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CHAPTER 5: Survey Research 147FreshmenSophomores1 Campbell 1 Broder2 Cowan 2 Bufford3 Douglas 3 Carnahan4 Fahey 4 Dunne5 Fedder 5 Foley6 Johnson 6 Hedlund7 Ludwig 7 Osgood8 Romero 8 Owens9 Taylor 9 Suffolk10 Thompson 10 ZimmermanJuniorsSeniors1 Adamski 1 Alderink2 Brown 2 Baxter3 Dawes 3 Bowen4 Gonzales 4 Cushman5 Harris 5 Dennis6 Klaaren 6 Martinez7 Nowaczyk 7 O’Keane8 Penzien 8 Powers9 Sawyer 9 Shaw10 Watterson 10 SondersDrawing a stratified random sample:Step 1. Arrange the sampling frame in strata. Forour example we stratified by class standing. In theexample the strata are equal in size, but this neednot be the case.Step 2. Number each element within each stratum,as has been done in the foregoing list.Step 3. Decide on the overall sample size youwant to use. For our example we will draw asample of 8.Step 4. Draw an equal-sized sample from eachstratum such that you obtain the desired overallsample size. For our example this would meandrawing 2 from each stratum.Step 5. Follow the steps for drawing a randomsample and repeat for each stratum. We used adifferent starting point in the Table of RandomNumbers (Table A.1), but this time we usedthe last two digits in each set of five. The numbersidentified for each stratum were Freshmen(04 and 01), Sophomores (06 and 04), Juniors(07 and 09), and Seniors (02 and 09).Step 6. List the names corresponding to the selectednumbers. Our stratified random samplewould include Fahey, Campbell, Hedlund, Dunne,Nowaczyk, Sawyer, Baxter, and Shaw.Key Conceptto describe such a heterogeneous population. In practice, the populations withwhich survey researchers work typically fall somewhere between these twoextremes.The representativeness of a sample can often be improved by using stratifiedrandom sampling. In stratified random sampling, the population is dividedinto subpopulations called strata (singular: stratum) and random samples aredrawn from each of these strata. There are two general ways to determine howmany elements should be drawn from each stratum. One way (illustrated inthe last example of Box 5.1) is to draw equal-sized samples from each stratum.The second way is to draw elements for the sample on a proportional basis.Consider a population of undergraduate students made up of 30% freshmen,30% sophomores, 20% juniors, and 20% seniors (class years are the strata). Astratified random sample of 200 students drawn from this population wouldinclude 60 freshmen, 60 sophomores, 40 juniors, and 40 seniors. In contrast,drawing equal-sized samples from each stratum would result in 50 studentsfor each class year. Only the stratified sample on a proportional basis would berepresentative.In addition to its potential for increasing the representativeness of samples,stratified random sampling is useful when you want to describe specificportions of the population. For example, a simple random sample of100 students would be sufficient to survey students’ attitudes on a campusof 2,000 students. Suppose, however, your sample included only 2 of the