Measuring*the*quality*of*a*survey**Ch.*7.2******How*Can*it*be?**à*we*see*polls*and*survey*results*all*of*the*time*à*how*can*2,019*British*adults*speak*on*behalf*of*over*50*million*British*adults**à*how*can*we*trust*what*we*read?**Measuring*Quality*à*it*is*hard*to*tell*whether*the*above*survery,*and*other*ones*like*it,*is*actually*good*or*bad*à*we*would*need*to*know*the*parameter*to*be*certain(see*last*lecture)*à*evaluate*the*method*used*to*estimate*a*particular*parameter*and*not*outcome*of*the*survery***Variation*in*Outcomes**à*Recall*the*Hot*hand*lab*3.*You*were*asked*to*draw*a**sample*and*then*compare*your*outcomes**à*everyone*had*the*same*software,*the*same*program*yet*each*sample*was*slightly*different,*some*were*close*to*the*mean*and*some*were*far.**à*what*is*important*is*how*your*statistics*looked*as*an*entire*group**After you leave Stat 10This is how most of you will encounter Statistics. As the results of survey or polls. Prince Charles has been trying to increase his popularity lately...69%*of*Britons*don’t*want*king*Charles******************Prince*Charles*and*his*wife*Camilla*are*the*lowest*ranked*members*of*the*Royal*in*research,*which*questioned*1506*Australian*adults,*2019*British*adults,**and*2005*Canadian*adults*and*has*a*margin*of*error*of*+/U2.2*%*Statistics(the*estimator/estimation*method)*can*be*understood*as*being*related*to*the*perameter*like*an*archer*or*a*golfer*(in*the*text*p.*303)**à*the*accuracy*is*measured*in*terms**bias,*is*measured*by*the*standard*error*****Using*Simulator*to*Understand*Estimators**à*Three*fundamental*rules**1. Statistics*or*estimator*vary*from*sample*to*sample.*Paramerters*do*not.**2. The*population*size*doe*not*affect*precision**3. Large*sample*sizes*produces*more*precise*estimates*or*statistics***Statistics*Estimators*may*vary*from*sample*to*sample**à*in*the*lab*“hot*hands”*you*were*asked*t*draw*a*sample*and*compare*your*results*to*those*of*your*neighbor.*Changes*are,*your*sample*was*different.***à*the*statistics*generated*from*samples*will*differ*from*sample*to*sample*because*those*statistics*are*dependent*on*a*random*process*(random*sampling)*STATISTICS (ESTIMATOR AKA ESTIMATION METHOD) CAN BE UNDERSTOOD AS BEING RELATED TO THE PARAMETER LIKE AN ARCHER OR A GOLFER (IN THE TEXT P. 303)ACCURACY IS MEASURED IN TERMS OF BIASPRECISION IS MEASURED BY THE “STANDARD ERROR”INACCURATE AND IMPRECISE ACCURATE AND PRECISEINACCURATE YET PRECISEACCURATE YET IMPRECISE****Important*Stuff*à^!*(p*hat)*is*not*always*the*same*as*parameter,*p.*^!*(p*hat)*is*random*because*it*is*calculated*from*the*result*of*a*random**process(*the*random*sample).*p*is*fixed*and*unchanging.***à*the*mean*of*a*distribution*of*sample*statistics*(sample*distribution)*is*the*same*as*p.*If*it*were*different*from*p,*the*distance*would*be*called*bias***àEven*though*^!*(p*hat)*is*not*always*equal*to*p,*we*are*never*that*far*away*form*it****The*sampling*distribution**à*The*mean*of*the*distribution*of*sample*statistics(*the*sample*distribution)*is*the*same*as*p*à*if*we*don’t*observe*the*sampling*distribution*in*real*life*we*can*simulate*it*and*we*know*that*it*exists*in*theory**Simulation*sampling*occurs*in*the*media*****Sampling*distribution****Review:*Sampling*Distribution**à*it*is*the*probability*distribution*of*a*statistic**à*gives*us*the*probabilities*for*a*statistic*àit*tells*us*how*frequently*we*can*expect*to*see*particular*values*of*our*stat istics**à*it*can*tell*us*about*the*presence*of*bias*(its*center*vs*the*true*parameter*à*it*can*tell*us*about*the*precision*of*out*statistics*with*its*standard*deviation(*AKA*the*standard*error)**SAMPLING AS IT APPEARS IN THE MEDIASAMPLING DISTRIBUTION WHAT YOU SHOULD UNDERSTAND AFTER STAT 10Population*Size*does*not*affect*precision**à*the*size*of*the*population*does*not*affect*the*precision*of*our*statistics*à*as*long*as*the*population*is*large*relative*to*the*sample*size,*the*precision*of*out*statistics*have*nothing*to*do*with*the*sixe*of*t he* population**à*precision*has*EVERYTHING*to*do*with*the*size*of*the*sample****How*can*the*level*of*precision*in*our*statistics*be*the*same*for*a*sample*(for*example*off*1000),*that*comes*from*a*country*of*50*million*be*the*same*as*as*that*for*a*country*of*500*million*** à*the*goal*of*statistics*is*to*take*a*small*part*of*a*whole*and*assuming*that*the*part*is*a*random*sample*of*the*underlying*population,*the*size*of*the*population*is*of*no*importance**Here*is*a*helpful*analogy*from*your*text:*à*if*the*bowls*are*well*mixed*it*doesn’t*matter*what*one*is*big*and*one*is*small*a*spoonful*should*reveal*the*same*about*each*******Large*Samples*Produce*More*Precise*Statistics*à*if*we*could*measure*populations*exactly*there*would*be*no*need*for*statistics.**à*if*we*have*very*small*samples*like*trying*to*measure*the*happiness*of*UCLA*students*based*on*a*sample*of*10*it*coule*be*very*difficult***Standard*Error*and*Precision**à*SE=!∗(!!!)!**Notice*n*in*the*denominator,*as*it*gets*larger*the*standard*error*gets*smaller*by*a*square*root*of*n*à*for*this*to*work:******1)the*samples*must*be*randomly*selected*and*we*must*be*trying*to*estimate*the*population*proportion*p******2)*if*we*are*sampling*without*replacement*the*population*should*be*10*times*larger*than*the*sample********Sample*size*and*precision**SE=!∗(!!!)!*******Real*Life:*Only*one*chance*• In*a*classroom,*we*can*draw*thousand*of*examples*to*see*how*sampleing*works**• But*in*real*life,*working*people*only*get*one*chance*to*draw*a*sample**o They*calculate*statistics*from*the*sample*and*then*they*must*live*with*the*results**• In*real*life*when*drawing*a*random*sample**you*must*emphasize*the*procedures*to*ensure*there*is*minimize*error*and*try*to*get*the*larges*affordable*sample**• In*real*life*we*usually*do*not*know*the*value*of*the*true*population*parameter*p.*So*the*formula*for*the*SE*changes*a*bit*to*fit*reality.*We*use*the*sample*proportion*instead*to*approximate*it*****We*will*investigate*this*further*next*lecture!*** **Sample Size & PrecisionSuppose p=0.50What is the SE when n=10, 100, 400?As the sample size increases, SE decreasesReal Life: Only One ChanceHow small must an SE be? That depends, and we’ll address that question later.Furthermore, we typically do not know the value of the true population parameter p. So our formula for the SE changes a bit to fit reality. We use the