H-SC MATH 121 - Lecture 9 - Systematic Sampling

Unformatted text preview:

1-in-k Systematic SamplingAssignmentSystematic SamplingLecture 9Section 2.7Robb T. KoetherHampden-Sydney CollegeWed, Feb 1, 2012Robb T. Koether (Hampden-Sydney College) Systematic Sampling Wed, Feb 1, 2012 1 / 13Outline11-in-k Systematic Sampling2AssignmentRobb T. Koether (Hampden-Sydney College) Systematic Sampling Wed, Feb 1, 2012 2 / 13Outline11-in-k Systematic Sampling2AssignmentRobb T. Koether (Hampden-Sydney College) Systematic Sampling Wed, Feb 1, 2012 3 / 13Systematic SamplingDefinition (1-in-k Systematic Sampling)1-in-k systematic sampling is a sampling method in which one of thefirst k members of the population is selected at random. Thenbeginning with that member, every kthmember is selected.For example, if k = 10, then one of the first 10 members isselected at random (using randInt(1,10)).Suppose member #6 is selected.Then beginning with member #6, every 10thmember 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 / 13Systematic Sampling1-in-k Systematic SamplingNumber the members of the population 1 through N.Using randInt(1,k), choose a random starting point in the firstblock of size k. That represents the first member of the sample.From that starting point, put every kthmember in the sample.Robb T. Koether (Hampden-Sydney College) Systematic Sampling Wed, Feb 1, 2012 5 / 13An ExampleExample (Sunday Hunting)Reconsider the population of 30 students and the question ofpermitting 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 / 13An ExampleExample (Sunday Hunting)N Y YYYYYYNYYYYYNYYYY YNYNYNNNNYN1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 30HuntersNot HuntersThe hunters and non-hunters and their opinionsRobb T. Koether (Hampden-Sydney College) Systematic Sampling Wed, Feb 1, 2012 7 / 13An ExampleExample (Sunday Hunting)NYYYYYYYNYYYYY NYY Y YYNYNYN NNNY N123 4567 8910111213 141516 171819 2021222324 252627282930Let’s randomize them. . .Robb T. Koether (Hampden-Sydney College) Systematic Sampling Wed, Feb 1, 2012 7 / 13An ExampleExample (Sunday Hunting)NYYYYYYYNYYYYY NYY Y YYNYNYN NNNY N1193 525615 1922223217 10412 143016 1729282024 2726818113And then re-number them 1 - 30Robb T. Koether (Hampden-Sydney College) Systematic Sampling Wed, Feb 1, 2012 7 / 13An ExampleExample (Sunday Hunting)NYYYYYYYNYYYYY NYY Y YYNYNYN NNNY N1193 525615 1922223217 10412 143016 1729282024 2726818113Choose a 1-in-4 systematic sampleRobb T. Koether (Hampden-Sydney College) Systematic Sampling Wed, Feb 1, 2012 7 / 13Estimating ParametersExample (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 / 13Estimating ParametersExample (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 / 13Estimating ParametersExample (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 / 13Estimating ParametersExample (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 / 13How to Determine kThe Determination of kDivide 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 / 13ExampleExample (Systematic Sampling)Suppose we want to select n = 8 members from a population ofsize N = 30.Compute k = 30/8 = 368≈ 4.Use randInt(1,4) to get a random integer from 1 to 4.Then include that number and every 4th number thereafter in thesample.Robb T. Koether (Hampden-Sydney College) Systematic Sampling Wed, Feb 1, 2012 10 / 13ExampleExample (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}.Random no. = 4 : Sample = {4, 8, 12, 16, 20, 24, 28}.Robb T. Koether (Hampden-Sydney College) Systematic Sampling Wed, Feb 1, 2012 11 / 13ExampleExample (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}.Random no. = 4 : Sample = {4, 8, 12, 16, 20, 24, 28}.Robb T. Koether (Hampden-Sydney College) Systematic Sampling Wed, Feb 1, 2012 11 / 13ExampleExample (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}.Random no. = 4 : Sample = {4, 8, 12, 16, 20, 24, 28}.Robb T. Koether (Hampden-Sydney College) Systematic Sampling Wed, Feb 1, 2012 11 / 13ExampleExample (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}.Random no. = 4 : Sample = {4, 8, 12, 16, 20, 24, 28}.Robb T. Koether (Hampden-Sydney College) Systematic Sampling Wed, Feb 1, 2012 11 / 13ExampleExample (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}.Random no. = 4 : Sample = {4, 8, 12, 16, 20, 24, 28}.Robb T. Koether (Hampden-Sydney College) Systematic Sampling Wed, Feb 1, 2012 11 / 13Outline11-in-k Systematic Sampling2AssignmentRobb T. Koether (Hampden-Sydney College) Systematic Sampling Wed, Feb 1, 2012 12 / 13AssignmentHomeworkRead 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


View Full Document

H-SC MATH 121 - Lecture 9 - Systematic Sampling

Documents in this Course
Load more
Download Lecture 9 - Systematic Sampling
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Lecture 9 - Systematic Sampling and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Lecture 9 - Systematic Sampling 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?