Department of Statistics Seminar
North Carolina State University

presents

Dr. Chuck Proctor

North Carolina State University

"The Underworld of Statistics behind Bulk Sampling with a Composite"

ABSTRACT

A whole lot of sampling of materials and of the environment goes on without benefit of random numbers, but it could be done with their aid. This is due in large part to the lack of a sampling frame, which is a list of every place-time where an observation could be made or, in the case of a lot of coal, where some material could be brought into the sample. When a frame is actually constructed and used, it turns out that it does not lead to a partitioning of the lot. It does, however, create a finite but very long list of possible outcomes (derived from all the ways the random numbers could have arisen) and this list deserves to be recognized as the sampled population. Recognition of this population of cross-sectional test portions, as they are called when making an ash determination, caused us to reformulate the variance formula for bulk sampling. Sampling variance formulas come in two varieties. One is used to estimate the standard error of a survey estimate based on data from that same survey, e.g., s2/n. The other is used to design a sampling plan and is based on population parameters, e.g., /n. The formula we derived is of the second type and is:

IS(1+CV12)(1+CV22)(1+CV32),
where IS is increment selection variance and depends on the number, sizes and spacings of the increments, while the CV's refer to how well the evenness of the increments is preserved through the stages of sample preparation and analysis.

In the talk we will first review this frame construction step and then derive the formula. We will then go back to review the literature, so to speak. Three themes seem to have guided statistical theories of bulk sampling, (1) general statistical theory, including time series, (2) particles as sampling units, and (3) enumerative survey sampling theory. We will attempt to show that enumerative sampling theory without frames or with only hypothetical frames may have retarded development of theory adequate for understanding the statistical consequences of the compositing operation.

Friday, January, 11, 2002

3:35 - 4:35 pm

206 Cox Hall

Refreshments will be served on the second floor of Dabney Hall (left of Room 222) at 3:00 pm.