Biostatistics subject sampling in research.pptx

Sampling

1. SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY Presented By B. DEEPTHI I MDS Department Of PROSTHODONTICS 1 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

2. CONTENTS: Introduction Definition Sample design Classification of sampling methods Probability sampling methods Non-probability sampling methods Sampling errors Descriptive Biostatistics Measures of central tendecy Conclusion References 2 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

3. Sample 3 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

4. DEFINITIONS Sampling: The process through which a sample is extracted from a population. Sampling units: The elementary units/ group/ cluster that form basis of sampling process. It is the basic level of investigation. The research objective should define the sample unit. Sampling frame : The list of the sampling units is called as sampling frame. Sample size: The number of sampling units to be selected. 4 C.R. Kothari, Research Methodology – Methods and Techniques, 2004, 2 nd edition, New age International (P) Ltd publishers, pg no: 55 – 65 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

5. ADVANTAGES OF SAMPLING It reduces the cost of investigation,the time required and the no.of personnel involved It allows thorough investigation of the units of observation It helps to provide adequate and indepth coverage of the sample units 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 5

6. Ideal requirements of sample Efficiency Representativeness Measurability Size Coverage Goal orientation Feasibility Economy and cost-efficiency 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 6

7. SAMPLE DESIGN: A sample design is a definite plan for obtaining a sample from a given population. CHARACTERSTICS OF A GOOD SAMPLE DESIGN; It must result in a truly representative sample. It must be which results in a small sampling error. It must be viable in the context of funds available for the research study. It must be such that systematic bias can be controlled in a better way. 7 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

8. Steps in sample design 1. Type of universe : a) Finite universe – number of items is certain eg : population of a city, number of students in a college Infinite universe – number of items is infinite eg : number of stars in the sky 8 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

9. 2 . Sampling unit : it may be Geographical unit such as city, district, village etc. Construction unit such as house, flat etc. Social unit such as school,college , family 3. Source list: Also known as sampling frame from which sample is to be drawn List should be comprehensive, correct, reliable and appropriate 4 . Size of sample: Refers to the number of items to be selected from universe to constitute a sample 9 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

10. 5. Parameters of interest: In determining the sample design, one must consider the question of the specific population parameters which are of interest. 6. Budgetary constraints: cost considerations 7. Sampling procedures: The researcher must decide the technique to be used in selecting the items for the sample. He must select that design which, for a given sample size and for a given cost, has a smaller sampling error. 10 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

11. Classification of Sampling Methods 11 C.R. Kothari, Research Methodology – Methods and Techniques, 2004, 2 nd edition, New age International (P) Ltd publishers, pg no: 55 – 65 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

12. Sampling based on element selection technique UNRESTRICTED SAMPLING: When each sample element is drawn individually from the population at large, then the sample so drawn is known as unrestricted sample RESTRICTED SAMPLING: All other forms of sampling other than unrestricted sampling are covered under the term restricted sampling. 12 C.R. Kothari, Research Methodology – Methods and Techniques, 2004, 2 nd edition, New age International (P) Ltd publishers, pg no: 55 – 65 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

13. Simple random sampling This method is used when the whole population is accessible and the investigators have a list of all subjects in this target population. Every member of the population has an equal chance of being selected Eg : Lottery method 13 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

14. Random tables First 30 sets of Tippette’s random numbers 14 C.R. Kothari, Research Methodology – Methods and Techniques, 2004, 2 nd edition, New age International (P) Ltd publishers, pg no: 55 – 65 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

15. Advantages: Known and equal chance of selection. Simple to conduct Disadvantages: Complete list of individuals in the universe is required. 15 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

16. Systematic random sampling In systematic sampling only the first unit is selected randomly and the remaining units of the sample are selected at fixed intervals. 16 C.R. Kothari, Research Methodology – Methods and Techniques, 2004, 2 nd edition, New age International (P) Ltd publishers, pg no: 55 – 65 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

17. Advantages: Time and labor involved in the collection of sample is relatively small. This design is simple, convenient to adopt. Disadvantages: Complete list of individuals in the universe is required. 17 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

18. Stratified sampling This method is followed when population is heterogeneous. The population is first divided into homogeneous groups or classes called strata according to certain common characteristics. Then random or systematic sampling is performed independently. 18 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

19. Advantages: Ensures a representative sample for a heterogeneous population. Superior to simple random sampling because the process of stratifying reduces sampling error and ensures a greater level of representation. Disadvantages: Requires a complete list of the population. 19 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

20. Cluster sampling When the total area of the research is too large a better way for the researcher is to divide the area into smaller part This method is used when the population of interest is large and widely geographically dispersed. 20 Ilker Etkin et al, Sampling and Sampling methods, Biometrics & Biostatistics International Journal, 2017, 5(6):00149 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

21. Advantages: Faster and less expensive than Simple random sampling. Does not require a list of all members of the universe. Possible for a large population. Disadvantages: The more homogeneous the cluster chosen, the more imprecise the sample results. 21 Moshin alvi et al, a Manual for selecting sampling techniques in research, MPRA ( Munich Personal RePEC Archive) paper no.70218, 2016 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

22. Area sampling: If cluster happens to be some geographic subdivisions, in that case cluster sampling is better known as area sampling. 22 Ilker Etkin et al, Sampling and Sampling methods, Biometrics & Biostatistics International Journal, 2017, 5(6):00149 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

23. Convenience sampling Also called as Chunk or Incidental or Accidental or Opportunity sampling. Samples drawn at the convenience of the interviewer. Often, respondents are selected because they happen to be in the right place at the right time. 23 Moshin alvi et al, a Manual for selecting sampling techniques in research, MPRA ( Munich Personal RePEC Archive) paper no.70218, 2016 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

24. Advantages : Least expensive Least time consuming and most convenient Disadvantages : Selection bias Sample not representative 24 Mohamed Elfil et al, Sampling methods in Clinical Research; An Educational Review, 2017, 5(1):e52 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

25. Purposive sampling Also known as Deliberate, Judgement, Selective or Subjective sampling. This sampling method involves purposive or deliberate selection of particular units of the universe for constituting a sample which represents the universe. The researcher’s judgement is used for selecting items which he considers as representative of the population. This method is useful for conducting studies in small samples and pilot study. 25 Moshin alvi et al, a Manual for selecting sampling techniques in research, MPRA ( Munich Personal RePEC Archive) paper no.70218, 2016 Ilker Etkin et al, Sampling and Sampling methods, Biometrics & Biostatistics International Journal, 2017, 5(6):00149 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

26. Advantages: Low cost Convenient Less time consuming Useful, if there are only limited number of primary data Disadvantages: Certain members of the population will have a smaller or no chance of selection compared to others. High levels of bias. Sampling units may vary in size at different stages and hence the ultimate units chosen may be quite different from the universe. 26 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

27. Snowball sampling: This method is used when the population cannot be located in a specific place and therefore, it is difficult to access this population. In this method, the investigator asks each subject to give access to his colleagues from the same population. Thus the sample group appears to grow like a rolling snowball. 27 Mohamed Elfil et al, Sampling methods in Clinical Research; An Educational Review, 2017, 5(1):e52 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

28. Advantages: It makes possible to approach a rarely available population. Disadvantages: Systematic errors are likely to occur. 28 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

29. Quota sampling In quota sampling, we select people non-randomly according to some fixed quota. These are samples that set a specific number of individuals to be interviewed. Advantages: Sample can be controlled for certain characteristics Disadvantages: Selection bias No assurance of representativeness. 29 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

30. Multistage sampling Complex form of cluster sampling. In this sampling procedure is carried out in several stages. Multi-stage sampling is applied in big inquires extending to a considerable large geographical area. Employed in large country survey 30 C.R. Kothari, Research Methodology – Methods and Techniques, 2004, 2 nd edition, New age International (P) Ltd publishers, pg no: 55 – 65 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

31. Advantages: It enables the use of existing division and sub-division which saves extra labour. It does not require sampling frame of the entire sampling universe. Disadvantages: Sampling error is usually higher in this technique. Group-level information is required. 31 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

32. Multiphase sampling Information is collected from the whole sample and additional part from the sub-sample. (Sub-sampling) For example, in a school health survey, all the children in the school are examined. From these, only the ones with oral health problems are selected in the second phase. A section needing treatment are selected in the third phase. The number of children in the sub-samples in 3 rd and 4 th phase becomes smaller and smaller. This method may be adopted when the interest is in any specific disease. 32 Anita S Acharya et al, Sampling: Why and How of it?, Indian Journal of Medical Specialities, 2013, vol. 4(2), pg.no. 330-333. SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

33. Types of errors Sampling errors Non sampling errors 33 K. Park, Textbook of Preventive and Social Medicine, 2019, 25 th edition, Banarsidas Bhanot Publishers, pg no: 912-913 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

34. SAMPLING ERROR Level of precision It is the range in which the true value of the population is estimated to be. Represented by ± 34 Glenn D. Israel, 2009, Program Evaluation and Organizational Development, IFAS extension, University of Florida, PEOD-6. SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

35. NON-SAMPLING ERROR Non-sampling errors arise due to Usage of inadequately calibrated instruments. Coverage error: due to non-response or non-cooperation of the informant. Observational error: due to interviewers bias or imperfect experimental technique or interaction of both Processing error: due to errors in statistical analysis 35 K. Park, Textbook of Preventive and Social Medicine, 2019, 25 th edition, Banarsidas Bhanot Publishers, pg no: 912-913 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

36. MEASURES OF CENTRAL TENDENCY 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 36

37. BIOSTATISTICS: It is the method of collection, organizing, tabulating, analyzing and interpretation of data related to living organisms and human beings. 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 37

38. 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 38 Statistics Descriptive Statistics Inferential Statistics

39. Descriptive Statistics Descriptive statistics means summarising/describing the data set There are various methods to describe the data Eg : percentage, mean, median and mode Based on the data distribution, the data should be appropriately summarized. Descriptive statistics has two parts : measures of central tendency measures of dispersion 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 39

40. Measure Of Central Tendency In any data distribution, normally data are concentrated around a central value or data tend to congregate around a central value, this tendency is called central value or central tendency, and measuring this value is called measures of central tendency. This value represents the entire group of values and helps in drawing some conclusion, e.g. average bond strength of an agent. There are several kinds of measures of central tendency, of which the commonly used are: ( i ) arithmetic mean , (ii) median and (iii) mode . 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 40

41. A good measure of central tendency should satisfy the following properties: It should be easy to understand and compute It should be based on each and every item in the series It should not be affected by extreme observations It should have sampling stability 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 41

42. Arithmetic Mean Arithmetic mean is the most commonly used measure, and it is obtained by summing up the values of all the observations, divided by the total number of observation. If X is a variable and X1 , X2 , X3 . Xn are individual values of n observation, then the arithmetic mean is given by X = X1 + X2 + X3 + + Xn /n Example: Values of pulse rate per min of a group are: 67, 72, 73, 68, 71, 74 Mean(X)=67 + 72 + 73 + 68 + 71 + 74/6 = 70.83/min The advantage of mean is easy to calculate and understand but it may not be representative when there are extreme values. 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 42

43. Median Median is the central value after arranging in ascending or descending order. Median is the value which divides the distribution in such a way that equal number of observations lie on either side of it. To obtain the median, first the data is arranged in ascending or descending order of magnitude, and the value of middle observation gives median value. If the number of observation(n) is odd, then the middle value is median, 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 43

44. If n is even, then average of middle two observation gives median. For example, DMFT of five children are as follows: 4, 2, 4, 3, 1 Arranging the observation in ascending or descending order gives: 1, 2, 3, 4, 4 then the Median = 3 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 44

45. Mode Mode is the value which most commonly occurs observation in the distribution, or occurs most frequently in a series. For example, values of pulse rate per min of a group are: 71, 72, 73,68, 71, 71 Mode = 71/min Though mode is more representative and easy to find, it is not unique, i.e. it may give two or more values sometimes . When mode is illdefined it can be calculated Mode= 3Median – 2Mean 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 45

46. Arithematic mean –most commonly used Median - if there are extreme values in the series of data Mode -If it is rquired to know the value that has high influence in the series 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 46

47. Measures Of Dispersion Measures of central tendency alone do not summarize the data completely. To give a better picture of the distribution of the data, we need to understand the variation in the data distribution within the sample. Measuring the variation between the observations is called as measure of dispersion 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 47

48. Also, measure of variation is important whenever the comparison of mean between the two or more is needed. For example, two sleep producing drugs are administered for two groups of patients. Results are as follows: Drug A: 6, 2, 4, 3, 5, 2 Mean = 3.7 hours Drug B: 1, 6, 7, 1, 2, 6 Mean = 3. 7 hours 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 48

49. 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 49 The Four Different Measures Of Dispersion Are: (i) range (ii) mean deviation (iii) standard deviation and (iv) co-efficient of variation.

50. 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 50 RANGE: Range is the simplest measure of dispersion. It can be used by one who has little knowledge of statistics . It is the difference between the highest and lowest. This is not a satisfactory measure as it is based only on two extreme values. It does not consider all the observations to find range

51. MEAN DEVIATION It is the average of the deviations from the arithmetic mean Mean deviation (MD)= ( x - X)/n Though simple, easy to calculate and better measure of variation, mean deviation is not used in statistical analysis as it cannot be used in further mathematical expressions. 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 51

52. 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 52 Example : The diastolic blood pressure of 10 individuals was as follows : 83, 75, 81 , 79, 71, 95, 75, 77, 84 and 90.Then mean deviation is calculated as.

53. Standard Deviation 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 53 Standard deviation is an improvement over mean deviation as a measure of dispersion, and is used most commonly in statistical analysis. It is defined as Root-Mean-Square-Deviation.

54. The steps involved in calculating the standard deviation are as follows : First of all, take the deviation of each value from the arithmetic mean, ( x -x) (b) Then, square each deviation - ( x - x ) 2 (c) Add up the squared deviations -  ( x - x ) 2 (d) Divide the result by the number of observations n : [or (n - 1) in case the sample size is less than 30) (e) Then take the square root, which gives the standard deviation 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 54

55. 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 55

56. Uses Of Standard Deviation: Standard deviation shows that how the data are scattered from mean. It helps to indicate whether variation of difference of an individual from the mean is by chance. It helps in finding the suitable size of sample in sampling technique 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 56

57. Co-efficient Of Variation It is a measure used to compare relative variability To compare the variability between two characteristics or group Quite often variation of the same character in two or more different series has to be compared e.g. Growth varies more in girls or in boys Variation of pulse rate is more in young or old. Co-efficient of variation is expressed in terms of percentage. It is calculated as follows: Co-efficient of Variation (CV) = (SD/Mean) X 100 03-07-2024 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 57

58. CONCLUSION A perfect representative sample is necessary to conduct a survey or research to know the statistics of a population. To get a representative sample of the population, one must follow the right sampling technique to draw the required sample size and type of data to be studied. At times, several methods of sampling may be used in the same study. 58 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

59. REFERENCES K. Park, Textbook of Preventive and Social Medicine, 2019, 25 th edition, Banarsidas Bhanot publishers: pg. no: 912-913 Mohamed Elfil et al, Sampling methods in Clinical Research; An Educational Review, 2017, 5(1):e52 Ilker Etkin et al, Sampling and Sampling methods, Biometrics & Biostatistics International Journal, 2017, 5(6):00149 Moshin alvi et al, a Manual for selecting sampling techniques in research, MPRA (Munich Personal RePEC Archive) paper no.70218, 2016 59 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024

60. Anita S Acharya et al, Sampling: Why and How of it?, Indian Journal of Medical Specialities, 2013, vol. 4(2), pg.no. 330-333. C.R. Kothari, Research Methodology – Methods and Techniques, 2004, 2 nd edition, New age international (P) Ltd publishers, pg no: 55 – 65. Bartati Banerjee, Mahajan’s method in Biostatistics for Medical students and Research workers, 2018, 9 th edition, Jaypee Brothers Medical Publishers (P) Ltd, pg. no- 130. Glenn D. Israel, 2009, Program Evaluation and Organizational Development, IFAS extension, University of Florida, PEOD-6. 60 SAMPLING IN RESEARCH AND MEASURES OF CENTRAL TENDENCY-60 03-07-2024