大学入学考试中心研究用测试的抽样方法

179BulletinofTestingandAssessment大學入學考試中心研究用測試的抽樣方法考試學刊第五期2008.12ՕᖂԵᖂەᇢխ֨ઔߒشྒྷᇢऱࢼᑌֱऄ೴ႁ଩ʳʳຑટဎʳՕᖂԵᖂەᇢխ֨!ኴ૞ՕᖂԵᖂەᇢխ֨ၞ۩ઔߒشྒྷᇢழΔආشψ೏խسࢼᑌֱऄωၞ۩ᑌءࢼᑌΖࢼᑌመ࿓ਢ٣ࠉᖕছԫڣٺ೏խᖂྒྷࢨਐەەس౨Ժ।෼Δ܂੡ءڣ৫ᇠீᖂس౨Ժऱ೶ەࠉᖕΔ٦ᙇנᖂسګᜎ։಻ፖ٤ഏەسઌۿհԿࠩնࢬ೏խΔٵழᒔᎁຍࠄᖂீ२ࠟڣᖂྒྷࢨਐەګᜎ।෼ਢ᡹ࡳऱΔঞނຍࠄ೏խऱ೏ԿᖂسิٽګࢼᑌᑌءΖڼऄऱᚌរਢฤٽڶயࢤΕױྒྷࢤࡉ១પऱ଺ঞΔ׊ڶڍጟิٽᖂீࠎྒྷᇢԳ୉ᙇشΖ܀ڶழࢼᑌਮዌլਢ٤ഏࢬڶ೏խΔۖႛওૻڇ௽ࡳऱᑇࢬ೏խΔءխ֨ઔ࿇ψ௽ࡳ՗ᆢ່ᔞףᦞऄωΔאԲڻ๵ቤࠐኙ௽ࡳ՗ᆢޣ൓່ᔞףᦞΔࠌףᦞ৵ᑌء౨Ժ։ؒ౨ፖئᆢ։ؒઌۿΖء֮տฯࢼᑌፖףᦞֱऄऱ෻ᓵΔೈאኔࠏᎅࣔޡᨏ؆Δࠀٌזᖂீᑌء᡹ࡳࢤᛀ᧭ऱመ࿓Ζᣂ᝶ဲΚࢼᑌֱऄΕԲڻ๵ቤ೴ႁ଩ΔՕᖂԵᖂەᇢխ֨ᇷ෡റ୮ຑટဎΔՕᖂԵᖂەᇢխ֨റ॰ࡡ୉180BulletinofTestingandAssessment考試學刊大學入學考試中心研究用測試的抽樣方法第五期2008.12TheSamplingMethodEmployedbyCollegeEntranceExaminationCenterYa-LunOu,Chiou-HwaLienCollegeEntranceExaminationCenterAbstractCollegeEntranceExaminationCenter(CEEC)employed“thehighschoolstudentssamplingmethod”toconductpretests.Basedonthetestscoresofthepreviousyear’suniversityentranceexams,acombinationof3to5seniorhighschoolsistobesampledtoexaminewhethertheirstudents’scoredistributionissimilartothescoredistributionofthepopulationoftheyear.Ifthetwosetsofdistributionaresimilarandthescoredistributionoftheselectedhighschoolshasbeenstableinthepasttwoyears,theseniorsoftheseselectedhighschoolswillbechosenasasample.Theadvantageofthissamplingmethodisthatitiseffective,measurableandfitintheprincipleofparsimony.Meanwhile,thismethodcanhelpgroupcombinationsinalargevarietyforvariouspurposesofresearch.However,thesamplingframedoesnotincludeallhighschoolsinTaiwan;itislimitedtoasmallnumberofspecifichighschoolsonly.Tosolvetheproblem,CEEChasdevelopeda“specificsubgroupoptimalweightingmethod”bymeansofquadraticprogramming.Thisarticleaimstodescribeanddemonstratethetheoryofsampling,theweightingmethod,andthetestingproceduresforthestabilityofsampling.Keywords:samplingmethod,quadraticprogrammingYa-LunOu,SeniorSpecialist,CollegeEntranceExaminationCenterChiou-HwaLien,Specialist,CollegeEntranceExaminationCenterছߢՕᖂԵᖂەᇢխ֨(១ጠՕەխ֨)إڤەᇢፖᠲ஄ऱࡎᠲՠ܂Δഗ࣍অയ෻طΔᇢᠲࠀլၞ۩ቃᇢΖ੡ࠌࡎᠲඒ඄౨ኙᇢᠲᣄ৫ڶࢬ༳༽Δޢڣઃ๻ૠઔߒشᇢ࠴Δൕ٤ഏ೏խسئᆢխࢼנࠠז।ࢤऱᖂسᑌءၞ۩ྒྷᇢΔྒྷᇢ৵ૠጩᇢᠲᣄ৫ፖᦸܑ৫Δຑٵઔߒشᇢ࠴༼ࠎࡎᠲඒ඄೶ەΖ੡൓ࠩᄷᒔऱᣄ৫۷ૠଖΔءխ֨ࠉᖕอૠᖂൄشऱԿႈ଺ঞΚψڶயωΕψױྒྷၦω֗ψ១໢ωΔࠐەၦ෻უऱࢼᑌֱऄ(ࣥ༡ੳΕຫإପΔ1999)Ζψڶயωਢਐࢼᑌᑌء౨壄ᒔං۷ئᆢ।෼Δࠐ֘ਠ٤ഏەس౨ԺΖᖂઝ౨Ժྒྷ᧭(១ጠᖂྒྷ)ፖਐࡳઝؾەᇢ(១ጠਐە)ऱئᆢ༉ਢ٤ഏԼ༓ᆄټऱ೏խسΔՕەխ֨ྒྷᇢᑌءԳᑇឈႛڶ500-900Գؐ׳Δ܀ࠡ౨Ժ։಻ؘႊ൷२ئᆢ։಻Ζψױྒྷၦωਢਐࢼᑌਮዌ(thesamplingframe)ႊຏመ᡹ࡳࢤᛀྒྷΔءխ֨ऱࢼᑌਮዌਢ٤ഏٺ೏խΔޢࢬ೏խڇ२ࠟڣਐەࢨᖂྒྷऱګᜎ։಻૞ຏመٵᔆࢤە᧭Δຏመە᧭ऱ೏խթ๯౏ԵࢼᑌਮዌΖψ១໢ωਐฤٽԫ౳อૠֱऄऱ១પ଺ঞ(principleofparsimony)Δլ܀ࢼᑌ࿓ݧ១໢Δྒྷᇢՠ܂Ո౨ઊᙒઊԺΖՕەխ֨ᎁ੡ᜯ໱ൕඒ৛խࢼנ֟ᑇᖂسऱ࿜ฃΔᖂீ۩ਙྤऄ಻ٽΔՈᄎᐙ᥼ᖂس܂࿠ൣፃΔྒྷᇢ࿨࣠լߩא֘ਠᖂس଺ڶ౨ԺΔࢬאᙟᖲࢼᑌլฤٽ෻უऱ១໢଺ঞΖءխ֨๻უऱ១໢Δਢࢼᑌऱ೏խீᑇ။֟။ړΔࠩຍ༓ࢬ೏խਜྒྷழઃਢ٤ڣ్ਜྒྷΔ࠹ྒྷऱᖂس᜔ᑇ༉౨ז।ئᆢΖൕՂ૪ጵٽհΔՕەխ֨ࢼᑌิٽԿࠩնࢬ೏խ੡ᑌءΔᑌءᖂீ२ࠟڣᖂྒྷࢨਐەګᜎ।෼ਢ᡹ࡳऱΔ׊ᑌءᖂسᖞ᧯ऱᖂྒྷࢨਐەګᜎ։಻ፖئᆢઌۿΔࢬאࢼᑌ৵ྒྷᇢਢආᑌءᖂீ٤ڣ్ԫದ࠹ྒྷΖڇڼᏁޣՀΔ੡ԱሒࠩຍᑌऱࢼᑌᏁޣΔءխ֨۞۩ၲ࿇ψ೏խسࢼᑌֱऄωΰࣥ٠ᔃΔ1990αፖψ௽ࡳ՗ᆢ່ᔞףᦞऄωΰᄘݛີΔ2008αΖء֮ؾऱܛտฯءխ֨ࢼᑌፖףᦞֱऄऱ෻ᓵፖޡᨏΔࠀॵኔࠏᎅࣔΔڇտฯֱऄհছΔ٣ᎅࣔᖂீᑌء᡹ࡳࢤᛀ᧭ऱመ࿓Ζ181BulletinofTestingandAssessment大學入學考試中心研究用測試的抽樣方法考試學刊第五期2008.12TheSamplingMethodEmployedbyCollegeEntranceExaminationCenterYa-LunOu,Chiou-HwaLienCollegeEntranceExaminationCenterAbstractCollegeEntranceExaminationCenter(CEEC)employed“thehighschoolstudentssamplingmethod”toconductpretests.Basedonthetestscoresofthepreviousyear’suniversityentranceexams,acombinationof3to5seniorhighschoolsistobesampledtoexaminewhethertheirstudents’scoredistributionissimilartothescoredistributionofthepopulationoftheyear.Ifthetwosetsofdistributionaresimilarandthescoredistributionoftheselectedhighschoolshasbeenstableinthepasttwoyears,theseniorsoftheseselectedhighschoolswillbechosenasasample.Theadvantageofthissamplingmethodisthatitiseffective,measurableandfitintheprincipleofparsimony.Meanwhile,thismethodcanhelpgroupcombinationsinalargevarietyforvariouspurposesofresearch.However,thesamplingframedoesnotincludeallhighschoolsinTaiwan;itislimitedtoasmallnumberofspecifichighschoolsonly.Tosolvetheproblem,CEEChasdevelopeda“specificsubgroupoptimalweightingmethod”bymeansofquadraticprogramming.Thisarticleaimstodescribeanddemonstratethetheoryofsampling,theweightingmethod,andthetestingproceduresforthestabilityofsampling.Keywords:samplingmethod,quadraticprogrammingYa-LunOu,SeniorSpecialist,CollegeEntranceExaminationCenterChiou-HwaLien,Specialist,CollegeEntranceExaminationCenterছߢՕᖂԵᖂەᇢխ֨(១ጠՕەխ֨)إڤەᇢፖᠲ஄ऱࡎᠲՠ܂Δഗ࣍অയ෻طΔᇢᠲࠀլၞ۩ቃᇢΖ੡ࠌࡎᠲඒ඄౨ኙᇢᠲᣄ৫ڶࢬ༳༽Δޢڣઃ๻ૠઔߒشᇢ࠴Δൕ٤ഏ೏խسئᆢխࢼנࠠז।ࢤऱᖂسᑌءၞ۩ྒྷᇢΔྒྷᇢ৵ૠጩᇢᠲᣄ৫ፖᦸܑ৫Δຑٵઔߒشᇢ࠴༼ࠎࡎᠲඒ඄೶ەΖ੡൓ࠩᄷᒔऱᣄ৫۷ૠଖΔءխ֨ࠉᖕอૠᖂൄشऱԿႈ଺ঞΚψڶயωΕψױྒྷၦω֗ψ១໢ωΔࠐەၦ෻უऱࢼᑌֱऄ(ࣥ༡ੳΕຫإପΔ1999)Ζψڶயωਢਐࢼᑌᑌء౨壄ᒔං۷ئᆢ।෼Δࠐ֘ਠ٤ഏەس౨ԺΖᖂઝ౨Ժྒྷ᧭(១ጠᖂྒྷ)ፖਐࡳઝؾەᇢ(១ጠਐە)ऱئᆢ༉ਢ٤ഏԼ༓ᆄټऱ೏խسΔՕەխ֨ྒྷᇢᑌءԳᑇឈႛڶ500-900Գؐ׳Δ܀ࠡ౨Ժ։಻ؘႊ൷२ئᆢ։಻Ζψױྒྷၦωਢਐࢼᑌਮዌ(thesamplingframe)ႊຏመ᡹ࡳࢤᛀྒྷΔءխ֨ऱࢼᑌਮዌਢ٤ഏٺ೏խΔޢࢬ೏խڇ२ࠟڣਐەࢨᖂྒྷऱګᜎ։಻૞ຏመٵᔆࢤە᧭Δຏመە᧭ऱ೏խթ๯౏ԵࢼᑌਮዌΖψ១໢ωਐฤٽԫ౳อૠֱऄऱ១પ଺ঞ(principleofparsimony)Δլ܀ࢼᑌ࿓ݧ១໢Δྒྷᇢՠ܂Ո౨ઊᙒઊԺΖՕەխ֨ᎁ੡ᜯ໱ൕඒ৛խࢼנ֟ᑇᖂسऱ࿜ฃΔᖂீ۩ਙྤऄ಻ٽΔՈᄎᐙ᥼ᖂس܂࿠ൣፃΔྒྷᇢ࿨࣠լߩא֘ਠᖂس଺ڶ౨ԺΔࢬאᙟᖲࢼᑌլฤٽ෻უऱ១໢଺ঞΖءխ֨๻უऱ១໢Δਢࢼᑌऱ೏խீᑇ။֟။ړΔࠩຍ༓ࢬ೏խਜྒྷழઃਢ٤ڣ్ਜྒྷΔ࠹ྒྷऱᖂس᜔ᑇ༉౨ז।ئᆢΖൕՂ૪ጵٽհΔՕەխ֨ࢼᑌิٽԿࠩնࢬ೏խ੡ᑌءΔᑌءᖂீ२ࠟڣᖂྒྷࢨਐەګᜎ।෼ਢ᡹ࡳऱΔ׊ᑌءᖂسᖞ᧯ऱᖂྒྷࢨਐەګᜎ։಻ፖئᆢઌۿΔࢬאࢼᑌ৵ྒྷᇢਢආᑌءᖂீ٤ڣ్ԫದ࠹ྒྷΖڇڼᏁޣՀΔ੡ԱሒࠩຍᑌऱࢼᑌᏁޣΔءխ֨۞۩ၲ࿇ψ೏խسࢼᑌֱऄωΰࣥ٠ᔃΔ1990αፖψ௽ࡳ՗ᆢ່ᔞףᦞऄωΰᄘݛີΔ2008αΖء֮ؾऱܛտฯءխ֨ࢼᑌፖףᦞֱऄऱ෻ᓵፖޡᨏΔࠀॵኔࠏᎅࣔΔڇտฯֱऄհছΔ٣ᎅࣔᖂீᑌء᡹ࡳࢤᛀ᧭ऱመ࿓Ζ182BulletinofTestingandAssessment考試學刊大學入學考試中心研究用測試的抽樣方法第五期2008.12ԫΕ೏խᖂீᑌء᡹ࡳࢤᛀ᧭Օەխ֨ྒྷᇢՠ܂ਢאᑌءᖂீ٤ڣ్ᖂس੡ኙွΔࢬאࢼᑌছ٣૞Աᇞޢࢬ೏խऱ౨Ժ࿓৫Ζءխ֨೗๻ٵԫࢬ೏խऱ࿓৫ດڣՕڍ᡹ࡳΔૉװڣᖂس।෼ᚌฆऱᖂீΔվڣᇠீᖂسٍ।෼ᚌฆΔঞຍࢬ೏խ२ڣᖂس౨Ժਢ᡹ࡳऱΙ֘հࠟڣ౨Ժ஁ฆৰՕऱᖂீΔᇠீᖂس౨Ժ।෼ለ੡լ᡹ࡳΖءխ֨ऱࢼᑌֱ