The right tool to use depends on the research question and the and the data collected. Without knowing those it's difficult to say. Best wishes David Booth
For a "descriptive survey study with a population of less than 20 respondents", all you need is a paper and a pencil. If you like to provide sample means and summing 20 numbers by hand seems too laborious you can use a calculator.
It depends you research questions and nature of the variables.Identifying these you can apply the appropriate non parameteric test. For each parameteric test there is a counter part non-parameteric. so, choice the appropriate one for you data type nature.
First of all, there is no such thing as non-parametric studies. There are only non-parametric test, which are the crudest of all.
Small sample sizes demand that:
- you squeeze as much information as possible out of individual participants. For questionnaires that means using multiple validated multi-item scales.
- you use the most powerful technique you can find.
If your situation is that you use a multi-scale inventory to test multiple hypotheses, that would be Structural Equation Modelling.
If I were you, I would not try that with n=20, and rather stay entirely descriptive, meaning figures and summary tables. But, what I would really do with n=20 is go entirely qualitative or mixed. You can't get precise measures with n = 20, but you can get a complete overview, if you ask the right questions in 20 interviews (or five focus groups).
Non-parametric statistical tools are used when data does not meet the assumptions of parametric tests such as normality, homogeneity of variance, and linearity. Some examples of non-parametric methods include the Mann-Whitney U test, the Kruskal-Wallis test, the Wilcoxon signed-rank test the Friedman test, and Spearman’s rank correlation coefficient.
I agree on what Devi wrote in the above answer. I add that when the sample studied is below 12 participants you are obliged to choose a non parametric test (despite data are normally distributed). I suggest you to use JASP, a free software for stat analysis conceived for researchers in Humanities. Here the download page https://jasp-stats.org/
here some tutorials https://jasp-stats.org/how-to-use-jasp/
You might look at Mosteller & Tukey (1977). Data analysis and regression.
With such a small sample size, exploratory data analysis techniques might be informative. Simple graphics with discussion can be used to show relations
For a descriptive survey study with less than 20 respondents, focus on basic descriptive statistics such as mean, median, mode, range, and standard deviation to summarize your data. Use frequency distributions and percentages for categorical variables, and consider visual aids like charts or graphs for a clear presentation of your findings. Avoid complex statistical tests due to the small sample size, as they may not provide meaningful results in this context. Keep the analysis straightforward and focused on summarizing the characteristics of your respondents.