An Improvement on Some Approximate Solutions to Dalenius Equation

Kareem, A.O., 2Oshungade, I.O. and *2Oyeyemi, G.M.

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Keywords: Precision, Stratified Sampling,, Approximate Boundary Value and Exact Boundary Value


Dalenius researched into the problem of strata boundary determination and came up with some sets of general equations that
must be satisfied to reach optimum points of stratification (OPS). These equations met a lot of criticism in terms of its
difficulty and time involved in solving them as well as its practical adaptability. Thus, for easy application, sets of
approximate solutions were suggested. Deficiencies in the suggested solutions include unavailability of a theory to guide the
choice of class interval in their application, use of Approximate Boundary Value (ABV) and overlapping within strata. This
study developed the Exact Boundary Value (EBV) approach which places the boundaries at their exact value, eliminates
overlapping within strata and produces more strata formation than the ABV. In terms of the precision of the two approaches,
the EBV approach was found to be much more precise than the ABV approach for both optimum and proportional allocation.