Systematic Sampling Lecture 9 Section 2 7 Robb T Koether Hampden Sydney College Wed Feb 1 2012 Robb T Koether Hampden Sydney College Systematic Sampling Wed Feb 1 2012 1 13 Outline 1 1 in k Systematic Sampling 2 Assignment Robb T Koether Hampden Sydney College Systematic Sampling Wed Feb 1 2012 2 13 Outline 1 1 in k Systematic Sampling 2 Assignment Robb T Koether Hampden Sydney College Systematic Sampling Wed Feb 1 2012 3 13 Systematic Sampling Definition 1 in k Systematic Sampling 1 in k systematic sampling is a sampling method in which one of the first k members of the population is selected at random Then beginning with that member every k th member is selected For example if k 10 then one of the first 10 members is selected at random using randInt 1 10 Suppose member 6 is selected Then beginning with member 6 every 10th member is selected That is members 6 16 26 36 and so on Robb T Koether Hampden Sydney College Systematic Sampling Wed Feb 1 2012 4 13 Systematic Sampling 1 in k Systematic Sampling Number the members of the population 1 through N Using randInt 1 k choose a random starting point in the first block of size k That represents the first member of the sample From that starting point put every k th member in the sample Robb T Koether Hampden Sydney College Systematic Sampling Wed Feb 1 2012 5 13 An Example Example Sunday Hunting Reconsider the population of 30 students and the question of permitting Sunday hunting This time we will take a 1 in 4 systematic sample Robb T Koether Hampden Sydney College Systematic Sampling Wed Feb 1 2012 6 13 An Example Example Sunday Hunting Hunters N Y Y Y Y Y Y Y N Y 1 2 3 4 5 6 7 8 9 10 Y Y Y N Y Y Y Y Y Y 11 12 13 14 15 16 17 18 19 20 N Y N N N N Y N Y N 21 22 23 24 25 26 27 28 29 30 Not Hunters The hunters and non hunters and their opinions Robb T Koether Hampden Sydney College Systematic Sampling Wed Feb 1 2012 7 13 An Example Example Sunday Hunting Y Y Y Y Y Y Y Y Y N 29 10 3 15 4 6 13 27 2 14 N Y N Y Y Y Y N Y N 1 16 30 17 7 19 20 28 8 23 Y N Y N Y N N Y N Y 12 9 11 24 5 26 25 22 21 18 Let s randomize them Robb T Koether Hampden Sydney College Systematic Sampling Wed Feb 1 2012 7 13 An Example Example Sunday Hunting Y Y Y Y Y Y Y Y Y N 1 2 3 4 5 6 7 8 9 10 N Y N Y Y Y Y N Y N 11 12 13 14 15 16 17 18 19 20 Y N Y N Y N N Y N Y 21 22 23 24 25 26 27 28 29 30 And then re number them 1 30 Robb T Koether Hampden Sydney College Systematic Sampling Wed Feb 1 2012 7 13 An Example Example Sunday Hunting Y Y Y Y Y Y Y Y Y N 1 2 3 4 5 6 7 8 9 10 N Y N Y Y Y Y N Y N 11 12 13 14 15 16 17 18 19 20 Y N Y N Y N N Y N Y 21 22 23 24 25 26 27 28 29 30 Choose a 1 in 4 systematic sample Robb T Koether Hampden Sydney College Systematic Sampling Wed Feb 1 2012 7 13 Estimating Parameters Example Sunday Hunting What was our sample size Robb T Koether Hampden Sydney College Systematic Sampling Wed Feb 1 2012 8 13 Estimating Parameters Example Sunday Hunting What was our sample size What sample proportion did we observe Robb T Koether Hampden Sydney College Systematic Sampling Wed Feb 1 2012 8 13 Estimating Parameters Example Sunday Hunting What was our sample size What sample proportion did we observe How does it compare to the population proportion Robb T Koether Hampden Sydney College Systematic Sampling Wed Feb 1 2012 8 13 Estimating Parameters Example Sunday Hunting What was our sample size What sample proportion did we observe How does it compare to the population proportion Do it again Robb T Koether Hampden Sydney College Systematic Sampling Wed Feb 1 2012 8 13 How to Determine k The Determination of k Divide the population size N by the desired sample size n Let k N n rounded off If you round down you may get one extra member If you round up you may get one less member It does not matter Robb T Koether Hampden Sydney College Systematic Sampling Wed Feb 1 2012 9 13 Example Example Systematic Sampling Suppose we want to select n 8 members from a population of size N 30 Compute k 30 8 3 68 4 Use randInt 1 4 to get a random integer from 1 to 4 Then include that number and every 4th number thereafter in the sample Robb T Koether Hampden Sydney College Systematic Sampling Wed Feb 1 2012 10 13 Example Example Systematic Sampling There are 4 possibilities Robb T Koether Hampden Sydney College Systematic Sampling Wed Feb 1 2012 11 13 Example Example Systematic Sampling There are 4 possibilities Random no 1 Sample 1 5 9 13 17 21 25 29 Robb T Koether Hampden Sydney College Systematic Sampling Wed Feb 1 2012 11 13 Example Example Systematic Sampling There are 4 possibilities Random no 1 Sample 1 5 9 13 17 21 25 29 Random no 2 Sample 2 6 10 14 18 22 26 30 Robb T Koether Hampden Sydney College Systematic Sampling Wed Feb 1 2012 11 13 Example Example Systematic Sampling There are 4 possibilities Random no 1 Sample 1 5 9 13 17 21 25 29 Random no 2 Sample 2 6 10 14 18 22 26 30 Random no 3 Sample 3 7 11 15 19 23 27 Robb T Koether Hampden Sydney College Systematic Sampling Wed Feb 1 2012 11 13 Example Example Systematic Sampling There are 4 possibilities Random no 1 Random no 2 Random no 3 Random no 4 Robb T Koether Hampden Sydney College Sample 1 5 9 13 17 21 25 29 Sample 2 6 10 14 18 22 26 30 Sample 3 7 11 15 19 23 27 Sample 4 8 12 16 20 24 28 Systematic Sampling Wed Feb 1 2012 11 13 Outline 1 1 in k Systematic Sampling 2 Assignment Robb T Koether Hampden Sydney College Systematic Sampling Wed Feb 1 2012 12 13 Assignment Homework Read Section 2 7 pages 117 121 Let s Do It 2 9 2 10 Page 121 exercises 28 30 32 Chapter 2 review p 136 exercises 44 46 48 50 51 53 55 56 63 Robb T Koether Hampden Sydney College Systematic Sampling Wed Feb 1 2012 13 13
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