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# Session basic concepts_in_sampling_and_sampling_techniques

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• ### Session basic concepts_in_sampling_and_sampling_techniques

1. 1. Note: The Slides were taken from Elementary Statistics: A Handbook of Slide Presentation prepared by Z.V.J. Albacea, C.E. Reano, R.V. Collado, L.N. Comia and N.A. Tandang in 2005 for the Institute of Statistics, CAS, UP Los Banos Training on Teaching Basic Statistics for Tertiary Level Teachers Summer 2008 BASIC CONCEPTS IN SAMPLING AND SAMPLING TECHNIQUES
2. 2. Session 3.2 TEACHING BASIC STATISTICS …. Sampling Process Sample Data Universe Inferences/Generalization (Subject to Uncertainty) INFERENTIAL STATISTICS
3. 3. Session 3.3 TEACHING BASIC STATISTICS …. Basic Terms UNIVERSE – the set of all entities under study VARIABLE – attribute of interest observable on each entity in the universe POPULATION – the set of all possible values of the variable SAMPLE – subset of the universe or the population
4. 4. Session 3.4 TEACHING BASIC STATISTICS …. SAMPLING – the process of selecting a sample PARAMETER – descriptive measure of the population STATISTIC – descriptive measure of the sample INFERENTIAL STATISTICS – concerned with making generalizations about parameters using statistics Basic Terms
5. 5. Session 3.5 TEACHING BASIC STATISTICS …. WHY DO WE USE SAMPLES? 1. Reduce Cost 2. Greater Speed or Timeliness 3. Greater Efficiency and Accuracy 4. Greater Scope 5. Convenience 6. Necessity 7. Ethical Considerations
6. 6. Session 3.6 TEACHING BASIC STATISTICS …. TWO TYPES OF SAMPLES 1. Probability sample 2. Non-probability sample
7. 7. Session 3.7 TEACHING BASIC STATISTICS …. Samples are obtained using some objective chance mechanism, thus involving randomization. They require the use of a complete listing of the elements of the universe called the sampling frame. (Session_5_DEFINING A SAMPLING FRAME.pptx) PROBABILITY SAMPLES
8. 8. Session 3.8 TEACHING BASIC STATISTICS …. The probabilities of selection are known. They are generally referred to as random samples. They allow drawing of valid generalizations about the universe/population. PROBABILITY SAMPLES
9. 9. Session 3.9 TEACHING BASIC STATISTICS …. Samples are obtained unevenly, selected purposively or are taken as volunteers. The probabilities of selection are unknown. NON-PROBABILITY SAMPLES
10. 10. Session 3.10 TEACHING BASIC STATISTICS …. They should not be used for statistical inference. They result from the use of judgment sampling, accidental sampling, purposively sampling, and the like. NON-PROBABILITY SAMPLES
11. 11. Session 3.11 TEACHING BASIC STATISTICS …. BASIC SAMPLING TECHNIQUES Simple Random Sampling Stratified Random Sampling Systematic Random Sampling Cluster Sampling Slide No. 3.20
12. 12. Session 3.12 TEACHING BASIC STATISTICS …. SIMPLE RANDOM SAMPLING Most basic method of drawing a probability sample Assigns equal probabilities of selection to each possible sample Results to a simple random sample
13. 13. Session 3.13 TEACHING BASIC STATISTICS …. STRATIFIED RANDOM SAMPLING The universe is divided into L mutually exclusive sub-universes called strata. Independent simple random samples are obtained from each stratum.
14. 14. Session 3.14 TEACHING BASIC STATISTICS …. ILLUSTRATION C D B A B Slide No. 3.13
15. 15. Session 3.15 TEACHING BASIC STATISTICS …. Steps in Stratified Random Sampling 1.Identify and define the population (sampling frame) 2.Determine the desired sample size 3.Identify the variable and subgroups (strata) for which you want to guarantee appropriate representation (either proportional or equal) 4.Classify all members of the population as members of one of the identified subgroups 5.Randomly select the individuals from each subgroup (using the table of random numbers or lottery)
16. 16. Formula: with = sample size of subgroup k n = Total sample size (determined using the specified methods) = Population size of subgroup k N = Total population size Session 3.16 TEACHING BASIC STATISTICS …. 1 1 L L h h h h N N n n Computation of Sample Size in SRS
17. 17. Session 3.17 TEACHING BASIC STATISTICS …. Example: The researcher would like to conduct a study on administrators’ performance in State Colleges and Universities in Caraga from which the distribution of population is given in the table. Suppose the researcher would like to get 80 samples. State University/ College Number of Administrators State University/ College Number of Administrators SUC1 7 SUC5 36 SUC2 9 SUC6 29 SUC3 14 SUC7 15 SUC4 45 SUC8 25 Computation of Sample Size in SRS
18. 18. Session 3.18 TEACHING BASIC STATISTICS …. Advantages of Stratification 1. It gives a better cross-section of the population. 2. It simplifies the administration of the survey/data gathering. 3. The nature of the population dictates some inherent stratification. 4. It allows one to draw inferences for various subdivisions of the population. 5. Generally, it increases the precision of the estimates.
19. 19. Session 3.19 TEACHING BASIC STATISTICS …. SYSTEMATIC SAMPLING Adopts a skipping pattern in the selection of sample units Gives a better cross-section if the listing is linear in trend but has high risk of bias if there is periodicity in the listing of units in the sampling frame Allows the simultaneous listing and selection of samples in one operation
20. 20. Session 3.20 TEACHING BASIC STATISTICS …. Population Systematic Sample ILLUSTRATION
21. 21. Session 3.21 TEACHING BASIC STATISTICS …. CLUSTER SAMPLING It considers a universe divided into N mutually exclusive sub-groups called clusters. A random sample of n clusters is selected and their elements are completely enumerated. It has simpler frame requirements. It is administratively convenient to implement. Slide No. 3.19 Slide No. 3.11
22. 22. Session 3.22 TEACHING BASIC STATISTICS …. ILLUSTRATION Population Cluster Sample Slide No. 3.18
23. 23. Steps in Cluster Sampling  Identify and define the population (sampling frame)  Determine the desired sample size  Identify and determine a logical cluster  List all clusters that comprise the population  Estimate the average population per cluster  Determine the number of clusters needed by dividing the sample size by the estimated average population per cluster  Randomly select the needed number of clusters  All members in the selected cluster are included as sample units Session 3.23 TEACHING BASIC STATISTICS ….
24. 24. Example of Cluster Sampling  Let us see how the superintendent would get a sample of teachers if cluster sampling were used. 1. The population is 5000 teachers in the superintendent’s school system. 2. The desired sample size is 500. 3. A logical cluster is a school. 4. There are 100 schools in the list. 5. Although the schools vary in the number of teachers, there is an average number of teachers per school. Session 3.24 TEACHING BASIC STATISTICS ….
25. 25. Example of Cluster Sampling 6. Suppose the average number of teachers per school is 50. So the number of clusters (schools) needed is: 7. There are 10 schools in the sample, which will be selected randomly from the 100 schools. 8. All teachers in each of the 10 schools are in the sample (if the desired sample size is not reached, add one cluster from the population, which will be chosen randomly from the 90 schools left). Session 3.25 TEACHING BASIC STATISTICS ….
26. 26. Session 3.26 TEACHING BASIC STATISTICS …. SIMPLE TWO-STAGE SAMPLING In the first stage, the units are grouped into N sub- groups, called primary sampling units (psu’s) and a simple random sample of n psu’s are selected. Illustration: A PRIMARY SAMPLING UNIT    
27. 27. Session 3.27 TEACHING BASIC STATISTICS …. SIMPLE TWO-STAGE SAMPLING In the second stage, from each of the n psu’s selected with Mi elements, simple random sample of mi units, called secondary sampling units ssu’s, will be obtained. Illustration: A SECONDARY SAMPLING UNIT SAMPLE
28. 28.  Accidental or Incidental Sampling Getting a subject of study that is only available during the period  Quota Sampling Getting a sample of subject of study using through quota system  Ex. All PolSci students of the different HEI’s in Caraga Non-Probability Sampling Techniques
29. 29.  Purposive Sampling The researcher simply picks out the subjects that are representatives of the population depending on the purpose of the study Non-Probability Sampling Techniques
30. 30.  End of Presentation Session 3.30 TEACHING BASIC STATISTICS ….