Sampling of Households Sampling Unit Different from Elementary Unit. Sampling of Households

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Polly Holland
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1 Samplig of Households Samplig Uit Differet from Elemetary Uit Ratio Estimator (which acts like a mea) Samplig of Households Samplig Uit Differet from Elemetary Uit Elemetary Uits r = Variable Variable = Packs smoked per day (equal iterval variable) Existece (,) = y m y =.5 m = 5 y,,.5 y,,. y,, m,, m,, m,, y,, y,, m,, m,, Number of clusters i = m i j = Existig persos i cluster i y i,j Value of variable i perso j i cluster i m = i = m i j = m i,j Existece of perso j i cluster i 44 y =. m = y =. m = 5 y,,. y,, m,, m,, y,, m,,. y,,. y,,.5 y,, m,, m,, m,, y,,.5 y,, m,, m,, 444 Secod stage samplig uits Elemetary uits Households Persos Samplig of Households Samplig Uit Differet from Elemetary Uit y,,.5 y,,. y,, m,, m,, m,, y,, y,, m,, m,, y,,. y,, m,, m,, y,,. m,, i = i = y i m i Example Samplig of Households y =.5 m = 5 y =. m = y =. m = 5 Elemetary Uits.5 y,, y,,. y,, m,, m,, m,, y,, y,, m,, m,, y,,. y,, m,, m,, y,,. m,, y,,. y,,.5 y,, m,, m,, m,, y,,.5 y,, m,, m,, y,,. y,,.5 y,, m,, m,, m,, y,,.5 y,, m,, m,, = 7.5 = Samplig of Households Samplig Uit Differet from Elemetary Uit Calculatig a Ratio Estimator of Mea (equal iterval variable) Sice two HHs were selected i each cluster, we ca drop HH desigatio focus is o two variables i each HH that are used for derivig the ratio estimator Tally the sum of the two variables i each cluster Variable oe existece (biomial) Variable two packs smoked per day (equal iterval) or Samplig of Households Samplig Uit Differet from Elemetary Uit Calculatig a Ratio Estimator of Mea (equal iterval variable) Variace for ratio estimator as a mea is similar to proportio v(y) = Cofidece iterval is also similar CI 95% = y i = (y i y m i ) (-) m +/- z x se(y)

Samplig of Households Samplig Uit Differet from Elemetary Uit Wat iformatio o subgroup i cluster Discussio of Readig Assigmet 9 Limit aalysis to those with a give characteristic smokers Tally cluster

2 Samplig of Households Samplig Uit Differet from Elemetary Uit Wat iformatio o subgroup i cluster Discussio of Readig Assigmet 9 Limit aalysis to those with a give characteristic smokers Tally cluster data oly for those with a give characteristic Packs smoked per day 447 Dowload from: 45 Samplig of Households Samplig Uit Differet from Elemetary Uit y =.5 m = 5 Elemetary Uits y,,.5 y,,. y,, m,, m,, m,, y,, y,, m,, m,, Populatio Two-Stage Cluster Sample of HHs First Stage Frame Sample of clusters For each cluster, frame of HHs i cluster Secod Stage Sample Elemets y =. m = y,,. y,, m,, m,, y,, m,, y =. m = 5 y,,. y,,.5 y,, m,, m,, m,, y,,.5 y,, m,, m,, 448 umber 45 Samplig of Households Samplig Uit Differet from Elemetary Uit Derive Packs Smoked per Smoker Still aalyzed as a ratio estimator Variable Variable Use same s for mea, variace of mea, ad 95% cofidece iterval Samplig Households or Persos Sample of Households withi a Cluster Populatio i Cluster 4 Households (HHs) But oly HHs are eligible HHs (i.e., have a eligible perso for the study)

Samplig Households or Persos Sample of Households withi a Cluster Populatio i Cluster Eligible HHs Each eligible HH cotais oe eligible perso Samplig Households or Persos Sample of Households withi a

Households withi a Cluster Populatio i Cluster Sice each eligible HH cotais oe eligible perso Samplig Persos Samplig withi for Immuizatio Surveys umber 4 5 6 7 we do ot eed to keep track of the HHs 4

3 Samplig Households or Persos Sample of Households withi a Cluster Populatio i Cluster Eligible HHs Each eligible HH cotais oe eligible perso Samplig Households or Persos Sample of Households withi a Cluster Populatio i Cluster While we stated that we sampled 7 perso I reality, we sampled 7 HHs, each of which had oe eligible perso i residece Samplig Households or Persos Sample of Households withi a Cluster Populatio i Cluster Sice each eligible HH cotais oe eligible perso Samplig Persos Samplig withi for Immuizatio Surveys umber we do ot eed to keep track of the HHs Samplig Households or Persos Sample of Households withi a Cluster Populatio i Cluster Withi the cluster there are eligible persos Samplig Households with oe Eligible Perso Samplig withi for Immuizatio Surveys umber We sample 7 of them

4 Samplig Households with oe Eligible Perso Samplig either HHs or persos results i the same variace if there is oly oe eligible perso per sampled HH First Stage () Probability proportioate to size based o persos or households Secod Stage ( Number) Sample persos or HHs with oe eligible perso 459 Example Immuizatio Survey Samplig Uit the Same or Differet from Elemetary Uit p i i = simple Proportio or Ratio Estimator actig like Proportio a i i = m i i = =.5 Whe there is either a costat umber of sampled persos or sampled HHs with oe eligible perso per HH, the two proportio (or mea) s provide the same results = Example Immuizatio Survey of Persos p =.4 p =.9 p =.86 Secod stage samplig uits same as elemetary uits a, a, a, a,4 a,5 a,6 a,7 a, a, a, a,4 a,5 a,6 a,7 a, a, a, a,4 a,5 a,6 a,7 Use the cluster-specific proportios to derive the sample variace 46 Example Immuizatio Survey Samplig Uit the Same or Differet from Elemetary Uit Variace of Proportio or Ratio Estimator actig like Proportio (p i p) i = (-) simple (a i p m i ) i = (-) m (.4 -.5) + (.9.5) + ( ) () =.9 Whe there is either a costat umber of sampled persos or sampled HHs with oe eligible perso per HH, the two variace s provide the same results [-(.5 x 7)] + [-(.5 x 7)] + [6-(.5 x 7)] =.9 () 7 46 Example Immuizatio Survey of HHs with Oe Eligible Perso a = m = 7 Secod stage samplig uits differet from elemetary uits a, a, a, a,4 m,4 m, m, m, a,5 a,6 a,7 m,5 m,6 m,7 Simple vs. Complex Variace Formula Aalysis of Subgroups (Males or Females) umber a = m = 7 a, a, a, a,4 m, a,5 m, a,6 m, a,7 m,4 m,5 m,6 m, a = 6 m = 7 a, a, a, a,4 m, a,5 m, a,6 m, a,7 m,4 m,5 m,6 m, Use the cluster-specific ratio estimators to derive the sample variace

5 Simple vs. Complex Variace Formula Aalysis of Subgroups (Males) umber HHs i the three clusters remai sampled, but the ratio estimator is ow based o rather tha persos. 465 Example Immuizatio Survey Aalysis of Males Samplig Uit the Same or Differet from Elemetary Uit Variace of Proportio or Ratio Estimator actig like Proportio (p i p) i = (-) simple (a i p m i ) i = (-) m ( ) + (..64) + (. -.64) =.8 () Whe there is ot either a costat umber of aalyzed persos or aalyzed HHs with oe eligible perso per HH, the two variace of proportio (or mea) s provide differet results [-(.66 x 5)] + [-(.66 x )] + [4-(.66 x 4)] =. () 4 m = = Aalysis of Subgroup Males Samplig Uit Differet from Elemetary Uit Proportio (for icorrect aalysis) p =.6 p =. p =. (for correct aalysis) a = m = 5 a = m = a = 4 m = 4 a, m, a,5 m,5 a, m, a, m, a,5 m,5 Elemetary Uits a, m, a,6 m,6 a, a, m, m, a, m, a,6 m,6 a, m, a,7 m,7 a,5 a,6 a,7 m,5 m,6 m,7 a, m, a,7 m,7 a,4 m,4 a,4 m,4 a,4 m,4 466 Samplig Households with Multiple Persos Samplig HHs (i.e., the samplig uit) with multiple persos (i.e., elemetary uit) requires use of the more s for mea ad variace s. First Stage () Probability proportioate to size based o persos or households Secod Stage ( Number) Sample equal umber of HHs i each cluster 469 Example Immuizatio Survey Aalysis of Males Samplig Uit the Same or Differet from Elemetary Uit Proportio or Ratio Estimator actig like Proportio p i i = =.64 Example Smokig Survey Samplig Uit differet from Elemetary Uit umber simple a i i = m i i = Whe there is ot either a costat umber of aalyzed persos or aalyzed HHs with oe eligible perso per HH, the two proportio (or mea) s provide differet results =

Aalysis of Subgroup Smokers Samplig Uit Differet from Elemetary Uit Mea (for icorrect aalysis) y =.7 (for correct aalysis) y =.5 m = y,.5 m, Elemetary Uits y,.5 m, y,.

6 Aalysis of Subgroup Smokers Samplig Uit Differet from Elemetary Uit Mea (for icorrect aalysis) y =.7 (for correct aalysis) y =.5 m = y,.5 m, Elemetary Uits y,.5 m, y,.5 m, Coclusio to Aalysis of Cluster Surveys Simple (i.e., EPI/WHO) Formulas vs. Complex Formulas simpler s used by EPI/WHO are oly correct i certai circumstaces EPI/WHO is correct for their specific applicatio (i.e., immuizatio surveys of youg childre i a arrow age rage where there is usually oly oe eligible child per HH y =.5 y =.5 m = y,. m, y,.5 m, ir approach remais useful i settigs were there are o computers ad o appropriate software for doig survey aalyses y =.7 y = 7. m = 6 y,. m, y,4 m,4.5 y,. m, y,5 m,5.5 y,.5 m, y,6.5 m,6 For persos doig rapid surveys Use the (more geeralizable) s for all aalyses Example Smokig Survey Aalysis of Smokers Samplig Uit Differet from Elemetary Uit y i i = simple y i i = m i i = Ratio Estimator actig like Mea Whe aalyzig varyig umbers of elemetary uits i a costat umber of HHs, the two s for estimatig the mea provide differet results = =.9 icorrect correct 47 Coclusio to Aalysis of Cluster Surveys Samplig at the Secod Stage after Samplig at the First Stage If oly oe eligible perso is likely to be i a HH Sample costat umber of eligible persos per cluster or Sample costat umber of eligible HHs per cluster If HHs likely cotai more tha oe eligible perso Sample costat umber of occupied HHs per cluster 475 Example Smokig Survey Aalysis of Smokers Samplig Uit Differet from Elemetary Uit v(y) = v(y) = (y i y) i = (-) simple (y i y m i ) i = (-) m Variace of Ratio Estimator actig like a Mea v(y) = (.7.9) + (.5.9) + (.7.9) =.77 () Whe aalyzig varyig umbers of elemetary uits i a costat umber of HHs, the two s for estimatig the variace of the mea provide differet results. [.5-(.8 x )] + [.5-(.8 x )] + [7.-(.8 x 6)] v(y) = =.6 ().67 m = =.67 icorrect correct 47 Readig Assigmet To be Discussed Next Dowload from: 476

7-1. Chapter 4. Part I. Sampling Distributions and Confidence Intervals

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