/Users/andrea/_magisterarbeit/korpus/clean/testkorpus/29/file16.html NN ----------------------------------------- : Statistics NP Glossary NN Basic JJ Definitions NNS Basic JJ Definitions NNS Contents NNS Statistical NP Inference NN Experiment NN Experimental JJ or CC Sampling VVG Unit NP Population NP Sample NP Parameter NN Statistic NN Sampling NN Distribution NN Estimate NP Estimator NN Estimation NN Back RB to TO Main JJ Contents NNS Statistical NP Inference NN Statistical NP Inference NN makes VVZ use NN of IN information NN from IN a DT sample NN to TO draw VV conclusions NNS inferences NNS about IN the DT population NN from IN which WDT the DT sample NN was VBD taken VVN . SENT Experiment NN An DT experiment NN is VBZ any DT process NN or CC study NN which WDT results VVZ in IN the DT collection NN of IN data NNS , , the DT outcome NN of IN which WDT is VBZ unknown JJ . SENT In IN statistics NNS , , the DT term NN is VBZ usually RB restricted VVN to TO situations NNS in IN which WDT the DT researcher NN has VHZ control NN over IN some DT of IN the DT conditions NNS under IN which WDT the DT experiment NN takes VVZ place NN . SENT Example NN Before IN introducing VVG a DT new JJ drug NN treatment NN to TO reduce VV high JJ blood NN pressure NN , , the DT manufacturer NN carries VVZ out RP an DT experiment NN to TO compare VV the DT effectiveness NN of IN the DT new JJ drug NN with IN that DT of IN one CD currently RB prescribed VVN . SENT Newly RB diagnosed VVN subjects NNS are VBP recruited VVN from IN a DT group NN of IN local JJ general JJ practices NNS . SENT Half NN of IN them PP are VBP chosen VVN at IN random JJ to TO receive VV the DT new JJ drug NN , , the DT remainder NN receiving VVG the DT present JJ one NN . SENT So RB , , the DT researcher NN has VHZ control NN over IN the DT type NN of IN subject JJ recruited VVN and CC the DT way NN in IN which WDT they PP are VBP allocated VVN to TO treatment NN . SENT Experimental JJ or CC Sampling VVG Unit NN A DT unit NN is VBZ a DT person NN , , animal NN , , plant NN or CC thing NN which WDT is VBZ actually RB studied VVN by IN a DT researcher NN . SENT the DT basic JJ objects NNS upon IN which WDT the DT study NN or CC experiment NN is VBZ carried VVN out RP . SENT For IN example NN , , a DT person NN . SENT a DT monkey NN . SENT a DT sample NN of IN soil NN . SENT a DT pot NN of IN seedlings NNS . SENT a DT postcode NN area NN . SENT a DT doctor's NNS practice NN . SENT Population NN A DT population NN is VBZ any DT entire JJ collection NN of IN people NNS , , animals NNS , , plants NNS or CC things NNS from IN which WDT we PP may MD collect VV data NNS . SENT It PP is VBZ the DT entire JJ group NN we PP are VBP interested VVN in IN , , which WDT we PP wish VVP to TO describe VV or CC draw VV conclusions NNS about RB . SENT In IN order NN to TO make VV any DT generalisations NNS about IN a DT population NN , , a DT sample NN , , that WDT is VBZ meant VVN to TO be VB representative JJ of IN the DT population NN , , is VBZ often RB studied VVN . SENT For IN each DT population NN there EX are VBP many JJ possible JJ samples NNS . SENT A DT sample NN statistic NN gives VVZ information NN about IN a DT corresponding JJ population NN parameter NN . SENT For IN example NN , , the DT sample NN mean NN for IN a DT set NN of IN data NNS would MD give VV information NN about IN the DT overall JJ population NN mean NN . SENT It PP is VBZ important JJ that IN the DT investigator NN carefully RB and CC completely RB defines VVZ the DT population NN before IN collecting VVG the DT sample NN , , including VVG a DT description NN of IN the DT members NNS to TO be VB included VVN . SENT Example NN The DT population NN for IN a DT study NN of IN infant JJ health NN might MD be VB all DT children NNS born VVN in IN the DT U NP . SENT K NP . SENT in IN the DT 1980 CD s PP . SENT The DT sample NN might MD be VB all DT babies NNS born VVN on IN 7 CD th NN May NP in IN any DT of IN the DT years NNS . SENT Sample NN A DT sample NN is VBZ a DT group NN of IN units NNS selected VVN from IN a DT larger JJR group NN the DT population NN . SENT By IN studying VVG the DT sample NN it PP is VBZ hoped VVN to TO draw VV valid JJ conclusions NNS about IN the DT larger JJR group NN . SENT A DT sample NN is VBZ generally RB selected VVN for IN study NN because IN the DT population NN is VBZ too RB large JJ to TO study VV in IN its PP$ entirety NN . SENT The DT sample NN should MD be VB representative JJ of IN the DT general JJ population NN . SENT This DT is VBZ often RB best RBS achieved VVN by IN random JJ sampling NN . SENT Also RB , , before IN collecting VVG the DT sample NN , , it PP is VBZ important JJ that IN the DT researcher NN carefully RB and CC completely RB defines VVZ the DT population NN , , including VVG a DT description NN of IN the DT members NNS to TO be VB included VVN . SENT Example NN The DT population NN for IN a DT study NN of IN infant JJ health NN might MD be VB all DT children NNS born VVN in IN the DT U NP . SENT K NP . SENT in IN the DT 1980 CD s PP . SENT The DT sample NN might MD be VB all DT babies NNS born VVN on IN 7 CD th NN May NP in IN any DT of IN the DT years NNS . SENT Parameter NN A DT parameter NN is VBZ a DT value NN , , usually RB unknown JJ and CC which WDT therefore RB has VHZ to TO be VB estimated VVN , , used VVN to TO represent VV a DT certain JJ population NN characteristic NN . SENT For IN example NN , , the DT population NN mean NN is VBZ a DT parameter NN that WDT is VBZ often RB used VVN to TO indicate VV the DT average JJ value NN of IN a DT quantity NN . SENT Within IN a DT population NN , , a DT parameter NN is VBZ a DT fixed JJ value NN which WDT does VVZ not RB vary VV . SENT Each DT sample NN drawn VVN from IN the DT population NN has VHZ its PP$ own JJ value NN of IN any DT statistic NN that WDT is VBZ used VVN to TO estimate VV this DT parameter NN . SENT For IN example NN , , the DT mean NN of IN the DT data NNS in IN a DT sample NN is VBZ used VVN to TO give VV information NN about IN the DT overall JJ mean NN in IN the DT population NN from IN which WDT that DT sample NN was VBD drawn VVN . SENT Parameters NNS are VBP often RB assigned VVN Greek JJ letters NNS e NN . SENT g NN . SENT , , whereas IN statistics NNS are VBP assigned VVN Roman NP letters NNS e NN . SENT g NN . SENT s PP . SENT Statistic NN A DT statistic NN is VBZ a DT quantity NN that WDT is VBZ calculated VVN from IN a DT sample NN of IN data NNS . SENT It PP is VBZ used VVN to TO give VV information NN about IN unknown JJ values NNS in IN the DT corresponding JJ population NN . SENT For IN example NN , , the DT average NN of IN the DT data NNS in IN a DT sample NN is VBZ used VVN to TO give VV information NN about IN the DT overall JJ average NN in IN the DT population NN from IN which WDT that DT sample NN was VBD drawn VVN . SENT It PP is VBZ possible JJ to TO draw VV more JJR than IN one CD sample NN from IN the DT same JJ population NN and CC the DT value NN of IN a DT statistic NN will NN in IN general JJ vary VVP from IN sample NN to TO sample NN . SENT For IN example NN , , the DT average JJ value NN in IN a DT sample NN is VBZ a DT statistic NN . SENT The DT average JJ values NNS in IN more JJR than IN one CD sample NN , , drawn VVN from IN the DT same JJ population NN , , will MD not RB necessarily RB be VB equal JJ . SENT Statistics NNS are VBP often RB assigned VVN Roman NP letters NNS e NN . SENT g NN . SENT m NN and CC s PP , , whereas IN the DT equivalent JJ unknown JJ values NNS in IN the DT population NN parameters NNS are VBP assigned VVN Greek JJ letters NNS e NN . SENT g NN . SENT and NP . SENT Sampling VVG Distribution NN The DT sampling NN distribution NN describes VVZ probabilities NNS associated VVN with IN a DT statistic NN when WRB a DT random JJ sample NN is VBZ drawn VVN from IN a DT population NN . SENT The DT sampling NN distribution NN is VBZ the DT probability NN distribution NN or CC probability NN density NN function NN of IN the DT statistic NN . SENT Derivation NN of IN the DT sampling NN distribution NN is VBZ the DT first JJ step NN in IN calculating VVG a DT confidence NN interval NN or CC carrying VVG out RP a DT hypothesis NN test NN for IN a DT parameter NN . SENT Example NN Suppose VVP that RB x SYM 1 CD , , . SENT . SENT . SENT . SENT . SENT . SENT . SENT , , xn NNS are VBP a DT simple JJ random JJ sample NN from IN a DT normally RB distributed VVN population NN with IN expected VVN value NN and CC known VVN variance NN . SENT Then RB the DT sample NN mean NN is VBZ a DT statistic NN used VVN to TO give VV information NN about IN the DT population NN parameter NN is VBZ normally RB distributed VVN with IN expected VVN value NN and CC variance NN Estimate NP An DT estimate NN is VBZ an DT indication NN of IN the DT value NN of IN an DT unknown JJ quantity NN based VVN on IN observed JJ data NNS . SENT More RBR formally RB , , an DT estimate NN is VBZ the DT particular JJ value NN of IN an DT estimator NN that WDT is VBZ obtained VVN from IN a DT particular JJ sample NN of IN data NNS and CC used VVN to TO indicate VV the DT value NN of IN a DT parameter NN . SENT Example NN Suppose VVP the DT manager NN of IN a DT shop NN wanted VVD to TO know VV the DT mean JJ expenditure NN of IN customers NNS in IN her PP$ shop NN in IN the DT last JJ year NN . SENT She PP could MD calculate VV the DT average JJ expenditure NN of IN the DT hundreds NNS or CC perhaps RB thousands NNS of IN customers NNS who WP bought VVD goods NNS in IN her PP$ shop NN , , that WDT is VBZ , , the DT population NN mean NN . SENT Instead RB she PP could MD use VV an DT estimate NN of IN this DT population NN mean NN by IN calculating VVG the DT mean NN of IN a DT representative JJ sample NN of IN customers NNS . SENT If IN this DT value NN was VBD found VVN to TO be VB 25 CD , , then RB 25 CD would MD be VB her PP$ estimate NN . SENT Estimator NN An DT estimator NN is VBZ any DT quantity NN calculated VVN from IN the DT sample NN data NN which WDT is VBZ used VVN to TO give VV information NN about IN an DT unknown JJ quantity NN in IN the DT population NN . SENT For IN example NN , , the DT sample NN mean NN is VBZ an DT estimator NN of IN the DT population NN mean NN . SENT Estimators NNS of IN population NN parameters NNS are VBP sometimes RB distinguished VVN from IN the DT true JJ value NN by IN using VVG the DT symbol NN hat NN . SENT For IN example NN , , true JJ population NN standard NN deviation NN estimated VVN from IN a DT sample NN population NN standard JJ deviation NN Example NN The DT usual JJ estimator NN of IN the DT population NN mean NN is VBZ where WRB n NN is VBZ the DT size NN of IN the DT sample NN and CC X NP 1 CD , , X NP 2 CD , , X NP 3 CD , , . SENT . SENT . SENT . SENT . SENT . SENT . SENT , , Xn NP are VBP the DT values NNS of IN the DT sample NN . SENT If IN the DT value NN of IN the DT estimator NN in IN a DT particular JJ sample NN is VBZ found VVN to TO be VB 5 CD , , then RB 5 CD is VBZ the DT estimate NN of IN the DT population NN mean NN . SENT Estimation NN Estimation NN is VBZ the DT process NN by IN which WDT sample NN data NNS are VBP used VVN to TO indicate VV the DT value NN of IN an DT unknown JJ quantity NN in IN a DT population NN . SENT Results NNS of IN estimation NN can MD be VB expressed VVN as IN a DT single JJ value NN , , known VVN as IN a DT point NN estimate NN . SENT or CC a DT range NN of IN values NNS , , known VVN as IN a DT confidence NN interval NN . SENT Back RB to TO Top NP of IN Page NP