A nonparametric set of data is said to be so because one assumes it is distribution-free, such as when the sample size is very small. Probability sampling formulae for sample calculation generally assumes standard deviations or means, from a normal distribution.

My opinion is that one does not calculate probability sample size for nonparametric data because to be honest, I know not of such. One uses nonparametric tests on sample (such as small samples) that one thinks do not come from a a population of normal distribution.

from http://www.statsoft.com/Textbook/Nonparametric-Statistics

"Large data sets and nonparametric methods. Nonparametric methods are most appropriate when the sample sizes are small. When the data set is large (e.g., n > 100) it often makes little sense to use nonparametric statistics at all. Elementary Concepts briefly discusses the idea of the central limit theorem. In a nutshell, when the samples become very large, then the sample means will follow the normal distribution even if the respective variable is not normally distributed in the population, or is not measured very well. Thus, parametric methods, which are usually much more sensitive (i.e., have more statistical power) are in most cases appropriate for large samples. However, the tests of significance of many of the nonparametric statistics described here are based on asymptotic (large sample) theory; therefore, meaningful tests can often not be performed if the sample sizes become too small. Please refer to the descriptions of the specific tests to learn more about their power and efficiency."

If I understand this question, I would recommend that you conduct a traditional power/sample-size analysis and treat that as a minimum for data gathering where you plan to use nonparametric statistics. Some nonparametric analyses, like replacing a parametric IRT model with a non-parametric IRT model, seem to require a LOT more data than is typical for parametric analyses.

Thank you Eddie and Alan. I appreciate your answers and try working on those suggestions. Regrads

Is it a qualitative study? If yes, then sampling saturation occurs when you do not get any new information from subsequent sample units. If the data are in frequencies, then you can calculate the sample size = p x q x (Z square/E square) [where Z is the standard error associated with confidence interval, say at 5% level, it is 1.96, and E is the error you are prepared to allow, say .05; p is the portion showing a characteristics and q is not showing the characteristics x).  D Suar

Sir, Thank you very much for your response. Most of the questions are Likert 5 point scale questions. There are few Constructs and different number of variables for each construct. The objective is to find out the relationship among constructs, if any.

May I ask about the sample size calculation for quantitative study? From the previous studies on the similar topic as my study I know the median and interquartile range in the 2 groups analyzed.

Hello Dominika Klimczak-Tomaniak .. You can refer to another similar question. Please check the url below..

https://www.researchgate.net/post/How_can_I_calculate_sample_size_from_a_median_and_range

Thank you very much for help!

If you are going to use structural equation modeling technique (SEM) to test the relationship between constructs, you should consider the following article:

Francisco J. Martínez-López, Juan C. Gázquez-Abad, Carlos M.P. Sousa, (2012),"Structural Equation modelling in Marketing and Business Research: Critical Issues and Practical Recommendations", European Journal of Marketing, Vol. 47 Iss: 1.

The subtitle that talks about the sample size is as follows:

4.5. Issues related to sample size

The size of the sample is important in terms of the generalization of results, the reliability of the parameters’ estimation of the model, and the power analysis of model testing. SEM modellers must ask themselves what the right sample size is. Two main streams of thought can be identified in this respect, depending on whether the size is considered in isolated terms or whether it is evaluated in relation to the number of parameters to be estimated.

Several sample size recommendations can be found for the first stream, either as general recommendations regardless of the particular characteristics in the data/variables, or as a minimum size recommendation for certain situations in the data/variables distribution or methods of estimation applied. For instance, Ding et al. (1995) suggest the use of a minimum of 100-150 individuals; others recommend at least 200 in order to reduce eventual biases in the model estimation (see: Kline, 2005; Loehlin, 1998); there are also recommendations depending on the SEM method of estimation applied, for example, for certain asymptotically distribution-free methods of estimation, a sample size in the range of 1,000-2,000 is suitable (see: Boomsma and Hoogland, 2001; Hoogland and Boomsma, 1998; Hoyle, 1995).

However, the second stream of thought seems more appropriate when this issue is considered in overall terms (Baumgartner and Homburg, 1996). Specifically in Table 2, based on the suggestions of Bentler (1995) and Bentler and Chou (1987) about the ratio value, differences can be seen between models with ratios as low as 5 (i.e. trustworthy parameter estimates) or 10 (i.e. suitable significant tests) individuals per parameter.