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# Population & Sampling Procedure * Dr. A. Asgari

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### Population & Sampling Procedure * Dr. A. Asgari

1. 1. POPULATION & SAMPLE <ul><li>Dr. Azadeh Asgari </li></ul>Research Methodology
2. 2. Population & Sample <ul><li>POPULATION: </li></ul><ul><li>all individuals in a group that has similar characteristics (one or more) to be studied by the researcher. </li></ul><ul><ul><li>e.g.: all counselors; all male teachers teaching in secondary schools; all UPM students </li></ul></ul>
3. 3. Population & Sample <ul><li>SAMPLE: </li></ul><ul><li>Part of a chosen population to be observed and analyzed. </li></ul><ul><li>By observing the randomized samples’ characteristics, several inferences on the population may be made. </li></ul><ul><li>Differences between sample, subjects, respondents. </li></ul>
4. 4. Parameter & Statistics <ul><li>Parameter: </li></ul><ul><li>values obtained from a population. </li></ul><ul><li>Statistics: </li></ul><ul><li>values obtained from a sample </li></ul>
5. 5. Randomization <ul><li>Basic to scientific observations and research </li></ul><ul><li>Assumption – even if we cannot precisely predict specific events (e.g.: Individual’s achievement), but we can precisely predict the average/mean achievement of the group </li></ul>
6. 6. Types of Sampling <ul><li>Probability Sampling </li></ul><ul><li>Non-probability Sampling </li></ul>
7. 7. Types of Probability Sampling <ul><li>Simple random sampling / selection </li></ul><ul><li>Systematic sampling </li></ul><ul><li>Stratified sampling </li></ul><ul><li>Cluster sampling </li></ul>
8. 8. Randomization of Sample <ul><li>BASIC TO RANDOMISATION = simple randomization = every individual in the group has equal opportunity (equal chance) to be chosen i.e. not biased </li></ul><ul><li>Choosing one subject is independent of the others . </li></ul><ul><li>Researcher can assume that the characteristics of the sample approximate the characteristics of total population </li></ul>
9. 9. Sampling Frame <ul><li>Assigning a number to all individuals in a population. </li></ul><ul><li>Using the sampling frame, the sample is chosen / drawn. </li></ul>
10. 10. Simple Random Sampling (selection) <ul><li>Using: </li></ul><ul><li>Fish Bowl Technique </li></ul><ul><li>Table of Random Numbers </li></ul><ul><li>Computer Generated Numbers </li></ul>
11. 11. Table of Random Numbers <ul><li>1 2 3 4 5 6 7 8 9 10 </li></ul><ul><li>______________________________________________________________ </li></ul><ul><li>1 10480 15011 01536 02011 81647 91646 69179 14194 62590 36207 </li></ul><ul><li>2 22368 46573 25595 85393 30995 89198 27982 53402 93965 34095 </li></ul><ul><li>3 24130 48360 22527 97265 76393 64809 15179 24830 49340 32081 </li></ul><ul><li>4 42167 93093 06243 61680 07856 16376 39440 53537 71341 57004 </li></ul><ul><li>5 37570 39975 81837 16656 06121 91782 60468 81305 49684 60672 </li></ul><ul><li>6 77921 06907 11008 42751 27756 53498 18602 70659 90655 15053 </li></ul><ul><li>7 99562 72905 56420 69994 98872 31016 71194 18738 44013 48840 </li></ul><ul><li>8 96301 91977 05463 07972 18876 20922 94595 56869 69014 60045 </li></ul><ul><li>9 89579 14342 63661 10281 17453 18103 57740 84378 25331 12566 </li></ul><ul><li>10 85475 36857 53342 53988 53060 59533 38867 62300 01858 17893 </li></ul>
12. 12. Systematic Sampling <ul><li>Steps: </li></ul><ul><li>Calculate the Interval </li></ul><ul><li>Draw the Initial Number </li></ul><ul><li>Select the Other Sample </li></ul>
13. 13. Systematic Sampling <ul><li>In this technique, randomization is done only on the initial number. </li></ul><ul><li>Drawing the initial number, fixed the other individuals in the sampling frame. </li></ul>
14. 14. Weakness of Systematic Sampling <ul><li>There are numbers which do not have equal opportunity to be chosen – thus a slight biasness. </li></ul><ul><li>Choice of a subject depends on another. </li></ul>
15. 15. Stratified Sampling <ul><li>To reduce sampling error and to increase precision without increasing sample size. </li></ul><ul><li>To ensure all strata are represented (not different from the population) </li></ul><ul><li>In a stratum the population is more homogenous </li></ul><ul><ul><li>e.g.: socio economic status, gender, level of intelligence, level of anxiety </li></ul></ul><ul><li>If variance is reduced and therefore, sampling error will be reduced </li></ul>
16. 16. Stratified Sampling <ul><li>Steps: </li></ul><ul><li>Determine the ratio between the strata </li></ul><ul><li>Ensure the sample size </li></ul><ul><li>Divide the number of sample according to the initial ratio within the population </li></ul><ul><li>Select the sample using randomisation technique </li></ul>
17. 17. Cluster Sampling <ul><li>Sampling is according to clusters and not individuals within each cluster </li></ul><ul><li>Conducted if individuals to be sampled are not known </li></ul><ul><li>This technique maintained the principles of randomisation </li></ul>
18. 18. Cluster Sampling <ul><li>Need not know individuals within each cluster. </li></ul><ul><li>If the clusters within the population are far apart . </li></ul><ul><li>Very suitable and more precise if many small clusters are chosen, therefore similar to the population. </li></ul><ul><li>Not suitable if a large cluster is chosen since it may not represent the population. </li></ul><ul><li>Sampling error is even larger if a big and homogeneous cluster is selected. </li></ul>
19. 19. Types of Non-Probability Sampling <ul><li>Sample of Convenience or Accidental Sampling </li></ul><ul><ul><li>Weak sampling procedure </li></ul></ul><ul><ul><li>Using available cases for the research </li></ul></ul><ul><ul><li>e.g.: Interviewing the first individual you meet; using you class students; interviewing volunteers </li></ul></ul>
20. 20. Types of Non-Probability Sampling <ul><li>Purposive Sampling - Judgment Sampling </li></ul><ul><ul><li>Sampling element is decided to represent the population. </li></ul></ul><ul><ul><li>e.g.: Interviewing all possible voters in a district, and using the result to predict the voting pattern for the whole state </li></ul></ul>
21. 21. Sampling Error <ul><li>Randomized sample may not represent population. </li></ul><ul><li>Variations my occur, called SAMPLING ERROR . </li></ul><ul><li>This variation is not an error caused by the researcher, but it occurs as a result of the sampling process. </li></ul>
22. 22. Selection of Biased Sample <ul><li>From a telephone directory </li></ul><ul><li>From a list of magazine subscribers </li></ul><ul><li>From a list of registered vehicles </li></ul>
23. 23. Sampling Error ( e ) <ul><li>Often occurs if the mean sample is used to estimate mean population. </li></ul><ul><li>Refers to the difference between population parameter and the sample statistics. </li></ul><ul><ul><li>_ </li></ul></ul><ul><ul><li>E = x - µ </li></ul></ul>
24. 24. Sample Size <ul><li>Large enough so that it is representative of the population. </li></ul><ul><li>Crucial issue is representativeness & not the sample size </li></ul><ul><li>e.g.: Sample of 200 which has been randomly selected is better than a randomly selected sample of 100; but a randomly selected sample of 100 is better than a biased sample of 2.5 million individuals. </li></ul>
25. 25. Aspects in Determining Sample Size <ul><li>ECONOMY – researcher’s financial situation </li></ul><ul><li>MANAGEABLE SAMPEL SIZE by researcher – during data collection </li></ul><ul><li>VALIDITY – a large enough size needed for high validity </li></ul><ul><li>RELIABILITY - a large enough size needed for high reliability </li></ul><ul><li>UTILIZATION OF INFERENTIAL STATISTICS – depends of the type of inferential statistics to be used </li></ul><ul><ul><li>Descriptive – large </li></ul></ul><ul><ul><li>Inferential – correlation, minimum 30 </li></ul></ul><ul><ul><li>Inferential – comparing two groups, 30 for each group </li></ul></ul><ul><ul><li>Inferential – comparing more two groups, 30 for each group </li></ul></ul><ul><ul><li>Experimental – small </li></ul></ul>
26. 26. Hypothesis Testing <ul><li>Testing null hypothesis using different tests based on type of measurement scales and data. </li></ul><ul><li>Make decision on the null hypothesis. </li></ul><ul><li>Make decision on the alternative hypothesis. </li></ul>
27. 27. Type I & II Error Scheme H O TRUE H O FALSE REJECT H O ACCEPT H O TYPE I ERROR CORRECT ACTION CORRECT ACTION TYPE II ERROR
28. 28. Type I & II Error <ul><li>Type I Error </li></ul><ul><li>Rejecting a true null hypothesis </li></ul><ul><li>e.g. Rejecting </li></ul><ul><li>h o = there exist no relationship between both variables – which is true </li></ul><ul><li>Type II Error </li></ul><ul><li>Accepting a false null hypothesis </li></ul><ul><li>e.g. Acceptin g </li></ul><ul><li>h o = there exist no relationship between both variables – which is false </li></ul>
29. 29. Level of Significance <ul><li>Researcher needs to weigh the consequences of type I and ii errors before conducting the research (how strong the evidence must be before they would reject h o ). </li></ul><ul><li>Level at which h o may be rejected = level of significance </li></ul>
30. 30. Level of Significance <ul><li>Researcher may avoid type I error by accepting h o all the time. </li></ul><ul><li>Or avoid type II error by rejecting it all the time. </li></ul><ul><li>Reducing the value of level of significance (from .05 to .01 or .001) reduces the risk of doing a type I error but increases the risk of doing a type II error. </li></ul>