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 parametric tests are met.

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 samples) – primitive non-parametric version of the t-test for for two independent populations
- Wilcoxon Signed-Rank Test for a Single Sample – 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 t-test for two independent populations
- Wilcoxon Signed-Rank Test for Paired Samples – non-parametric version of t-test for paired samples
- McNemar Test – similar to the sign test for before and after studies
- Runs Test – to determine whether a sequence of number is randomly ordered
- Resampling Procedures – using Monte Carlo random number techniques

Elsewhere in the website we look at the following additional non-parametric tests:

- Chi-square Test of Independence
- Kolmogorov-Smirnov (KS) test
- Kruskal-Wallis Test
- Mood’s Median Test
- Spearman’s Rank Correlation
- Kendall’s Tau Correlation
- Friedman Test
- Cochran’s Q Test

As we will see, 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.

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