Sampling Basics Nonprobability and Simple Random Samples Chapter

Sampling Basics, Nonprobability and Simple Random Samples Chapter 15

Six-Step Procedure for Drawing a Sample Step 1 Define the Target Population Step 2 Identify the Sampling Frame Step 3 Select a Sampling Procedure Step 4 Determine the Sample Size Step 5 Select the Sample Elements Step 6 Collect the Data from the Designated Elements SLIDE 15 -1

Target Population The collection of elements about which the researcher wishes to make an inference or the totality of cases that conform to some designated specifications Some possibilities: ? Adults ? Children ? Households ? Manufacturing firms ? Wholesalers ? Retailers ? Nonprofit institutions ? Credit card transactions SLIDE 15 -2

Sampling Frame The list of sampling units from which the sample will be drawn Some Possibilities: ? Individuals ? Geographic Areas ? Institutions ? Credit card transactions SLIDE 15 -3

Classification of Sampling Techniques Sampling Designs Nonprobability Samples Convenience Judgment Quota Probability Samples Simple Random Stratified Proportionate Disproportionate Cluster Systematic Area SLIDE 15 -4

Probability Sample A sample in which each target population element has a KNOWN, NONZERO chance of being included in the sample SLIDE 15 -5

Nonprobability Sample A sample that relies on personal judgment somewhere in the selection process and therefore prohibits estimating the probability that any population element will be included in the sample. Basic Types: Convenience sample A sample that is sometimes called an accidental sample because those included in the sample enter by accident in that they just happen to be where the study is being conducted when it is being conducted. Judgment sample A sample that is sometimes called a purposive sample in that the sample elements are handpicked because they are expected to serve the research purpose. Quota Sample A sample chosen in such a way that the proportion of sample elements possessing certain characteristics is approximately the same as the proportion of the elements with the characteristics in the population; each field worker is assigned a quota that specifies the characteristics of the people he or she is to contact. SLIDE 15 -6

Parent Population of Discs in an Urn where A B C D E F A=3 D=12 B=6 E=15 C=9 F=18 SLIDE 15 -7

Derived Population of all Possible Distinguished Samples Mean Xj 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ABC ABD ABE ABF ACD ACE ACF ADE ADF AEF BCD BCE BCF BDE BDF BEF CDE CDF CEF DEF 18 21 24 27 30 30 33 36 27 30 33 33 36 39 42 45 6 7 8 9 10 10 11 12 9 10 11 11 12 13 14 15 SLIDE 15 -8

Relationship Between Parameters of Parent Population and Derived Population Parent Population Mean: = Element A Total 3 B 6 C 9 D 12 E 15 F 18 3 + 6 + 9 + 12 + 15 + 18 Xi = N 6 = 10. 5 = Variance: 2 = (Xi- )2 = N = 157. 5 = 26. 25 6 (3 -10. 5)2 +. . . +(18 -10. 5)2 6 SLIDE 15 -9

Relationship Between Parameters of Parent Population and Derived Population Mean: Variance: L xj j =1 E( x ) = = L 2 σ_ x = 6 + 7 +. . . + 15 20 105 = 10. 5 = 20 L ( xj - E(x))2 j =1 L =(6 -10. 5)2 + (7 -10. 5)2 +. . . + (15 -10. 5)2 20 = 5. 25 SLIDE 15 -10

Distribution of Variables in Parent and Derived Population Parent Population 1 Absolute Frequency 0 Values of X Derived Population 3 2 Absolute Frequency 1 0 Values of x SLIDE 15 -11

Distribution of Sample Means for Samples of Various Sizes and Different Population Distributions Parent Population - Distribution of X Derived Population - Sampling Distribution of X n=2 n=5 n=30 SLIDE 15 -12

Abridged List of Random Numbers 10 09 73 25 33 37 54 20 48 05 08 42 26 89 53 99 01 90 25 29 12 80 79 99 70 66 06 57 47 17 31 06 01 08 05 85 26 97 76 02 63 57 33 21 35 73 79 64 57 53 98 52 01 77 67 11 80 50 54 31 83 45 29 96 34 88 68 54 02 00 99 59 46 73 48 65 48 11 76 74 80 12 43 56 35 74 35 09 98 17 69 91 62 68 03 09 89 32 05 05 81 49 91 45 23 76 52 01 35 86 34 67 35 48 76 64 89 47 42 96 24 80 52 40 37 19 64 50 93 03 23 20 90 25 60 09 37 67 07 15 38 31 13 11 65 80 15 73 61 47 64 03 23 66 53 34 07 27 68 50 36 69 73 61 70 45 57 18 24 06 35 30 34 26 14 02 05 16 56 92 68 66 57 48 18 05 32 54 70 48 90 55 35 65 48 03 52 96 47 78 35 80 83 42 82 14 90 56 86 07 22 10 94 05 58 39 80 82 77 32 50 72 56 82 48 06 28 89 80 83 13 74 67 00 78 86 50 75 84 01 36 76 66 79 51 87 51 76 49 69 91 82 60 89 28 17 46 85 09 50 58 04 77 69 74 17 72 70 80 15 45 31 82 23 74 77 40 27 72 14 43 23 60 02 10 66 25 22 91 48 36 93 68 72 03 14 22 56 85 14 46 42 75 67 88 68 47 02 76 86 46 16 28 35 54 80 20 15 88 98 65 86 73 28 60 60 29 18 90 93 73 21 45 76 96 94 95 63 95 67 95 81 79 05 46 93 97 40 47 36 76 03 11 52 62 29 75 90 61 33 67 11 33 30 38 82 52 09 52 54 47 56 95 57 16 11 77 08 91 04 47 43 68 98 74 52 87 03 34 42 06 64 13 71 82 42 39 89 99 17 02 64 97 77 85 39 47 09 44 33 01 10 93 68 86 53 37 90 22 23 39 00 35 04 12 11 23 18 83 35 50 52 68 29 23 40 14 96 94 54 37 29 82 08 43 17 19 40 62 49 27 50 77 71 60 47 21 38 28 40 38 08 27 29 03 62 17 92 30 38 12 38 07 56 17 91 83 81 55 60 05 21 92 49 16 36 76 68 91 97 85 56 84 39 78 78 10 41 65 37 26 64 45 00 SLIDE 15 -13 45 65 06 59 33 70 32 79 24 35 98 51 17 62 13 44 63 55 18 98 48