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StatisticsinSurveysandPollsPart2studentnotes-1.pptxStatistics in Surveys and Polls Part 2: Random Sampling Methods
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Chapter 2: The Problem with Samples (Part 1)
Good sampling techniques produce sample
information that does reflect the population
Random sampling techniques
Simple random sampling (SRS)
Systematic sampling
Stratified sampling
Cluster sampling
Multi-stage sampling
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Simple Random Sample
Label population of units from 1 to N
Use Random Numbers Table (Table A) to choose “n” numbers
Select the units with the n chosen numbers
Consider the previous examples; How can we conduct Simple Random Samples?
The following example illustrates this sampling method.
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Example 3. How to choose an SRS
Joan’s small accounting firm serves 30 business clients. Joan wants to interview a sample of five clients to find ways to improve client satisfaction. To avoid bias, she chooses an SRS of size 5.
Step 1: Label. Give each client a numerical label, using as few digits as possible. Two digits are needed to label 30 clients, so we use labels
01, 02, 03, …, 28, 29, 30
It is also correct to use labels 00 to 29 or even another choice of 30 two-digit labels. Here is the list of clients, with labels attached:
| 01 A-1 Plumbing | 16 JL Records |
| 02 Accent Printing | 17 Johnson Commodities |
| 03 Action Sport Shop | 18 Keiser Construction |
| 04 Anderson Construction | 19 Liu’s Chinese Restaurant |
| 05 Bailey Trucking | 20 MagicTan |
| 06 Balloons, Inc. | 21 Peerless Machine |
| 07 Bennett Hardware | 22 Photo Arts |
| 08 Best’s Camera Shop | 23 River City Books |
| 09 Blue Print Specialties | 24 Riverside Tavern |
| 10 Central Tree Service | 25 Rustic Boutique |
| 11 Classic Flowers | 26 Satellite Services |
| 12 Computer Answers | 27 Scotch Wash |
| 13 Darlene’s Dolls | 28 Sewer’s Center |
| 14 Fleisch Realty | 29 Tire Specialties |
| 15 Hernandez Electronics | 30 Von’s Video Store |
Sampling frame
List of all sampling units (people, households, organizations etc.)
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First page of Random Number Table
Line 130
Table A
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Step 2: Table. Enter Table A anywhere and read two-digit numbers. Suppose we enter at line 130, which is
69051 64817 87174 09517 84534 06489 87201 97245
The two-digit numbers in this line are
69 05 16 48 17 87 17 40 95 17 84 53 40 64 89 87 20 19 72 45
Each two-digit number in Table A is “equally likely”, so samples chosen based on these numbers are “random”
The first five unique two-digit numbers between 1 and 30 are (sometimes you have to move to another line)
69 05 16 48 17 87 17 40 95 17 84 53 40 64 89 87 20 19 72 45
So, the SRS of size 5 that Joan wants is Bailey Trucking (05), JL Records (16), Johnson Commodities (17), Magic Tan (20), and Liu’s Chinese Restaurant (19)
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SRS Practice
What is the sampling frame for each of the following?
Determine what people think about product X?
Determine what students think about textbook costs?
Determine if parents would have children again?
Determine if the ambulance service should be kept?
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Systematic Sampling
Also called Interval Sampling
Used in industry for quality control (assembly line)
Process
List all units in population
Select every Ith unit from all units
Sampling interval = I = N/n
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Systematic Sampling Example
Want to test 500 parts from an assembly line of 10,000 parts
I = N/n =
1. Number each part from 1 to N
2. Randomly select starting point between 1 and I
3. Starting with that part, select every Ith part
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Stratified Sampling
Grouping population of units into relatively homogeneous subgroups before sampling
Sample within each strata using SRS or Systematic sampling
Proportion of each stratum in sample should be the same as in the population (proportional allocation)
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Stratified Sampling
Political Exit Poll Example
Estimate proportion of registered voters who voted for a particular candidate
Strata = ____________________
Why these strata?
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Stratified Sampling Example
Example:
30,000 students enrolled at a university
(3000 graduate students)
Want to poll 500 students about cost of textbooks
Strata = _________________
Perform SRS within the stratum
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Stratified Sampling Example
CAFLS
CECAS
CAAH
CBSHS
CBUS
Strata
Clemson University
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CSCI
CED
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Stratified Sampling Example
| Gender/employment status | Count |
| Male/Full time | 90 |
| Male/Part time | 18 |
| Female/ Full time | 9 |
| Female/ Part time | 63 |
Proportional Allocation
Want to poll 40 employees about their opinion concerning changes in management
Consider gender and employment status.
%male, full time = (90/180) x 100 = 50%
%male, part time = (18/180) x 100 = 10%
%female, full time = (9/180) x 100 = 5%
%female, part time = (63/180) x 100 = 35%
| Gender/employment status | # People to Poll |
| Male/Full time | |
| Male/Part time | |
| Female/ Full time | |
| Female/ Part time |
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Cluster Sampling
Divide population of units into groups called clusters
Randomly select clusters (using SRS) and then survey all units within the clusters
Examples of clusters = schools, counties
Difference between stratified and cluster sampling
Stratified sampling = randomly select units within groups
Cluster sampling = randomly select groups and then survey all within groups
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Cluster Sampling Examples
Interested in what sports 11th graders participate
Randomly select 100 high schools
Survey every 11th grader in those schools
Cluster? ____________________
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Multi-stage Sampling
Similar to cluster sampling but select sample within cluster rather than all units within a cluster
At least 2 stages of sampling
Clusters selected
Select units from clusters
Could even have sub-clusters
Example: School, grade, class
Example: Electoral sub-divisions from cities, blocks of
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What does the author believe contributed to erroneous exit polls in the earlier hours after the 2004 presidential election?
Whose vote is never included in an exit poll?
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545Table A
Table A Random digits
Line
101 19223 95034 05756 28713 96409 12531 42544 82853
102 73676 47150 99400 01927 27754 42648 82425 36290
103 45467 71709 77558 00095 32863 29485 82226 90056
104 52711 38889 93074 60227 40011 85848 48767 52573
105 95592 94007 69971 91481 60779 53791 17297 59335
106 68417 35013 15529 72765 85089 57067 50211 47487
107 82739 57890 20807 47511 81676 55300 94383 14893
108 60940 72024 17868 24943 61790 90656 87964 18883
109 36009 19365 15412 39638 85453 46816 83485 41979
110 38448 48789 18338 24697 39364 42006 76688 08708
111 81486 69487 60513 09297 00412 71238 27649 39950
112 59636 88804 04634 71197 19352 73089 84898 45785
113 62568 70206 40325 03699 71080 22553 11486 11776
114 45149 32992 75730 66280 03819 56202 02938 70915
115 61041 77684 94322 24709 73698 14526 31893 32592
116 14459 26056 31424 80371 65103 62253 50490 61181
117 38167 98532 62183 70632 23417 26185 41448 75532
118 73190 32533 04470 29669 84407 90785 65956 86382
119 95857 07118 87664 92099 58806 66979 98624 84826
120 35476 55972 39421 65850 04266 35435 43742 11937
121 71487 09984 29077 14863 61683 47052 62224 51025
122 13873 81598 95052 90908 73592 75186 87136 95761
123 54580 81507 27102 56027 55892 33063 41842 81868
124 71035 09001 43367 49497 72719 96758 27611 91596
125 96746 12149 37823 71868 18442 35119 62103 39244
126 96927 19931 36809 74192 77567 88741 48409 41903
127 43909 99477 25330 64359 40085 16925 85117 36071
128 15689 14227 06565 14374 13352 49367 81982 87209
129 36759 58984 68288 22913 18638 54303 00795 08727
130 69051 64817 87174 09517 84534 06489 87201 97245
131 05007 16632 81194 14873 04197 85576 45195 96565
132 68732 55259 84292 08796 43165 93739 31685 97150
133 45740 41807 65561 33302 07051 93623 18132 09547
Table A546
Table A Random digits (continued)
Line
134 27816 78416 18329 21337 35213 37741 04312 68508
135 66925 55658 39100 78458 11206 19876 87151 31260
136 08421 44753 77377 28744 75592 08563 79140 92454
137 53645 66812 61421 47836 12609 15373 98481 14592
138 66831 68908 40772 21558 47781 33586 79177 06928
139 55588 99404 70708 41098 43563 56934 48394 51719
140 12975 13258 13048 45144 72321 81940 00360 02428
141 96767 35964 23822 96012 94591 65194 50842 53372
142 72829 50232 97892 63408 77919 44575 24870 04178
143 88565 42628 17797 49376 61762 16953 88604 12724
144 62964 88145 83083 69453 46109 59505 69680 00900
145 19687 12633 57857 95806 09931 02150 43163 58636
146 37609 59057 66967 83401 60705 02384 90597 93600
147 54973 86278 88737 74351 47500 84552 19909 67181
148 00694 05977 19664 65441 20903 62371 22725 53340
149 71546 05233 53946 68743 72460 27601 45403 88692
150 07511 88915 41267 16853 84569 79367 32337 03316
