A Generalized Formula for Variance in Unequal Probability Sampling

A variance formula is given for a general class of estimators for any fixed sample size design. A formula for an unbiased estimator of the variance is also provided. These results generalize the Yates-Grundy variance formula of the Horvitz-Thompson estimator. </jats:p

Cyclic Group Divisible Designs

New cyclic solutions of several group divisible incomplete block designs arc presented, A new group divisible desian is reported whose solution is also cyclic. We also present non-isomorphic solutions of several group divisible designs listed in the catalogue of Clatworthy (1973). </jats:p

Addition or deletion?

Suppose it is desired to have an optimal' resolution III fraction of a 2p factorial in N runs where N [reverse not equivalent] 2 (mod 4). A design for this purpose can be obtained by adding two runs optimally to the n x p matrix derived by a suitable choice of p columns of Hn, a Hadamard matrix of order n. Alternatively, one can think of deleting two runs in an optimal manner from the (n + 4) x p matrix derived from Hn+4. A natural question then arises: do these two strategies give designs that are equally efficient in terms of a well defined optimality criterion? We show that for p = 2 or 3, the design obtained by deletion is as good as the addition design under the A- or the D-optimality criterion. However, for p [greater-or-equal, slanted] 4, the performance of the deletion design compared to the optimal addition design is rather poor as per the D-criterion, especially for large values of p. Under the A-criterion, the addition design is always better than the deletion design for p [greater-or-equal, slanted] 4, but the loss of efficiency using the deletion design is not too large for moderate values of p.Resolution III fractions Optimality

Some efficient estimators of the domain parameters

We have proposed, under a general probability sampling design, a two-phase sampling procedure, when the size of a domain (small area) is not known, for estimating the domain total, the first phase being exclusively devoted to arriving at a good estimator of the size of the domain and the second phase being designed to deal with the domain estimation. Apart from this, we have, assuming knowledge of the domain size, mooted two generalized direct estimators. These estimators which have been examined from the standpoint of conditional mean square error are shown to acquit themselves quite well. We have undertaken an assessment of performance sensitivity of one of the estimators in the optimal case when it is based on a predetermined value, say, of domain coefficient of variation and have established that it is worth putting premium on the same in the face of broad-ranging deviations from . An illustrative example has been provided to underscore viability and efficacy of the proposed estimators.Conditionally unbiased Conditional mean square error Two-phase sampling Performance sensitivity

Modified Clopper-Pearson Confidence Interval for Binomial Proportion

We introduce expected coverage probability as a measure for constructing confidence intervals for the binomial proportion, p. We propose a model based confidence interval for p using the expected coverage probabilities of the Clopper-Pearson interval. The method provides intervals comparable or better than the alternative intervals, such as the Wilson, Agresti-Coull and Jeffreys intervals

Preliminary Statistical Analysis of PAH-Contaminated Soils

Current research has proven bioremediation to be extremely effective for the cleanup of contaminated soils. Although bioremediation is effective, it still faces serious doubts on its implementation at a full-scale site. This is primarily due to minute differences encountered with each specific microbial species, supplemental nutrients, and the interaction between microbe and nutrient used at each site. The objective of this research was to determine the statistical significance of the choice of microorganism, nutrient solution, and their respective interaction effects. Specifically, the use of three different bacteria and three supplemental nutrient solutions was investigated for the remediation of soil contaminated with polycyclic aromatic hydrocarbons

Construction of Nested Incomplete Block Designs

Nested balanced incomplete block designs were introduced by Preece (1967). Generalization of these designs were studied by Home! and Robinson (1975). In this communication, we present some systematic methods of construction of nested balanced and partially balanced incomplete block designs. These methods unify and generalize some of the existing ones. </jats:p

Statistical Analysis of Olefins Yield in Fixed Bed Conversion of Dimethyl Ether

Selective conversion of dimethyl ether to lower olefins is a process of commercial significance. Lower olefins are intermediates in the conversion of dimethyl ether to higher hydrocarbons. Conversion of dimethyl ether to hydrocarbons has significant advantages over its counterpart methanol conversion process in the areas of heat duties, hydrocarbon selectivities, product yield, and reactor size. The present work examines the effect of key process variables on the dimethyl ether conversion to lower olefins in a fixed bed reactor system. The effect of process variables, namely reactor temperature, reactor pressure, feed dilution with nitrogen, and the weight hourly space velocity of dimethyl ether has been investigated using a 24 full factorial experimental design, with three replicates of the center point of the design. The estimates of significant main and interactive effects have been quantified using the Yates algorithm and conducting F-tests. A computational model has been formulated to predict the olefin yield at different values of process variables. Normal probability plots have been obtained to test model adequacy. The predictive capability of the developed model has been proved as illustrated by parity plot