Solved – Sample size calculation for proportion

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I am in a doubt about using Absolute and Relative precision for sample size calculations. Suppose if I want to conduct a study to asses the prevalence of Hypertension in a general population, which formula should I use among these two-

  1. $n= Z^2 P(1-P)/d^2$
    where $n$ = sample size; $Z$ = C.I.; $P$= anticipated prevalence or prevalence estimated from pilot study and $d$ = absolute precision.

  2. $n = Z^2(1-P) / e^2 P$

    Where $e$ = relative precision.

Please suggest me with some example.

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Best Answer

Both formulas are right. In the first formula, the intent is to estimate the proportion within d percentage points of the true value P. In the second formula, you want to estimate the proportion within e of the true proportion P (ie, within e*P). That means, while in the first formula the precision is fixed, in the second formula the precision fluctuates based on the value of P.

Both formulas are discussed with examples in the book by Lemeshow et al (1990).

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