Characteristics
In general, non-parametric tests:
- make few or no assumptions about the distribution of the data
- reduce the effect of outliers and heterogeneity of variance
- can often be used even for ordinal, and sometimes even nominal, data
Since non-parametric tests do not estimate population parameters, in general, there are
- no estimates of variance/variability
- no confidence intervals
- fewer measures of effect size
Also, non-parametric tests are generally not as powerful as parametric alternatives when the assumptions of the corresponding parametric tests are met.
Topics
In this part of the website we study the following non-parametric tests:
- Sign Test – primitive non-parametric version of the t-test for a single population
- Mood’s Median Test (for two independent samples) – primitive non-parametric version of the t-test for two independent populations
- Wilcoxon Signed-Rank Test for a Single Sample – a non-parametric version of the t-test for a single population
- Wilcoxon Rank Sum Test for Independent Samples – non-parametric version of t-test for two independent populations
- Mann-Whitney Test for Independent Samples – an alternative non-parametric version of the t-test for two independent populations
- Permutation Test for Independent Samples – an alternative non-parametric version of the t-test for two independent populations (used with small samples)
- Wilcoxon Signed-Rank Test for Paired Samples – a non-parametric version of a t-test for paired samples
- Permutation Test for Paired Samples – a non-parametric version of a t-test for (small) paired samples
- Fligner-Policello Test – determines whether the population medians corresponding to two independent samples are equal.
- McNemar Test – similar to the sign test for before and after studies
- One Sample Runs Test – determines whether a sequence of numbers is randomly ordered
- Two Sample Runs Test – determines whether two samples come from the same distribution
- Siegel-Tukey Test for Equal Variability – determines whether two samples come from distributions with the same variance
- Moses’ Test for Equal Variability – determines whether two samples come from distributions with the same variance
- Resampling Procedures – testing using Monte Carlo random number techniques
Other non-parametric tests
Elsewhere on the website, we describe the following additional non-parametric tests:
- Chi-square Test of Independence
- Kolmogorov-Smirnov (KS) test
- Kruskal-Wallis Test
- Jonckheere-Terpstre Test
- Mood’s Median Test
- Spearman’s Rank Correlation
- Kendall’s Tau Correlation
- Kendall’s Coefficient of Concordance W
- Tc Correlation between Judges and a Criterion
- Kendall’s u for Paired Comparisons
- Kendall’s u for Paired Rankings
- Lambda Measure of Asymmetric Association
- Gamma Measure of Symmetric Association
- Somers’ d Measure of Asymmetric Association
- Change Point Test
- Friedman Test
- Page’s Test
- Cochran’s Q Test
- Permutational MANOVA
- LOESS Regression
- Kendall-Theil-Sen Regression
Many of the non-parametric tests are based on analysis of the ranks of the data elements, often comparing the median instead of the mean.
References
Zar. J. H. (2010) Biostatistical analysis 5th Ed. Pearson
Stricker, D. (2016) Brightstat nonparametric tests
https://secure.brightstat.com/index.php?p=c&d=1&c=2
Siegel, S., Castellan, N. J. (1988) Nonparametric statistics for the behavioral sciences, 2nd ed.
https://psycnet.apa.org/record/1988-97307-000
Sheskin, (2000) Handbook of parametric and nonparametric statistical procedures. 2nd ed. Chapman & Hall/CRC
https://dl.icdst.org/pdfs/files3/22a131fac452ed75639ed5b0680761ac.pdf
Howell, D. C. (2010) Statistical methods for psychology (7th ed.). Wadsworth, Cengage Learning.
https://labs.la.utexas.edu/gilden/files/2016/05/Statistics-Text.pdf
Hi Charls,
If i have unequal variances and non-normal distributions and unequal sample sizes, what analysis should i do instead of two way anova? Or will that still be valid with an stringent significance level?
Thanks,
Mitra
Mitra,
I don’t know of a non-parametric test for this. One approach that might work for you is to use Two Factor ANOVA with the Regression option (since the sample sizes are unequal) and then ignore the omnibus test results and instead focus on the follow-up tests. Games-Howell might be the best test in this case.
Charles
Dr buenos días, por favor me aclara, si para una investigación donde se debe comparar un grupo de individuos en tres ocasiones diferentes, que responden a una encuesta de mejoramiento en salud, es apropiado aplicar una prueba de Mc Nemar dos veces, para comparar en tres ocasiones los mismos individuos.
Que pena otra pregunta, en el Análisis de Componentes principales, como podría hacer la gráfica de vectores?
Muchas gracias
Dr Good morning, please clarify, if for an investigation where a group of individuals must be compared on three different occasions, which respond to a health improvement survey, it is appropriate to apply a Mc Nemar test twice, in order to compare in Three occasions the same individuals.
Excuse me another question, in the main Component Analysis, how could the vector graphics do?
Thank you very much
Gerardo,
Sorry, but I don’t understand the situations well enough to provide an answer.
Charles
Dr gracias, solo es comparar tres veces el mismo conjunto de individuos con respuestas binarias (Lo ideal sería la prueba de Cocharn, creo)
Pero, una pregunta que me surge en ACP es podría hacer el gráfico de ACP con vectores?
Dr thanks, it’s just compare three times the same set of individuals with binary answers (The ideal would be Cocharn’s test, I think)
But, one question that arises in ACP is, could I make the ACP chart with vectors?
Gerard,
What is ACP? This may be an abbreviation in Spanish.
Charles
Dear Charles,
Need some advice for my study.
I have data of exercise study after chest operation, where I took physical data for several days towards their full recovery. In this study, I would like to know whether or not certain exercise, let say breathing in regards with lung volume, will lead to full recovery after 6-days post-operative.
So, I have data of the lung volume of several patients from day-1 to day-5 post-operation, and within those data, I have those patients who successfully recovered after day-5 and those who failed. The distribution of daily data among patients are very wide, the standard deviation are big.
My question is, what statistical analysis is needed to be done in order to see the correlation of daily data (i.e. lung volume) with the successful recovery?
Thank in advance for your advice,
Nasam,
You can simply calculate the correlation coefficient, by using the CORREL function in Excel.
Charles