TY - JOUR

T1 - Estimating Desired Sample Size for Simple Random Sampling of a Skewed Population

AU - Gregoire, Timothy G.

AU - Affleck, David L.R.

N1 - Publisher Copyright:
© 2018 American Statistical Association.

PY - 2018/4/3

Y1 - 2018/4/3

N2 - A simulation study was conducted to assess how well the necessary sample size to achieve a stipulated margin of error can be estimated prior to sampling. Our concern was particularly focused on performance when sampling from a very skewed distribution, which is a common feature of many biological, economic, and other populations. We examined two approaches for estimating sample size—one being the commonly used strategy aimed at regulating the average magnitude of the stipulated margin of error and the second being a previously proposed strategy to control the tolerance probability with which the stipulated margin of error is exceeded. Results of the simulation revealed that (1) skewness does not much affect the average estimated sample size but can greatly extend the range of estimated sample sizes; and (2) skewness does reduce the effectiveness of Kupper and Hafner's sample size estimator, yet its effectiveness is negatively impacted less by skewness directly, and to a much greater degree by the common practice of estimating the population variance via a pilot sampling from the skewed population. Nonetheless, the simulations suggest that estimating sample size to control the probability with which the desired margin of error is achieved is a worthwhile alternative to the usual sample size formula that controls the average width of the confidence interval only.

AB - A simulation study was conducted to assess how well the necessary sample size to achieve a stipulated margin of error can be estimated prior to sampling. Our concern was particularly focused on performance when sampling from a very skewed distribution, which is a common feature of many biological, economic, and other populations. We examined two approaches for estimating sample size—one being the commonly used strategy aimed at regulating the average magnitude of the stipulated margin of error and the second being a previously proposed strategy to control the tolerance probability with which the stipulated margin of error is exceeded. Results of the simulation revealed that (1) skewness does not much affect the average estimated sample size but can greatly extend the range of estimated sample sizes; and (2) skewness does reduce the effectiveness of Kupper and Hafner's sample size estimator, yet its effectiveness is negatively impacted less by skewness directly, and to a much greater degree by the common practice of estimating the population variance via a pilot sampling from the skewed population. Nonetheless, the simulations suggest that estimating sample size to control the probability with which the desired margin of error is achieved is a worthwhile alternative to the usual sample size formula that controls the average width of the confidence interval only.

KW - Confidence interval estimation

KW - Margin of error

KW - Tolerance probability

UR - http://www.scopus.com/inward/record.url?scp=85044058577&partnerID=8YFLogxK

U2 - 10.1080/00031305.2017.1290548

DO - 10.1080/00031305.2017.1290548

M3 - Article

AN - SCOPUS:85044058577

SN - 0003-1305

VL - 72

SP - 184

EP - 190

JO - American Statistician

JF - American Statistician

IS - 2

ER -