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- 1. Sampling DesignD.A. Asir John Samuel, BSc (Psy),MPT (Neuro Paed), MAc, DYScEd, C/BLS, FAGE
- 2. Basic definitions• Population- Collection of all the units that are of interest to the investigator• Sample- Representative part of population• Sampling- Technique of selecting a representative group from a population Dr. Asir John Samuel (PT), Lecturer, ACP 2
- 3. Why ?• Only feasible method for collecting information• Reduces demands on resources (time, finance,.)• Results obtained more quickly• Better accuracy of collected data• Ethically acceptable Dr. Asir John Samuel (PT), Lecturer, ACP 3
- 4. Steps in sampling design Target population Study population Sample Study participation Dr. Asir John Samuel (PT), Lecturer, ACP 4
- 5. Characteristic of good sample design• True representation of population• May result in small sampling error• Each member in population should get an opportunity of being selected• Systematic bias can be controlled in a better way• Results should be capable of being extrapolated Dr. Asir John Samuel (PT), Lecturer, ACP 5
- 6. Types of sample design• Probability/Random sampling- Selection of subjects are according to any predicted chance of probability• Non-probability/non-random sampling- Does not depend on any chance of predecided probability Dr. Asir John Samuel (PT), Lecturer, ACP 6
- 7. Types of sample design Sample design Random Non-random sampling samplingSimple Stratified Systematic Cluster Multistage convenience Quota Judgment Dr. Asir John Samuel (PT), Lecturer, ACP 7
- 8. Simple random sampling• Equal and independent chance or probability of drawing each unit• Take sampling population• Need listing of all sampling units (sampling frame)• Number all units• Randomly draw units Dr. Asir John Samuel (PT), Lecturer, ACP 8
- 9. How to ensure randomness?• Lottery method• Table of random numbers- e.g. Tippett’s series- Fisher and Yates series- Kendall and Smith series- Rand corporation series Dr. Asir John Samuel (PT), Lecturer, ACP 9
- 10. SRS - Merits• No personal bias• Easy to assess the accuracy Dr. Asir John Samuel (PT), Lecturer, ACP 10
- 11. SRS - Demerits• Need a complete catalogue of universe• Large size sample• Widely dispersed Dr. Asir John Samuel (PT), Lecturer, ACP 11
- 12. Stratified Random Sampling• Used for heterogeneous population• Population is divided into homogeneous groups (strata), according to a characteristic of interest (e.g. sex, religion, location)• Then a simple random sample is selected from each stratum Dr. Asir John Samuel (PT), Lecturer, ACP 12
- 13. SRs - Merits• More representative• Greater accuracy• Can acquire information about whole population and individual strata Dr. Asir John Samuel (PT), Lecturer, ACP 13
- 14. SRs - Demerits• Careful stratification• Random selection in each stratum• Time consuming Dr. Asir John Samuel (PT), Lecturer, ACP 14
- 15. Systematic Sampling• Sampling units are selected in a systematic way, that is, every Kth unit in the population is selected• First divide the population size by the, required sample size (sampling fraction). Let the sampling fraction be K Dr. Asir John Samuel (PT), Lecturer, ACP 15
- 16. Systematic Sampling• Select a unit at random from the first K units and thereafter every Kth unit is selected• If, N=1200• And n=60• Then, SF=20 Dr. Asir John Samuel (PT), Lecturer, ACP 16
- 17. SS - Merits• Simple and convenient• Less time and work Dr. Asir John Samuel (PT), Lecturer, ACP 17
- 18. SS - Demerits• Need complete list of units• Periodicity• Less representation Dr. Asir John Samuel (PT), Lecturer, ACP 18
- 19. Cluster Sampling• The sampling units are groups or clusters• The population is divided into clusters, and a sample of clusters are selected randomly• All the units in the selected clusters are then examined or studied Dr. Asir John Samuel (PT), Lecturer, ACP 19
- 20. Cluster Sampling• It is always assumed that the individual items within each cluster are representation of population• E.g. District, wards, schools, industries Dr. Asir John Samuel (PT), Lecturer, ACP 20
- 21. CS - Merits• Saving of travelling time and consequent reduction in cost• Cuts down on the cost of preparing the sampling frame Dr. Asir John Samuel (PT), Lecturer, ACP 21
- 22. CS - Demerits• Units close to each other may be very similar and so, less likely to represent the whole population• Larger sampling error than simple random sampling Dr. Asir John Samuel (PT), Lecturer, ACP 22
- 23. Multistage Sampling• Selection is done in stages until final sampling units are arrived• At first stage, Random sampling of large sized sampling units are selected, from the selected 1st stage sampling units another sampling units of smaller sampling units are selected, randomly Dr. Asir John Samuel (PT), Lecturer, ACP 23
- 24. Multistage Sampling• Continue until the final sampling units are selected• E.g. Few states – District – Taulk Dr. Asir John Samuel (PT), Lecturer, ACP 24
- 25. MS - Merits• Cut down the cost of preparing the sampling frame Dr. Asir John Samuel (PT), Lecturer, ACP 25
- 26. MS - Demerits• Sampling error is increased compared to simple random sampling Dr. Asir John Samuel (PT), Lecturer, ACP 26
- 27. Quota Sampling• Interviewers are requested to find cases with particular types of people to interview Dr. Asir John Samuel (PT), Lecturer, ACP 27
- 28. Judgment (Purposive Sampling)• Researcher attempts to obtain sample that appear to be representative of the population selected by the researcher subjectively Dr. Asir John Samuel (PT), Lecturer, ACP 28
- 29. Convenience Sampling• Sampling comprises subject who are simply avail in a convenient way to the researcher• No randomness and likelihood of bias is high Dr. Asir John Samuel (PT), Lecturer, ACP 29
- 30. Snowball Sampling• Investigators start with a few subjects and then recruit more via word of mouth from the original participants Dr. Asir John Samuel (PT), Lecturer, ACP 30
- 31. Merits• Easy• Low cost• Limited time• Total list population Dr. Asir John Samuel (PT), Lecturer, ACP 31
- 32. Demerits• Selection bias• Sample is not representation of population• doesn’t allow generalization Dr. Asir John Samuel (PT), Lecturer, ACP 32
- 33. Sample SizeDetermination
- 34. p-value• Probability of getting a minimal difference of what has observed is due to chance• Probability that the difference of at least as large as those found in the data would have occurred by chance Dr. Asir John Samuel (PT), Lecturer, ACP 34
- 35. Hypothesis• Alternate hypothesis (HA)- Statement predict that a difference or relationship b/w groups will be demonstrated• Null hypothesis (H0)- Researcher anticipate “no difference” or “no relationship” Dr. Asir John Samuel (PT), Lecturer, ACP 35
- 36. Decision for 5% LOS• If p-value <0.05, then data is against null hypothesis• If p-value ≥0.05, then data favours null hypothesis Dr. Asir John Samuel (PT), Lecturer, ACP 36
- 37. Type I & II errors Possible states of Null Hypothesis Possible True Falseactions on Accept Correct Type II Null Action errorHypothesis Reject Type I Correct error Action Prob (Type I error) – α (LoS) Prob (Type II error) – β 1-β – power of test Dr. Asir John Samuel (PT), Lecturer, ACP 37
- 38. Z valuesZ 0.05 – 1.96 – 95%Z 0.10 – 1.282 – 90%Z 0.20 – 0.84 – 80% Dr. Asir John Samuel (PT), Lecturer, ACP 38
- 39. Comparison of 2 means n= 2 [(Zα+Zβ)s/d]²Zα – LoSZβ – power of studys – pooled SD of the two sampled – clinically significant difference Dr. Asir John Samuel (PT), Lecturer, ACP 39
- 40. Eg. for Comparison of 2 means• A RCT to study the effect of BP reduction. One group received a control diet and other-test diet. What would be the sample size in order to provide the study with power of 90% to detect a difference in sys. BP of 2 mm Hg b/w two groups at 5% LoS? The SD of sys. BP is observed to be 6 mmHg. Dr. Asir John Samuel (PT), Lecturer, ACP 40
- 41. Estimating proportion n = Z α² P (1-P) / d²P – proportion of event in populationd – acceptable margin of error in estimating thetrue population proportion Dr. Asir John Samuel (PT), Lecturer, ACP 41
- 42. Eg. Estimating proportion• To determine the prevalence of navicular drop in ACL injured population by anticipating of 15% with acceptable margin of error is 3%= (1.96)²(0.15)(0.85) / (0.03)²= 544.2 Dr. Asir John Samuel (PT), Lecturer, ACP 42
- 43. Estimating mean n = (Zα σ / d)²σ – anticipated SD of populationd – acceptable margin of error in estimating truepopulation mean Dr. Asir John Samuel (PT), Lecturer, ACP 43
- 44. Eg. Estimating mean• To determine the mean no. of days to ambulate pt undergoing stroke rehabilation among stroke pts. Where anticipated SD of days are 60 and acceptable margin of error is 20 daysn = (1.96 x 60/20)²n = (5.88)² = 34.6 Dr. Asir John Samuel (PT), Lecturer, ACP 44
- 45. Comparison of 2 proportions n = (Zα √2PQ + Zβ√P1Q1+P2Q2)²/(P1-P2)²P = P1+P2/2 Q = 1-P Dr. Asir John Samuel (PT), Lecturer, ACP 45
- 46. Eg. Comparison of 2 proportions• To see whether there is any sig. difference in percentage of strength increase after 4 wks of intervention b/w a new technique and standard one• Standard one – 70% (P1)• New technique – 75% (P2) Dr. Asir John Samuel (PT), Lecturer, ACP 46

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