For some strange reason, the classical sample size for single proportion is not that intuitive in Stata. There is a user written command, svysampsi that works but I found the mix of proportions and prevalecne that it expects to be a bit much. Further it does include design effects.

As an epidemiologist, I think in terms of Prevalence percentages, relative errors and percentage response rates when I am thinking about sample sizes for single sampel prevalence.

// FIRST INSTALL svysampsi as a one time package 
ssc install svysampsiCode language: Stata (stata)

So I have written this program that acts as a wrapper around the ‘svysampsi’ commands.

Here it goes

*** ESTIMATE SAMPLE SIZE for Proportions
cap prog drop ssSurvey
program define ssSurvey
args prevPercent  margErrorPer responsePer  designEffect fpcSize
 * local prevPercent = 000.09452
 * local margErrorPer= 25
 * local responsePer = 85
 * local fpcSize = 1000000
local responseProp = `responsePer' /100

local prevProp = `prevPercent'/100
local moe = `prevProp'* `margErrorPer'

// di as input  _newline(1)  "Prevalence % =" `prevPercent' " % which is Equal to proprotion = " `prevProp'
// di "Absolute error at `margErrorPer'% Relative  Error = " `prevProp'* `margErrorPer' "% or" `moe'
di as error "Estimating Sample size"

qui svysampsi `fpcSize', prop(`prevProp') moe(`moe') lev(95) response(`responseProp')
di as text _newline(1) "Sample size	= " as result round(r(resp_adjss) * `designEffect') as text	 _newline(1)" For "
di as text "	Prevalence  	= " as result `prevPercent' "% 
di as text "	Relative Error 	= " as result r(moe)*100 / r(prop)   "%" 	as text "  Abs error = " as result r(moe)*100 "%" 
di as text "	Response Rate 	= " as result r(resp)*100  "%" as text "  and 95% Confidence"
di as text "	Design Effect  	= " as result `designEffect'  
endCode language: Stata (stata)

Usage

It takes four arguments, inorer of sequence

• Prevalence expressed as (%)
• Relative error expressed as percentage (%)
• Response rate expressed as percentage (%)
• design effect expressed as a multiplier
• Finite population correction – – keep it at one million for large sizes

Example

ssSurvey 0.0955 25 85  1.5 1000000Code language: Stata (stata)

Result

Estimating Sample size

Sample size     = 106613
 For 
    Prevalence      = .0955%
    Relative Error  = 25%  Abs error = .023875%
    Response Rate   = 85%  and 95% Confidence
    Design Effect   = 1.5

. 
end of do-file
Code language: Stata (stata)