In this work empirical models describing sampling error (Δ) are reported based upon analytical findings elicited from 3 common probability density functions (PDF): the Gaussian, representing any real-valued, ...In this work empirical models describing sampling error (Δ) are reported based upon analytical findings elicited from 3 common probability density functions (PDF): the Gaussian, representing any real-valued, randomly changing variable x of mean μ?and standard deviation σthe Poisson, representing counting data: i.e., any integral-valued entity’s count of x (cells, clumps of cells or colony forming units, molecules, mutations, etc.) per tested volume, area, length of time, etc. with population mean of μ?and;binomial data representing the number of successful occurrences of something (x+) out of n observations or sub-samplings. These data were generated in such a way as to simulate what should be observed in practice but avoid other forms of experimental error. Based upon analyses of 104 Δ?measurements, we show that the average Δ?() is proportional to ?(σx•μ-1;Gaussian) or ?(Poisson & binomial). The average proportionality constants associated with these disparate populations were also nearly identical (;±s). However, since ?for any Poisson process, . In a similar vein, we have empirically demonstrated that binomial-associated ?were also proportional to σx•μ-1. Furthermore, we established that, when all ?were plotted against either ?or σx•μ-1, there was only one relationship with a slope = A (0.767 ± 0.0990) and a near-zero intercept. This latter finding also argues that all , regardless of parent PDF, are proportional to σx•μ-1?which is the coefficient of variation for a population of sample means (). Lastly, we establish that the proportionality constant A is equivalent to the coefficient of variation associated with Δ?() measurement and, therefore, . These results are noteworthy inasmuch as they provide a straightforward empirical link between stochastic sampling error and the aforementioned Cvs. Finally, we demonstrate that all attendant empirical measures of Δ?are reasonably small (e.g., ) when an environ展开更多
文摘In this work empirical models describing sampling error (Δ) are reported based upon analytical findings elicited from 3 common probability density functions (PDF): the Gaussian, representing any real-valued, randomly changing variable x of mean μ?and standard deviation σthe Poisson, representing counting data: i.e., any integral-valued entity’s count of x (cells, clumps of cells or colony forming units, molecules, mutations, etc.) per tested volume, area, length of time, etc. with population mean of μ?and;binomial data representing the number of successful occurrences of something (x+) out of n observations or sub-samplings. These data were generated in such a way as to simulate what should be observed in practice but avoid other forms of experimental error. Based upon analyses of 104 Δ?measurements, we show that the average Δ?() is proportional to ?(σx•μ-1;Gaussian) or ?(Poisson & binomial). The average proportionality constants associated with these disparate populations were also nearly identical (;±s). However, since ?for any Poisson process, . In a similar vein, we have empirically demonstrated that binomial-associated ?were also proportional to σx•μ-1. Furthermore, we established that, when all ?were plotted against either ?or σx•μ-1, there was only one relationship with a slope = A (0.767 ± 0.0990) and a near-zero intercept. This latter finding also argues that all , regardless of parent PDF, are proportional to σx•μ-1?which is the coefficient of variation for a population of sample means (). Lastly, we establish that the proportionality constant A is equivalent to the coefficient of variation associated with Δ?() measurement and, therefore, . These results are noteworthy inasmuch as they provide a straightforward empirical link between stochastic sampling error and the aforementioned Cvs. Finally, we demonstrate that all attendant empirical measures of Δ?are reasonably small (e.g., ) when an environ
