Research Method (I) --Knowledge on Sampling (Simple Random Sampling)

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1 Research Method (I) --Kowledge o Samplig (Simple Radom Samplig) 1. Itroductio to samplig 1.1 Defiitio of samplig Samplig ca be defied as selectig part of the elemets i a populatio. It results i the fact that, coclusios from the sample may be exteded to that about the etire populatio. 1.2 Advatages of samplig There are several advatages of samplig over cesus (i.e. selectio of whole populatio for aalysis). Firstly, the costs o samplig should be much lower tha that o cesus. For example, for the govermet by-cesus (ote: populatio cesus is usually coducted oce every te years ad a by-cesus is coducted i the middle of the itercesal period), oe fifth of the populatio is large eough to declare what the govermet wats to kow. There is o eed to sped several times of dollars to iterview the etire populatio i the society. Secodly, a quality guru (Demig, 196) argued that the quality of a study was ofte better with samplig tha with a cesus. He suggested that, Samplig possesses the possibility of better iterviewig(testig), more thorough ivestigatio of missig, wrog, or suspicious iformatio, better supervisio, ad better processig tha is possible with complete coverage. Research fidigs substatiate this opiio. More tha 9% of survey error i oe study was from o-samplig error 1, ad 1% or less was from samplig error 2. (Doald et al., 1995) Thirdly, samplig ca save the time. The speed of executio reduces the time betwee the recogitio of a eed for iformatio ad the availability of that iformatio. 1 No-samplig error is the error of research due to factors other tha the sample size ad samplig method, icludig o-respose, bad commuicatio with iterviewees, measuremet error, etc. 2 Samplig error is the error durig research due to the sample size ad samplig method. Page 1

2 1.3 Importace to lear samplig Statistical applicatio is maily cocered with the collectio, presetatio of data, aalysis ad iterpretatio of iformatio. Data collectio is the first step. Most statistical aalysis methods are derived based o the assumptio of the radomizatio used i data collectio. Whe the assumptio of the radomizatio/represetatio of samplig caot hold, the applicatios of the statistical aalysis ad the respective iterpretatio from the aalysis are meaigless. Therefore, it is ecessary to acquire the kowledge o samplig before learig the statistical aalysis. 2. Type of samplig desig There are two types of samplig desig, i.e. probability samplig ad o-probability samplig. Probability samplig is based o the cocept of radom selectio - a cotrolled procedure that assures that each populatio elemet is give a kow ozero chace of selectio. No-probability samplig is oradom ad subjective. Each member does ot have a kow o-zero chace to be selected. Whe you distribute a questioaire to the customers i a restaurat to idetify Macao residets opiios o the gamig idustry i Macau, the samplig you draw is o-probability samplig because before the study, the probability of each residet draw is ukow, ad most of the populatio is ot covered i the study whose probability to be selected is zero. May people mistakely thik that the sample is represetative if people do ot kow who will be chose before the samplig. Such samplig method is o-radom ad o-represetative. Ideed oly probability samplig is represetative ad radom samplig which ca determie the precisio of the estimate from the sample draw. Almost all of the statistical aalyses are derived based o the assumptio of probability samplig. This article will illustrate the simplest probability samplig simple radom sample. The remaiig probability samplig methods will be dealt with later. Page 2

3 3. Simple Radom Sample (SRS) 3.1 Itroductio SRS is the simplest form of probability samplig. Each populatio elemet of SRS has a kow ad equal chace of selectio. For example, 1% of MGRA members are selected from MGRA member listig via radom umber geeratio. It is oted that, SRS requires a samplig frame which is the list of all elemets. The sample is actually draw from the samplig frame. 3.2 Sample size calculatio of SRS What sample size should be appropriate? is a commo questio amog researchers. Ideed this questio is ot easy to aswer. From the techical poit of view, the sample size required depeds o the samplig method, the populatio size, the expected margi of error (boud of error betwee true value ad the estimated value), reliability ad stadard deviatio of the variables that we are iterested i. From the practical poit of view, it also depeds o the budget ad the time. It is oted that, there are some explaatios o the reliability ad margi of error. The followig are two examples. We wat to have a SRS providig 95% of cofidece o the gap betwee the true value ad the estimated value less tha, say $1. It represets that, we wat a sample size, such that the probability that the gap betwee the true value ad the estimated value is less tha $1 is at least 95%. The 95% represets the reliability, while the $1 represets the margi of error. A SRS is desired to provide 9% of cofidece o the maximum gap betwee the true probability ad the estimated probability of selected groups less tha.2. It represets that, the sample size ca satisfy that, the likelihood that the maximum gap is less tha.2 is at least 9%. The 9% represets the reliability, while the.2 represets the margi of error. If we oly cosider the techical poit of view, for SRS, the sample size () required ca be calculated via the followig formulatio. Page 3

4 = reliability *SD d 2 ( ) = 1+ N where: N: populatio size Reliability: critical poit (Z) of stadard ormal distributio correspodig to the value α/2 3, where we wat to have cofidece 1-α. For example, the cofidece is 95% which may be the most prevailig figure, the correspodig Z value is d: Margi of error SD: Stadard deviatio of the variable we are iterested i. The idetificatio ca be referred to the followig. (i) Variables we are iterested i are cotiuous data The stadard deviatio ca be calculated from the previous study or pre-test. If we have ot coducted the previous study or formal pre-test, we may cosider the rough approach by takig oe sixth of the expected rage (max.-mi.) of the variable. For example, a seve-poit Likert scale is ofte adopted i questioaire surveys. May treat these scales as cotiuous variables. If o previous study is coducted, we may estimate the stadard deviatio as 1 ((7-1)/6). (ii) Variables we are iterested i are discrete data max i i, i If there is a previous study or a pre-test, the the SD is take as p (1-p ) where p i represets the probability of the i th group. 3 α ca be represeted as the probability of error betwee the true value ad the estimate which is out of boud. Page 4

5 However, if o iformatio o p are kow, we may take the coservative SD=1/2, max where p (1-p ) =1/2 for all i. pi 1 i i For survey study, this approach is ofte adopted. If we wat to coduct a ad-hoc survey which has ot bee coducted before ad for which o formal pre-tests have bee coducted, the sample size () ca be simply writte as: Z α/2 2 = ( ) 2d = 1+ N Note: The defiitios of Z, d, N, α are the same as that i last page. 3.3 More characteristics o SRS Pros: SRS is easy to implemet with radom umber geeratio whe the samplig frame exists, especially for the telephoe survey with automatic dialig (radom digit dialig) ad with computerized voice respose system. Cos: SRS requires a listig of populatio elemet, which is ot practical for may busiess scearios. For example, whe we coduct the visit survey, it is ot feasible to possess the listig of elemet of visitors. SRS produces larger errors tha some of other research methods, e.g. stratified samplig (which will be discussed ext time) whe the sample size is fixed. This pheomeo ca be prove by mathematics. I order to offset the lower accuracy of SRS, larger sample size is demaded, which will result i higher costs ad lower efficiecy. O the other had, comparig to cluster samplig (which will be discussed i Research Method (III)), the data collectio method of SRS is much more expesive ad more iefficiet. SRS may ot cover the segmets that we are iterested i or the sub-sample sizes of there segmets are ot large eough so that people caot coduct i-depth Page 5

6 aalysis or make i-depth iferece o these segmets. Bibliography Assael Hery ad Keo Joh. (1982). Nosamplig versus Samplig Errors i Survey Research. Joural of Market Research, Sprig Cooper Doald R., Emory C. William. (1995) 5 th ed. Busiess Research Methods. Richard D. Irwi, INC. Demig W.E.. (196) Sample Desig i Busiess Research. New York: Joh Wiley & Sos. Page 6

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