R7 PM Uncertainty Analysis in Risk Assessment: Influences on Decision-making
Thursday, 17 November 2005: 1:50 PM - 5:30 PM in 327-329

(FER-1117-839772) The tradeoff between measurement precision and sample size: should we get more or better data?

Ferson, S.¹, Kreinovich, V.², ¹ Applied Biomathematics² University of Texas at El Paso

ABSTRACT- One intuitively expects there to be a tradeoff between precision and sample size of measurements. For instance, one might be able to spend a unit of additional resources to be devoted to measurement either to increase the number of samples, or to improve the precision of the individual samples. Many practitioners apparently believe, however, that the tradeoff always favors increasing the number of samples over improving their precision. This belief is understandable given that most of the statistical literature of the last century has focused on assessing and projecting sampling uncertainty, and has in comparison neglected the problem of assessing and projecting measurement uncertainty. The belief is nevertheless mistaken, as can easily be shown by straightforward numerical examples. Consider, for example, the problem of conservatively estimating an exposure point concentration (EPC) from sparse and imprecise data. We might use an upper confidence limit on the mean to account for the sampling uncertainty associated with having made only a few measurements. This value is affected by the sample size, but, if the calculation also accounts for the imprecision of the values in a reasonable way, it is also affected by the measurement precision. Using recent algorithms to compute basic statistics for interval data sets, we consider the EPC and describe a nonlinear tradeoff between precision and sample size. This nonlinearity means the optimal investment of empirical resources between increasing sampling and improving precision depends on the quantitative details of the problem. We describe how an analyst can plan an optimal empirical design.

Key words: sampling uncertainty, measurement uncertainty, sample design, exposure point concentration