Most of the tests that we study in this website are based on some distribution. These are called parametric tests. Parametric tests require that certain assumptions are satisfied. We now look at some tests that are not linked to a particular distribution. These non-parametric tests are usually easier to apply since fewer assumptions need to be satisfied.
Topics
- Introduction
- Sign Test
- Trinomial Test
- Mood’s Median Test
- Brunner-Munzel Test
- Wilcoxon Rank Sum Test
- Mann-Whitney Test
- Permutation Test for Two Independent Samples
- Wilcoxon Signed-Ranks Test
- Permutation Test for Paired Samples
- Fligner-Policello Test
- McNemar’s Test
- One Sample Runs Test
- Two Sample Runs Test
- Siegel-Tukey Test for Equal Variability
- Moses’ Test for Equal Variability
- Goodness of Fit Tests
- One-Sample Kolmogorov-Smirnov Test
- Two-Sample Kolmogorov-Smirnov Test
- One Sample Anderson-Darling Test
- Two-Sample Anderson-Darling Test
- One-Sample Chi-square Goodness of Fit Test
- Goodness-of-fit for Benford’s Distribution
- Real Statistics Data Analysis Tools
- Goodness-of-fit using the Characteristic Function
- Resampling Procedures
- Non-parametric Tests Data Analysis Tool
- Resampling Data Analysis Tool
- Jackknife
- Bootstrapping
- McNemar-Bowker Test
- Gini coefficient
- Tolerance intervals
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
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
Hello Charles,
I hope all is well. I got help from you a while back on which statistical test to use for my study that I am about to remind you of (in short). You directed me to the Wilcoxon Sign Rank test to compare student’s averaged exam score to their final exam score. I am looked to see if there is a significant difference in students averaged exam score and their final exam score across semesters (related pairs) for a math course. This is from 2019 to 2025 in which we taught the traditional way (pre-pandemic), the totally online (pandemic) , and now recently online/traditions. The data is not normally distributed and each semester had a total count from 225 to 937. Each semester data for the course ran several sections, taught by multiple teachers in a common way with common exams. I lumped all of the data together for each semester. I am not sure if a particular student took the class twice. We an excuse that thought for now.
You mentioned that the following and used 7 semester due to me thinking I would just do this for 7 semesters. My question is, how come you suggested me using a family-was error. I am not running multiply test on any of the data. I will be comparing:
Fall 2019 averaged exam score to Fall 2019 final exam score
Spring 2020 averaged exam score to Spring 2020 final exam score
..etc. I will continue this all the way until Spring 2025.
I am only using the data sets once. Am I missing something? Do I have to apply the family-wise error using alpha = 1-(1-.05)^12 ?? Thank you!!
“Usually the level of significance is alpha = .05. The same approach can be used for the other semesters, except that now you may need to take into account the familywise error (depending on what is your null hypothesis for all 7 semesters). This can be done using an error correction. E.g. use alpha = 1-(1-.05)^7.”
Hello Virginia,
1. If in the following you are testing each semester then you are making seven tests. if you merge the data across all the semesters then you only have one test
Fall 2019 averaged exam score to Fall 2019 final exam score
Spring 2020 averaged exam score to Spring 2020 final exam score
..etc. I will continue this all the way until Spring 2025.
2. For each semester it is important that the same students are measured for the average exam scores and the final score
Charles
Thank you Charles!
Charles,
I hope all is well. Thanks for always helping me out! I need your help again please.
I want to make sure I am choosing the right statistical test.
I am working with 7 semesters of exams scores for a particular course.
Each semester the course ran with many sections. However, the students no matter what section they were in, not matter which teacher, they were given the same exams.
Let A = exam average (two exams were given within the semester and they were averaged)
Let B = final exam score (the course ends with a final)
Overall for each semester, I want to compare A to B to see if there is a significant difference is found. Which non-parametric test should I use? What should my level of significance be?
Which test should I use to see if there is a correlation between A and B for each of the semesters?
I tested semester 1 (A & B) through semester 7 (A & B) and found that the data sets for all is no normal. I used the Shapiro Wilks test (all p<.01).
Thank you!!!
Charles,
Thanks so much for the valuable feedback you always give. Can you verify I am will approaching analyzing this study in the right manner.
I have exam scores that are all not normally distributed.
Set A (N=84) ; Set B (N=76) ; Set C (N=162) ; Set D (N=137)
I used the Shapiro Wilk’s test in SPSS and obtained the following p values respectively (.56, .042, .000, .001).
I want to compare the means in Set A to Set B; Set A to Set C and Set A to Set D
Should I use the Kruskal-Wallis non-parametric test? Should I used also a Bonferroni correction and use alpha = .05/3 = .017 as the significance level?
Thanks
Virginia,
Since the normality assumption is violated you can use Kruskal-Wallis. If you get a significant result, you can use one of the KW post-hoc tests (e.g. Nemenyi), as described at
https://www.real-statistics.com/one-way-analysis-of-variance-anova/kruskal-wallis-test/
Kruskal-Wallis is a reasonable choice provided the homogeneity of variances assumption is met (see Levene’s test).
Charles
Dear Charles,
thank you for your appreciated effort and may I ask you a question, what are the tests i should perform before going forward with Mann Kendall test and other tests, most papers i read were applied trend tests forward without check any assumption in addition how can i apply parametric and non-parametric tests at the same data, it really make me confused.
thanks a lot
The main assumption is that there is no autocorrelation. See the following webpage for more information about autocorrelation and how to test for it: https://www.real-statistics.com/multiple-regression/autocorrelation/
Charles
hi charles! Do me a favor.
i have some questions….
now covid 19 vaccines have some side effect. i want to compare vaccine brands through severe side effect incidence rate(ex, death rate)
In england,
England(2021-05-21) Pfizer AZ
vaccination 21600000 32900000
death 374 786
in case, what testing is needed for H0 : Pfizer death rate = AZ death rate?
If I understand the question correctly, you can use a two-sample proportion test, as described at
https://www.real-statistics.com/binomial-and-related-distributions/proportion-distribution/two-sample-proportion-testing/
CHarles
thank you. i will try.
How can i get the book on non-parametric statistics with their statistical tables
There are a number of such books. Here is one:
Gibbons, J. D. and Chakraborti (2011) Non-parametric statistical inference, 5th edition. CRC Press
Charles
Hi Charles,
I am trying to figure out how to apply a non-parametric method analog to Nested ANOVA. My data is not normally distributed even after transformed, still no normal. Please if you can give me any advise?
Marie,
I don’t know of such a nonparametric approach, but I did google “non-parametric version of nested anova” and found a lot of entries, including the following. I hope this is helpful.
https://www.researchgate.net/post/Is_there_a_non-parametric_test_equivalent_of_a_nested_2-way_ANOVA_measured_with_SPSS
Charles
Hi,
Thank you very much for your response!
Your work is beneficial,
Best,
Marie
Hi, I am trying to figure out how to arrange 8 sets of data, with age ranges in a non-parametric method using 2.5 and 97.5 % cut offs. Please if you can give me some directions.
Hello Barbara,
I don’t completely understand what you are looking for or which non-parametric test you are looking to apply. Can you explain in a little more detail.
Charles
Hi Charles
How do I perform non-parametric tests in excel using the real statistics add in? Ctrl-m isn’t working to take me there.
Hello Paula,
If Ctrl/m is not working then it is likely that the Real Statistics software has not been installed. What do you see when you enter the formula =VER() in any cell?
Charles
This article proposes a “Divergence Index” for ordinal categorical variables using the Jensen-Shannon Divergence:
https://www.datasciencecentral.com/profiles/blogs/the-divergence-index-a-new-polarization-measure-for-ordinal-1
I have never heard of the Jensen-Shannon Divergence. Would it be possible to compute it using Real Statistics for Excel?
Thank you for your great work.
What is Non-parametric test equivalent to mixed ANOVA?
Muito bom. Extremamente útil.
Hi,
How can I perform a Nemenyi test? Is there an equivalent within the real-statistics download?
Yes, you can learn more about how to perform Nemenyi’s test using a Real Statistics data analysis tool on the webpage
Follow-up to Kruskal-Wallis
Charles
Sir,
How can I use non parametric methods using data analysis tool in Excel?
Thanking you,
Rajesh Tailor
Rajesh,
If you press Ctrl-m and select the T Test and Non-parametric equivalents option you can access the Mann-Whitney test for two independent samples and the Wilcoxon tests for one sample and paired samples.
Charles