In case of non-parametric instrument design, how should the sample size be calculated? In case of parametric, we consider population distribution and parameters, and then derive sample size. Non-parametric being distribution free, what should be the guide line for sample size determination. I sincerely appreciate your suggestion and reference if any. Thank you
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
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