a non-parametric test for identifying trends in time series data.
Why Has Poverty Increased in Zimbabwe?
This paper by Jeffrey Alwang, Bradford F. Mills, and Nelson Taruvinga talks about the sources of the increase in Zimbabwean poverty, with the use of non-parametric, and parametric statistical methods. These techniques support the conclusion that the deteriorating economic environment along with drought are the major sources of increase in poverty in Zimbabwe.
