within each stratum: , where and is a constant such that . An "optimum allocation" is reached when the sampling rates within the strata are made directly proportional to the standard deviations within the strata and inversely proportional to the square root of the sampling cost per element within the strata, : where is a constant such that , or, more generally, when Qualitative research Sample size determination in qualitative studies takes a different approach. It is generally a subjective judgment, taken as the research proceeds. One approach is to continue to include further participants or material until saturation is reached. The number needed to reach saturation has been investigated empirically. There is a paucity of reliable guidance on estimating sample sizes before starting the research, with a range of suggestions given. A tool akin to a quantitative power calculation, based on the negative binomial distribution, has been suggested for thematic analysis. See also Design of experiments Engineering response surface example under Stepwise regression Cohen's h References General references Rens van de Schoot, Milica Miočević (eds.). 2020. Small Sample Size Solutions (Open Access): A Guide for Applied Researchers and Practitioners. Routledge. Further reading NIST: Selecting Sample Sizes ASTM E122-07: Standard Practice for Calculating Sample Size to Estimate, With Specified Precision, the Average for a Characteristic of a Lot or Process External links A MATLAB script implementing Cochran's sample size formula Sampling (statistics) de:Zufallsstichprobe#Stichprobenumfang