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-

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

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

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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