The American Community Survey Sample Design: An Experimental Springboard

Transcription

1 The Ameican Communit Suve Sampe Design: An Epeimenta Spingboad Megha Joshipua, Steven Hefte U.S. Census Bueau 4600 Sive Hi Road Washington, D.C., 033 Intoduction In an ongoing effot to impove the quait of the Ameican Communit Suve (ACS) estimates and contain data coection costs, the Census Bueau outine impements a seies of epeimenta tests incuding testing of poposed new content, evisions to the cuent set of ACS questions, and poposed enhancements to data coection methods. This ea testing pogam is caed the ACS Methods ane. In 007, the ACS Methods ane oigina incuded one epeiment designed to assess the effectiveness of obtaining accuate esponses to two diffeent vesions of a poposed fied of degee question on the ACS questionnaie, and to evauate the diffeence between asing the basic demogaphic items (age/date of bith, ace, ethnicit, se, and eationship) in a gid vesus a sequentia questionnaie design. This epeiment, heeinafte caed the Oigina Content Test, was canceed in Decembe 006 since the budget fo fisca ea 007 had not et been detemined. unding was, howeve, avaiabe to cove one epeimenta component of the Oigina Content Test, the gid and sequentia questionnaie design, with sevea constaints on the mode of data coection. This test was caed the Gid/Sequentia Questionnaie Test. Additiona, once funding was eceived fo fisca ea 007, we wee abe to einstate the epeimenta testing of a new fied of degee question as a sepaate epeiment caed the 007 ACS Content Test. So utimate, the 007 ACS Methods pane incuded two tests the Gid/Sequentia Questionnaie Test, and the 007 ACS Content Test. Whie thee wee on two ACS Methods ane tests conducted in 007, we designed sampes fo the two epeiments that wee fieded in addition to the Oigina Content Test that was canceed. This pape descibes the sampe design fo a thee epeiments. The equiements of each epeiment necessitated simia, et unique sampe designs. The Oigina Content Test and the 007 ACS Content test wee designed to coect data via maiout, Compute Assisted Teephone Inteview (CATI), and Compute Assisted esona Inteview (CAI) in sequentia months. These sampes empoed sevea samping ates, which ae popotiona to the 007 ACS sampe pobabiities of seection. The Gid/Sequentia Questionnaie Test was a mai on test. This sampe was seected using constant ovea samping ates within each teatment. Each sampe consists of 30,000 addesses seected in pais. Of paticua inteest is the cacuation of the seection pobabiities to account fo pevious sampes, incuding the ACS sampe, dawn fom the same fame at diffeent points in time. This pape discusses the unique oppotunities povided b the ACS fame, sampe design, and seection fo epeimenta sampe designs and samping fames to be deived fom it. The added benefit of using the ACS sampe, given the eadi avaiabe esponse data which can be used as epeimenta contos is aso highighted. o each epeimenta design we focus on the statistica equiements, incuding eiabiit cacuations, the seection pobabiit deivations accounting fo the diffeentia, two-phase sampe design of the ACS, and povide seected esuts of the sampes b teatment. ACS Sampe Design An independent sampe fo the ACS is seected fo each of the 3,4 counties and count equivaents in the United States, incuding the Distict of Coumbia, and each of the 78 municipios in ueto Rico. The ACS samping fame is deived fom the Maste Addess ie (MA). Each ea the ACS sampes appoimate 3 miion housing unit (HU) addesses in the This epot is eeased to infom inteested paties of eseach and to encouage discussion. An views epessed on statistica, methodoogica, technica, o opeationa issues ae those of the authos and not necessai those of the U.S. Census Bueau.

2 United States and appoimate 36,000 HU addesses in ueto Rico. The sampe is seected in two phases eve ea, efeed to as the main and suppementa phase espective. The main phase sampe is seected in August/Septembe of the ea pio to the sampe ea fom an etact of the MA deiveed at that time. Appoimate 99 pecent of the tota annua ACS sampe is seected duing main phase samping and is aocated to each of the tweve month panes fo the sampe ea. In Janua of the sampe ea, a sampe of addesses that have been added to the MA since the Main MA etacts wee ceated is seected. This is nown as the Suppementa phase and accounts fo appoimate one pecent of the tota ACS sampe. These addesses ae aocated to the ast nine month panes of the ea. The samping fo each phase is caied out in two stages. The fist stage sampe consists of spitting the entie fame into five pieces, each one incuding appoimate 0 pecent of the addesses on the fame. These 0 pecent sampes ae maintained ove time and units new to the twice-ea fames ae sstematica aocated to these five patitions o sampes. These sampes ae otated each ea and the 0 pecent sampe designated to the sampe ea becomes the univese fo the secondstage of seection. This means each addess is on eigibe to be seected in sampe fo the ACS once eve five eas, minimiing espondent buden. The fist-stage sampe seection divides the sampe into two stata: one fo eisting addesses and one fo new addesses. The fist-stage samping pocedue aocates twent pecent of a new addesses to each of the 4 bacsampes and the cuent ea s fist stage sampe. The second-stage samping pocedue subsampes the units seected in the fist-stage. Based on the sie (numbe of estimated occupied housing units) of the aea the boc is in, it is assigned to one of the five second-stage stata empoed duing this stage. A eduction facto is used in two second-stage stata. The initia sampe within these two stata is educed b 8 pecent whee the oveap aeas epected to have the highest combined mai/cati coopeation ates. This, in pactice, povides seven unique ACS taget samping ates. The taget second-stage samping ates (R) used in each second-stage statum ae as foows: Base Rate 0.9 Base Rate 3 Base Rate.5 Base Rate 0.75 Base Rate Base Rate 0% Si of the seven second-stage samping ates ae a function of a base ate, which is ecacuated each ea using a taget sampe sie of 3 miion addesses (U.S.). The second-stage ates ae educed in tacts with high epected mai/cai coopeation ates. This was designed to offset the additiona cost incued fom the impementation of diffeentia CAI samping ates. The CAI samping is seected fom two categoies of cases. Maiabe addesses with neithe a esponse to the maiout no a teephone inteview ae samped at a ate of one-in-two, two-in-five, o one-in-thee. Unmaiabe addesses ae samped at a ate of two-in-thee. Refe to Asiaa (005) fo compete detais on the diffeentia CAI sampe design eseach. The ACS coects data in thee modes: mai, CATI, and CAI. The maiabe addesses seected in the second-stage sampe ae sent a questionnaie in the mai. An non-esponding addesses with a teephone numbe ae sent to CATI. A subsampe of both the non-esponding addesses afte CATI and the unmaiabe addesses is sent to CAI. o detaied infomation about the ACS pogam, pease see U.S. Census Bueau (006). The Oigina Content Test The fist epeiment, the Oigina Content Test, was designed to assess the effectiveness of obtaining accuate esponses to two diffeent vesions of a poposed fied of degee question on the ACS questionnaie, and to evauate the diffeence between asing the basic demogaphic items in a gid vesus sequentia method. This sampe design was age based on the ACS design in ode to simuate the conditions unde which the new fied of degee question ma utimate be ased. Unde this design thee wee both CATI and CAI foow-up of non-esponding addesses. This test did not incude Aasa, Hawaii, and ueto Rico. This test aso incuded a teephone e-inteview of the

3 topics of inteest such as the fied of degee question fo a espondents. As the test was to be maied out in Mach 007, the coesponding ACS pane was to seve as the conto fo this test. The taget univese fo the Oigina Content Test consisted of a vaid, esidentia housing unit addesses in a count and count equivaents in the United States, ecept Aasa, Hawaii, and ueto Rico. o moe infomation on how housing unit addesses ae deemed vaid, see Zimoa and Rose (007) and Bates (006). The samping fame was the 007 ACS main phase fist-stage sampe that was not seected in second-stage samping o in an othe opeation (taining, othe tests, etc.). In ode to detemine the taget sampe sie fo this test, the minimum detectabe diffeences (MDD) wee cacuated fo the goss diffeence ate (GDR) fo the ied of Degee question fo sampe sies of 50,000, 40,000, and 30,000. The foowing fomua was used: ( Q) DE ( ) MDD α β, whee E(GDR ), Q( ), DE the compe sampe design effect, noma distibution fo a significant diffeence between the GDR fo the two teatments, ( β ) the standad noma distibution fo a powe eve of at east 80% fo this test. α the cutoff point on the standad the cutoff point on The diffeence in the MDDs fo vaing sampe sies showed no appeciabe gain with a sampe age than 30,000. The Oigina Content Test sampe design empoed the seven ACS second-stage samping stata with each boc assigned to one of the stata. The epeimenta design of the test is shown in Tabe beow: Tabe : Epeimenta Design of the Oigina Content Test ied of Degee Question Vesion ied of Degee Question Vesion Gid Design Sequentia Design Gid Design Sequentia Design The equiements of the Oigina Content Test wee as foows: Each of the 5,000 addesses in each teatment sampe is seected with pobabiit popotiona to the ACS sampe pobabiit of seection (OS). The sampe seection shoud be a paied design. That is, fo each seected addess, the net addess on the ist is aso seected. Each teatment pane has the same numbe of addesses aocated to it. Each pai is not assigned the same questionnaie design o the same fied of degee question. The sampe seection pocedue used a paied design in which a sampe of 5,000 was seected and the neaest avaiabe neighbo is aso seected into the Oigina Content Test sampe. This heps to ensue that the two sampes of 5,000 ae simia. Whee possibe, a pais of sampe ecods came fom the same state/count/acs second-stage samping statum combination. Unbiased samping weights wee aso cacuated. Each sampe of 5,000, when weighted, is epesentative of the entie univese. Each seected addess was designated to one of fou teatment panes based on the coss of the two teatments: fied of degee question vesion and gid o sequentia vesion of the shot-fom data questionnaie. Each pane had an equa numbe of sampe cases aocated to it. o futhe detai on sampe design, see Joshipua and Hefte (006). The Oigina Content Test sampe design was diven b the equiement that each of the 5,000 addesses in each teatment sampe be seected with pobabiit popotiona to the ACS sampe pobabiit of seection (OS). The tota numbe

4 seected fo the Oigina Content Test sampe was 30,000. Each design pane was aocated 7,500 addesses. The tota numbe of ecods aocated to each individua teatment was 5,000. See Joshipua and Hefte (007a) fo additiona esuts. Deivation of the Seection obabiities fo the Oigina Content Test Define the Content Test OS, (CT) within each count /sub-statum to be: ( CT ) C [] whee C epesents a constant scaa used to achieve the desied sampe sie of 5,000 epesents the facto of that is popotiona to the ACS second-stage OS fo the i th count, j th fist-stage ACS samping statum, and th ACS second-stage samping statum. i,..., ( # of counties avaiabe on the Content Test samping fame). j,..., ( # of fist-stage stata in count i),..., ( # of second-stage stata in fist-stage statum j The equiement that the seection pobabiities be popotiona to the ACS eads to the foowing necessa condition: n R whee [] R epesents the ovea taget samping ate fo the th ACS second-stage statum. epesents the tota numbe of addesses avaiabe in the cuent ea s (ea 0) ACS fist-stage sampe fo the i th count, j th fist-stage ACS samping statum, and th ACS second-stage statum. n epesents the cuent ea s ACS second-stage sampe fo the i th count, j th fist-stage ACS samping statum, and th ACS second-stage statum. epesents the tota numbe of vaid addesses on the Main 007 MA etact in the i th count, j th fist-stage ACS samping statum, and th ACS second-stage statum. Within each count, fist-stage samping statum, and second-stage samping statum, an adjustment to R is made so that the second-stage OS () ieds the desied ovea sampe sie as foows: R [3] Thus, R can be witten as: R [4] We have estabished that we need to find such that: n R [5] Substituting [4] fo R we get:

5 n [6] We woud ie to epess in tems of. Since the pobabiit of not being seected in the ACS second-stage sampe is ( ), we can use the eationship to ewite [6] as: ( ) n [7] ( ) Soving fo we get: [8] [9] ( ) Substituting this in [] we get: C ( ) [0] We equie that i j Substituting fom [0] we get: i j Soving fo C we get: ( n ) 5, 000 [] ( ) C [] ( n ) 5, 000 C 5,000 i j ( ) ( n ) [3] Theefoe the foowing is the pobabiit of seection fo the i th count, j th fist-stage statum, and th second-stage statum: 5,000 i j ( ) ( n ) ( ) [4]

6 Since b constuct when appied to the avaiabe univese, n, ieds the same taget samping ate as the ACS ate, R, with espect to the ovea univese,, the Oigina Content Test Base Weight (the invese of the ovea pobabiit of seection) fo each ecod in sub-statum is cacuated as: ( C R ) CTBW [5] In pactice, the pobabiit (CT) fo each unit was simp cacuated as: (in fist - stage sampe) ( CT ) C. (not in second -stage) The Gid/Sequentia Questionnaie Test Afte the Oigina Content Test was canceed, the Gid/Sequentia Questionnaie Test was enacted to on evauate potentia esponse diffeences fom asing the basic demogaphic items using a gid vesus sequentia fomat. The ACS has taditiona used a hoionta gid fomat, whee the names ae isted down the side of the page and the questions appea acoss the top of the questionnaie, to coect the basic demogaphic data. Census 00 pans to use a sequentia fomat whee each peson s data appea in a distinct coumn, and within each coumn, the names ae at the top and the questions ae isted down the page. In suppot of consistenc effots between the ACS and Census, the ACS tested whethe the aout fo these items affects esponse. This test, efeed to as the Gid/Sequentia Questionnaie Test, was impemented to assess if one fomat impoves data quait and esponse ates. It was a mai on test and did not incude Aasa, Hawaii, o ueto Rico. The taget univese fo the 007 Gid/Sequentia Questionnaie Test consists of a vaid, esidentia housing unit addesses in a count and count equivaents in the United States, ecuding Aasa, Hawaii, and ueto Rico. A sampe with a taget sie of 30,000 was seected fom the 007 ACS Main fist-stage sampe that was not seected in the ACS second-stage samping o in an othe opeation (taining, othe tests, etc.). Because this test was impemented instead of the Oigina Content Test, the units seected in that sampe wee sti eigibe to be seected fo this test. Sampe seection used ates that achieve equa ovea pobabiities of seection within esponse statum fom the samping univese in ode to have a sufficient amount of data to anae esponses fom ow esponse aeas as we as the fu esuts. The 006 ACS Content Test aso had a simia sampe design. See Asiaa (006) fo moe detais. The basic epeimenta design of the test is dispaed in Tabe beow. Tabe : Epeimenta Design of the Gid/Sequentia Questionnaie Test Gid Questionnaie Design Sequentia Questionnaie Design High Response Statum Low Response Statum High Response Statum Low Response Statum The sampe design equiements fo this test wee as foows: Each of the 5,000 addesses in each teatment sampe has an equa ovea pobabiit of seection fom the samping univese within esponse statum. 60% of the sampe addesses ae seected fom the ow esponse statum and 40% ae seected fom the high esponse statum. The sampe seection is a paied design. That is, fo each seected addess, the net addess on the ist is aso seected. One addess in each pai is andom assigned to the Gid teatment pane and the othe to the Sequentia teatment pane.

7 A census tacts wee statified b thei Census 000 ong fom mai esponse ate into eithe a high o ow esponse statum. The two stata wee defined such that the high esponse statum contained housing unit addesses esiding in tacts with a mai esponse ate highe than o equa to 63%. The emaining tacts wee assigned to the ow esponse statum. The 63% cutoff point paces appoimate 75% of the tota numbe of addesses in the high esponse statum. The Gid/Sequentia Questionnaie Test sampe was aocated so that the epected numbe of mai etuns was equa within both stata. This wi, in epectation, esut in simia vaiances b esponse statum. The sampe seection pocedue used a paied design in which a sampe of 5,000 was seected and the neaest avaiabe neighbo was aso seected into the Gid Sequentia Questionnaie Test sampe. Whee possibe, a pais of sampe ecods came fom the same esponse statum/state/count/acs fist-stage samping statum/acs second-samping statum combination. Unbiased samping weights wee aso cacuated. Each sampe of 5,000, when weighted, is epesentative of the univese. The samping pocedue aso andom assigned each sampe of 5,000 to one of two teatment panes: gid o sequentia questionnaie design. The samping fame fo the test was the unused potion of the 007 ACS Main fist-stage ACS sampe. The sampe seection was designed such that, within esponse statum, each addess in the fame has equa pobabiit of seection fom the univese. To achieve this, thee stages of samping needed to be accounted fo: ) ACS fist-stage samping, ) ACS secondstage samping, and 3) the Gid/Sequentia (o thid stage) sampe seection. o futhe detais on the sampe design, see Joshipua and Hefte (007b). Deivation of the Seection obabiities fo the Gid/Sequentia Questionnaie Test The Gid/Sequentia Questionnaie Test pobabiit of seection, (GS), fom the ecods in the ACS fist-stage sampe not seected in the ACS second-stage sampe, within each count/fist-stage statum/second-stage statum/esponse statum can be denoted as:. whee i,..., ( # of counties avaiabe on the Gid/Sequentia Questionnaie samping fame (GSRAME)). j,..., ( # of substata in count j),..., ( # of second-stage stata in count i and fist-stage statum j), ( ow esponse statum, high esponse statum) The equiement of each addess in the fame having equa pobabiit of seection fom the univese eads to the foowing necessa condition: n whee t [] epesents the tota numbe of addesses avaiabe in the cuent ea s (ea 0) ACS fist-stage sampe fo the i th count, j th fist-stage ACS samping statum, th ACS second-stage statum, and the th esponse statum. n epesents the cuent ea s ACS second-stage sampe fo the i th count, j th fist-stage ACS samping statum, th ACS second-stage statum, and the th esponse statum. epesents the tota numbe of vaid addesses on the Main 007 MA etact in the i th count, j th fist-stage ACS samping statum, th ACS second-stage statum, and the th esponse statum. t epesents the sampe sie fo the th esponse statum (i.e. t 0.6 5,000 fo the ow esponse statum and t 0.4 5,000 fo the high esponse statum) epesents the tota numbe of vaid addesses on the Main 007 MA etact in each esponse statum.

8 Equation [] can aso be witten as: since ( ) t [] Soving fo ( ) n [3], we get: t [4] ( ) Anaogous to the cacuation of the Oigina Content Test base weight deived eaie, it then foows fom [] that the Gid/Sequentia Questionnaie Test Base Weight (GSBW) fo each ecod in esponse statum is cacuated as: GSBW [5] t Theefoe, the ovea pobabiit fom the univese,, was then cacuated as foows: (in fist-stage sampe) (not in second-stage sampe) (in thid stage sampe), whee (in thid-stage sampe) is the pobabiit of seection used to sampe addesses fom the Gid/Sequentia samping fame n. Seected Resuts fo the Gid/Sequentia Questionnaie Test Tabe 3 beow shows the two ovea pobabiities of seection (OS) fom the samping univese: Tabe 3: Ovea OS fom the Samping Univese b Response Statum Response Statum Ovea obabiit of Seection High Low The tota numbe in sampe was 9,998. Both the gid teatment pane and the sequentia teatment pane contained 4,999 addesses. Thee wee 9,000 ecods in the ow esponse statum and 5,999 ecods in the high esponse statum in each teatment pane. Tabe 4 shows the pecent of the entie sampe in each esponse statum. Tabe 4: ecent in Sampe b Response Statum Response Statum umbe in Sampe ecent of Sampe High, % Low 8, % Tota 9,998 00% See Joshipua and Hefte (007c) fo futhe esuts.

9 The 007 ACS Content Test Once funding was eceived fo fisca ea 007, we woed quic to einstate the epeimenta testing of the new ied of Degee question in an effot caed the 007 ACS Content Test. This test was designed to assess the effectiveness of obtaining accuate esponses to two diffeent vesions of a poposed fied of degee question on the ACS questionnaie. A seconda goa of this test was to evauate an change in the tenue distibution caused b changes in question woding that wee enacted fo the 00 census and thus, adopted fo the 008 ACS questionnaie. The 007 ACS Content Test was impemented in addition to the Gid/Sequentia Questionnaie Test; both tests wee eecuted in ieu of the Oigina Content Test. The 007 ACS Content Test sampe design is age based on the ACS design in ode to simuate the conditions unde which the new fied of degee question ma utimate be ased. Unde this design thee is both CATI and CAI foow-up of non-esponding addesses. This test does not incude Aasa, Hawaii, and ueto Rico. This test aso incudes a teephone e-inteview of the topics of inteest such as the tenue and ied of Degee questions fo a esponding househods. This test was maied out in Ju 007, so the coesponding ACS pane is to seve as the conto fo this epeiment. This test has the same taget univese, taget sampe sie, and sampe design as the Oigina Content Test. Howeve, the samping fame is the 007 Main and Suppementa ACS fist-stage sampe that was not seected in the ACS second-stage samping o in an othe opeation (taining, othe tests, etc.). Distinctions between the two phases wee necessa in the pobabiit of seection cacuation. The equiements of the Content Test sampe wee: Each of the 5,000 addesses in each teatment sampe is seected with pobabiit popotiona to the ACS sampe pobabiit of seection. The sampe seection shoud be a paied design. That is, fo each seected addess, the net addess on the ist is aso seected. Each teatment pane has the same numbe of addesses aocated to it. Both addesses within a pai ae not assigned the same fied of degee question. The sampe seection pocedue used a paied design in which a sampe of 5,000 is seected and the neaest avaiabe neighbo is aso seected into the Content Test sampe. Whee possibe, a pais of sampe ecods came fom the same state/count/acs second-samping statum combination. Unbiased samping weights ae aso cacuated. Each sampe of 5,000, when weighted, is epesentative of the univese. Each sampe of 5,000 was andom assigned to one of two teatment panes: vesion of the fied of degee question o vesion. The Content Test sampe design was diven b the equiement that each of the 5,000 addesses in each teatment sampe be seected with pobabiit popotiona to the ACS sampe pobabiit of seection (OS). The fame fo this test was the unused potion of the fist stage ACS sampe. This is the potion of both the Main and Suppementa fist-stage sampe not seected in the second-stage ACS sampe o the 007 Gid/Sequentia Questionnaie Design Test. o futhe detais on sampe design, see Joshipua and Hefte (007d). Deivation of the Seection obabiities fo the ACS Content Test Define ACS Content Test OS, (CT) to be: ( CT ) C [] whee C epesents a constant scaa used to achieve the desied sampe sie of 5,000 epesents the facto of that is popotiona to the ACS second-stage OS fo the i th count, j th fiststage ACS samping statum, th second-stage samping statum, th samping phase, and s th Gid/Sequentia esponse statum. i,..., ( # of counties avaiabe on the content samping fame). j,..., ( # of fist-stage stata count i),..., ( # of second-stage stata in count i and fist-stage statum j)

10 s, ( main, suppementa), ( Gid/Sequentia ow esponse statum, Gid/Sequentia high esponse statum) The equiement stated above eads to the foowing necessa condition: n m R [] whee R epesents the ovea taget samping ate fo the th ACS second-stage statum. epesents the tota numbe of addesses avaiabe in the cuent ea s (ea 0) ACS fist-stage sampe fo the i th count, j th fist-stage ACS samping statum, th ACS second-stage statum, th samping phase, and s th esponse statum. n epesents the cuent ea s ACS second-stage sampe fo the i th count, j th fist-stage ACS samping statum, th ACS second-stage statum, th samping phase, and s th esponse statum. m epesents the numbe in sampe in the Gid/Sequentia Questionnaie Design Test fo the i th count, j th fist-stage ACS samping statum, th ACS second-stage statum, th samping phase, and s th esponse statum. (ote that this numbe is 0 when.) epesents the tota numbe of vaid addesses in the i th count, j th fist-stage ACS samping statum, th ACS second-stage statum, th samping phase, and s th esponse statum. As noted eaie, duing ACS samping, within each count, fist-stage samping statum, and second-stage samping statum, an adjustment to R is made so that the second-stage OS () ieds the desied ovea sampe sie as foows: R [3] Thus, R can be witten as: R [4] We have estabished in [] that we need to find such that: n m R [5] Substituting [4] fo R we get: n m [6]

11 Since the pobabiit of not being seected in the Gid/Sequentia Questionnaie Design Test, within each Gid/Sequentia esponse statum, is ( GOS ) we have the foowing eationship: As noted eaie, ( GOS ) ( n ) n m [7] whee GOS s is two times the pobabiit of seection used fo the Gid/Sequentia Questionnaie Design Test (GSOS s ) since two sampes of 5,000 wee seected fo the Gid/Sequentia Test and GOS s is equa to eo. ( ) n [8] We can ewite [5] as: Soving fo we get: ( ) ( GOS ) [9] ( ) ( GOS ) [0] Substituting this in [] we get: C ( ) ( GOS ) [] We equie that i j s Soving fo C in [], we get C ( n m ) 5,000 [] C i j s 5,000 Let Q ( n m ) ( n m ) [3] The foowing pobabiities of seection ae assigned to each ecod in the i th count, j th fist-stage statum, th second-stage statum, th samping phase, and the s th esponse statum:

12 o cases eigibe fom the Main phase fist-stage sampe: 5,000 i j s Q ( ) ( GOS ) s s s [4] o cases eigibe fom on the Suppementa phase fist-stage sampe: 5,000 i j s Q s ( ) s [5] ote: Using the definition of Q in equation [], we get that i j Q R n. Thus the ijs summation Q can aso be witten as sampe sie fo the ACS. n i j, which is equa to the tota epected Since b constuct when appied to the avaiabe univese, Q, ieds the taget ACS samping ate, R, with espect to the ovea univese,, it foows that the ACS Content Test Base Weight (CTBW) fo each ecod in sub-statum is cacuated as: ( C R ) CTBW [6] The pobabiit fo each unit, (CT), was theefoe cacuated as foows: (in fist - stage sampe) ( CT ) C. (not in second - stage) (not in Gid/Sequentia sampe) Seected Resuts fo the ACS Content Test The tota numbe of cases in the ACS Content Test sampe is 30,000. Both panes wee aocated 5,000 addesses (40% and 60% fom the espective esponse stata). The ACS Content Test was designed such that the pecent of the sampe in each unique taget samping ate statum woud be simia to the 007 ACS. The compaison between the two is shown in Tabe 5 beow. Tabe 5: ecent of Content Test Sampe b Statum Second-Stage Samping Rate 007 Content Test 007 ACS Base Rate.59%.56% 0.9 Base Rate 4.59% 4.60% 3 Base Rate 3.8% 3.8%.5 Base Rate 3.83% 3.8% 0.75 Base Rate 0.33% 0.33% Base Rate.77%.78% 0% 4.09% 4.09% See Joshipua and Hefte (007e) fo futhe esuts.

13 Concusion The ACS sampe design has povided an eceent jumping off point o spingboad fo these thee epeimenta sampe designs. The samping fames that wee deived fom it have enabed sampe seections that wi not ovebuden the househods seected whie achieving each design s objectives. Each addess seected in these epeimenta sampes is not eigibe to be in an ACS sampe o an ACS eated sampe fo the net fou eas. The samping fames aso aow fo man sampe designs that mimic the ACS at eithe phase of samping o uses a constant ovea samping ate fo each teatment. In addition, othe suves ma use the ACS to design high efficient sma-scae sampe designs in which the can combine the ACS esponse data. Aso, the pobabiities of seection aead assigned to the fist-stage sampe easi faciitate these sampe designs, whethe mioing the ACS o not. Refeences Asiaa, M. (005), Ameican Communit Suve Reseach Repot: Diffeentia Sub-Samping in the Compute Assisted esona Inteview Sampe Seection in Aeas of Low Coopeation Rates, Intena Census Bueau Memoandum to R. Singh fom D. Hubbe, Washington, DC, ebua 5, 005. Asiaa M. (006), Epeimenta Design fo the 006 Ameican Communit Suve Content Test, 006 oceedings of the Joint Statistica Meeting, Ameican Statistica Association, Washington DC. Bates, L. M. (006), Editing the MA Etacts and Ceating the Unit ame Univese fo the Ameican Communit Suve, Intena U.S. Census Bueau Memoandum fom D. Kostanich to L. Bummeman, Daft, Washington, DC, Septembe 0, 006. Joshipua, M. and Hefte, S. (006) Specifications fo Seecting the 007 Ameican Communit Suve Content Test Sampe ied of Degee Question Design, 007 Ameican Communit Suve Samping Memoandum Seies #ACS07-S-8a, Intena U.S. Census Bueau Memoandum fom D. Whitfod to S. Schechte, Daft, Washington, DC, Decembe 7, 006. Joshipua, M. and Hefte, S. (007a) 007 Content Test Sampe Resuts Documentation Memoandum, 007 Ameican Communit Suve Samping Memoandum Seies #ACS07-S-, Intena U.S. Census Bueau Memoandum fom A. avao to D. Whitfod, Daft, Washington, DC, Janua 30, 007. Joshipua, M. and Hefte, S. (007b) Specifications fo Seecting the 007 Gid/Sequentia Questionnaie Test Sampe, 007 Ameican Communit Suve Samping Memoandum Seies #ACS07-S-8b, Intena U.S. Census Bueau Memoandum fom D. Whitfod to S. Schechte, Washington, DC, Janua 8, 007. Joshipua, M. and Hefte, S. (007c) 007 Gid/Sequentia Questionnaie Test Sampe Resuts Documentation Memoandum, 007 Ameican Communit Suve Samping Memoandum Seies #ACS07-S-3, Intena U.S. Census Bueau Memoandum fom A. avao to D. Whitfod, Washington, DC, ebua 6, 007. Joshipua, M. and Hefte, S. (007d) Specifications fo Seecting the 007 Ameican Communit Suve Content Test Sampe, 007 Ameican Communit Suve Samping Memoandum Seies #ACS07-S-4, Intena U.S. Census Bueau Memoandum fom D. Whitfod to S. Schechte, Daft, Washington, DC, June 9, 007. Joshipua, M. and Hefte, S. (007e) 007 Ameican Communit Suve Content Test Sampe Resuts, 007 Ameican Communit Suve Samping Memoandum Seies #ACS07-S-5, Intena U.S. Census Bueau Memoandum fom A. avao to D. Whitfod, Washington, DC, June 8, 007. U.S. Census Bueau (006), Design and Methodoog: Ameican Communit Suve, U.S. Govenment inting Office, Washington, DC, 006 ( Zimoa, M. and Rose, S. (007), Custome Requiements Documents fo Ameican Communit Suve Data oducts, Vesion.0, Intena Census Bueau Memoandum, Washington, DC, June 3, 007.