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# Sampling Theory

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Sampling Theory- Definition, Target and accessible population, Factors effecting sampling, sampling frame, Sampling technique, Sampling Process, Sample size, sampling error, sampling bias

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### Sampling Theory

1. 1. Prof Suja Santosh RVS College of Nursing, Sulur, Coimbatore
2. 2. Is one grain of rice or one teaspoon of rice to conclude the rice is boiled?
3. 3. Checking Hemoglobin and blood glucose Is One drop is enough for the conclusion?
4. 4. SAMPLING
5. 5. Sampling
6. 6. Sampling process of selecting a small number of elements (samples) from a larger defined target group of elements (Population) such tha the information gathered from the samples will allow judgments to the population
7. 7. Sampling • Sampling is used for more than just survey research – All forms of research • Quantitative research – Probability and Non Probability Sampling • Qualitative research – Non Probability Sampling
8. 8. Census Method •Complete Enumeration Survey Method - Each and every item in the universe is selected for the data collection •Whenever the entire population is studied to collect the detailed data about every unit, then the census method is applied.
9. 9. Sample vs. Census
10. 10. Purpose of Sampling 1. Economical 2. Improved quality of data 3. Quick study results 4. Precision and accuracy of data
11. 11. Basics of Sampling Theory Population Element Defined target population Sampling unit Sampling frame
12. 12. Defining Population of Interest • Population of interest is entirely dependent on Research Problems, and Research Design. • Some Bases for Defining Population: – Geographic Area – Demographics – Usage/Lifestyle – Awareness Population : A complete set of elements (persons/objects) that possess some common characteristic defined by the sampling criteria established by the researcher Eg: study to be conducted among female teachers in India
13. 13. Target Population The entire group of people or objects to which the researcher wishes to generalize the study findings EG: All low birth weight infants, all people with AIDS
14. 14. Accessible Population The portion of the population to which the researcher has reasonable access may be a subset of the target population EG: All people with AIDS in Tamilnadu, All low birth weight infants admitted to the neonatal ICUs in Tamilnadu
15. 15. ELEMENT A single member of the population or sample
16. 16. • SAMPLING UNIT : It may be geographical one such as state, district, village or it may be social unit like family, school or construction unit like house or it may be an individual and from which data is collected • SAMPLE DESIGN: It is a definite plan for obtaining sample from a given population. It refers to the technique / procedure the researcher would adapt in selecting items for the sample in the research
17. 17. Factors to Consider in Sample Design Research objectives Degree of accuracy Statistical analysis needs Time frame Knowledge of target population Resources Research scope
18. 18. Sampling Frame • A list of population elements (people, companies, houses, cities, etc.) from which units to be sampled can be selected. • Difficult to get an accurate list. • Sample frame error occurs when certain elements of the population are accidentally omitted or not included on the list. • Eg: A list of All low birth weight infants admitted to the neonatal ICUs in Tamilnadu
19. 19. CHARACTERISTICS OF GOOD SAMPLE • Representativeness • Accuracy – degree to which bias is absent from the sample • Precision – amount of error can be tolerate • Size – adequate in size and in order to be reliable • Not have any substitution of originally selected unit by some other unit • Free from bias and errors • Appropriate Sample size
20. 20. Sampling Process Identifying and defining the Target Population Describing Accessible Population Determine Sampling Frame Specifying Sampling Unit Select Sampling Technique Determine the Sample size Specifying the Sampling Plan Selecting a Desired Sample
21. 21. FACTORS INFLUENCING SAMPLING PROCESS Nature of the Researcher •Inexperienced investigator •Lack of interest •Lack of honesty •Intensive workload • Inadequate Supervision Nature of the Sample •Inappropriate Sampling Technique •Sample size •Defective Sampling frame Circumstances •Lack of Time •Large Geographic area •Lack of cooperation •Natural Calamities Target Accessible
22. 22. Classification of Sampling Techniques Sampling Techniques Non probability Sampling Techniques Probability Sampling Techniques Convenience Sampling Purposive Sampling Quota Sampling Snowball Sampling Systematic Sampling Stratified Sampling Cluster Sampling Sequential Sampling Simple Random Sampling
23. 23. Probability Sampling • representativeness is most important • equal chances to all individuals in the population to be selected as sample
24. 24. Advantages Disadvantages Easy to conduct Identification of all members of the population can be difficult High representativeness of including sample Heterogeneous population cannot apply Meet assumptions of many statistical procedures
25. 25. Simple Random Sampling Every member of population has an equal chance of being selected as sample
26. 26. Simple Random Sampling (SRS) • Population should be Homogeneous and finite • As sample size increases, sample becomes more and more representative of population. • Sampling is generally without replacement • Problem: Very costly if population is large. Choices come from a list (sampling frame )
27. 27. Simple Random Sampling • Lottery method •Random Number table •Use of Computer Generation for selection
28. 28. Simple Random Sampling
29. 29. Simple Random Sampling 1. Select a suitable sampling frame 2. Each element is assigned a number from 1 to N (pop. size) 3. Generate n (sample size) different random numbers between 1 and N 4. The numbers generated denote the elements that should be included in the sample
30. 30. ADVANTAGES • Most reliable & unbiased method • Requires minimum knowledge of study population • Free from sampling errors & bias DISADVANTAGES • Needs up-to-date complete list of all the members of the population • Expensive and time consuming Simple Random Sampling
31. 31. Stratified Random Sampling method of probability sampling in which the population is divided into different subgroups (strata) and samples are selected from each by SRS
32. 32. • A two-step process in which the population is partitioned into subpopulations, or strata. • The strata should be mutually exclusive and collectively exhaustive in that every population element should be assigned to one and only one stratum and no population elements should be omitted. • Next, elements are selected from each stratum by a random procedure, usually SRS. • A major objective of stratified sampling is to increase precision without increasing cost. Stratified Sampling
33. 33. Stratified Sampling • The elements within a stratum should be as homogeneous as possible, but the elements in different strata should be as heterogeneous as possible. • The stratification variables should also be closely related to the characteristic of interest.
34. 34. Stratified Sampling Number of samples selected based on the proportionate to the relative size of that stratum in the total population. Proportionate stratified sampling Disproportionate stratified sampling Equal number of samples from each stratum
35. 35. Disproportionate stratified sampling
36. 36. ADVANTAGES • Ensures representative sample in heterogeneous population • Comparison is possible in two groups DISADVANTAGES • Requires complete information of population • Large population is required • Chances of faulty classification of strata Stratified Sampling
37. 37. 44 Systematic Sampling • Homogeneous and Finite population
38. 38. Systematic Sampling 1. Select a suitable sampling frame 2. Each element is assigned a number from 1 to N (Population size) 3. Determine the sampling interval i; i=N/n. If i is a fraction, round to the nearest integer 4. Select a random number, r, between 1 and i, as explained in simple random sampling 5. The elements with the following numbers will comprise the systematic random sample: r, r+i,r+2i,r+3i,r+4i,...,r+(n-1)i
39. 39. Systematic Random Sampling method of probability sampling in which the defined target population is ordered and the sample is selected according to position using a skip interval
40. 40. ADVANTAGES • Convenient and simple to carry out • Distribution of sample over entire population DISADVANTAGES • Less representative sample if subjects are non randomly distributed • Sometimes may result in biased sample Systematic Sampling
41. 41. Cluster (area) Random Sampling
42. 42. Cluster Sampling • The target population is first divided into non overlapping and collectively exhaustive subpopulations, or clusters. • Then a random sample of clusters is selected, based on a probability sampling technique such as SRS. • For each selected cluster, either all the elements are included in the sample (one-stage) or a sample of elements is drawn probabilistically (two-stage). • Elements within a cluster should be as heterogeneous as possible, but clusters themselves should be as homogeneous as possible. Ideally, each cluster should be a small-scale representation of the population.
43. 43. Types of Cluster Sampling Cluster Sampling One-Stage Sampling Multistage Sampling Two-Stage Sampling sample all members of the cluster random sampling within the clusters
44. 44. One stage Cluster Sampling Examples: • There are 420 nurses working at the 22 hospitals in Coimbatore Region • We wish to interview a sample of these nurses for the research study about the workload of nurses - select a simple random of samples of 3 hospitals - interview all nurses employed at the 3 selected hospitals
45. 45. Two stage Cluster Sampling • From above example - interview only 30 nurses from the 3 selected hospitals using Simple random
46. 46. Multi stage Cluster Sampling COIMBATORE CITY Panchayat
47. 47. ADVANTAGES • Less Cost, quick and easy for a large population • More no of samples included in small time period • Large Coverage of samples from Population DISADVANTAGES • Possibility of high sampling error • Chances of least representative sample due to over-represented or under represented cluster Cluster Sampling
48. 48. 55 Difference Between Cluster and Stratified Sampling Population of L strata, stratum l contains nl units Population of C clusters Take simple random sample in every stratum Take srs of clusters, sample every unit in chosen clusters
49. 49. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z D H L P T X Systematic Sampling
50. 50. SEQUENTIAL SAMPLING The investigator initially select small sample and tries to make inferences, if not able to draw result, he then adds subjects until clear cut inferences can be drawn
51. 51. Non Probability Sampling • Each elements in the population does not guarantee equal chance to be a sample
52. 52. Non Probability sampling • Qualitative researchers are not as concerned about representativeness – Relevance to the research topic – Importance of context • Sample size does not have to be determined in advance. – Selection of cases gradually over time • Important: many statistics assume random sampling
53. 53. Non Probability Sampling Methods Convenience sampling Purposive sampling Quota sampling Snowball sampling Consecutive Sampling
54. 54. Convenience Sampling Convenience sampling attempts to obtain a sample of convenient elements. Investigator pick up all the available sample who are meeting the preset inclusion and exclusion criteria
55. 55. Convenience Sampling - sample whoever is available. – use of students, and members of social organizations – department stores using charge account lists – “people on the street” interviews
56. 56. •Used by both quantitative and qualitative researchers •Used when limited availability of time and resources Convenience Sampling
57. 57. Convenience Sampling ADVANTAGE • Easiest method • Helps in saving time, money and resources • Used in pilot study DISADVANTAGES • Chances of sampling bias • Non representative sample • Findings cannot be generalized
58. 58. Purposive Sampling  Subjects are chosen to be part of sample with a specific purpose in mind
59. 59. Purposive Sampling  Requires in-depth knowledge about accessible population  Used when limited number of individuals possess the trait of interest
60. 60. Purposive Sampling
61. 61. Purposive Sampling ADVANTAGE • Simple to draw a sample • Saves resources as it requires less field work DISADVANTAGES • Requires considerable knowledge about the population • Conscious biases may occur
62. 62. Quota Sampling The researcher ensures equal or proportionate representation of subjects, depending on which trait is considered as the basis of the quota
63. 63. Quota Sampling Quota sampling may be viewed as two-stage – The first stage consists of dividing population into non overlapping subgroups or quotas – In the second stage, sample elements are selected based on convenience or purposive.
64. 64. Quota Sampling The bases of the quota are usually age, gender, education, race, religion, socio-economic status etc ADVANTAGES • Economically cheap •Suitable where the field has to be done like studies related to market and public opinion polls DISADVANTAGES • Always does not guarantee representative sample •Chances of sampling bias
65. 65. Snowball Sampling • In snowball sampling, an initial group of respondents is selected, usually at random. • After being interviewed, these respondents are asked to identify others who belong to the target population of interest. • Subsequent respondents are selected based on the referrals.
66. 66. – Locating the initial subject and then taking assistance from the subject to identify people with a similar trait of interest
67. 67. Used by the researchers to identify potential subjects in studies where subjects are hard to locate Snowball Sampling
68. 68. - Subject refers only one other subject - Subject gives multiple referrals and each referral gives some more until required sample size reached - Subject refers multiple people but only one is chosen as sample Snowball Sampling
69. 69. The bases of the quota are usually age, gender, education, race, religion, socio-economic status etc ADVANTAGES • Facilitates sampling for people difficult to locate • Cheap, Simple and cost-efficient • Needs little planning and lesser workforce DISADVANTAGES • Little control of researcher over the sampling method • Representativeness of the sample is not guaranteed • Changes of poor coverage of entire population Snowball Sampling
70. 70. Consecutive Sampling • More like convenient sampling • Picks up all the available subjects who are meeting the preset inclusion and exclusion criteria • Used for continuously changing population, such as hospital patients
71. 71. Non Probability Sampling Methods Convenience sampling relies upon convenience and access Purposive sampling relies upon belief that participants fit characteristics Quota sampling emphasizes representation of specific characteristics Snowball sampling relies upon respondent referrals of others with like characteristics
72. 72. Difference between probability & Non probability Sampling Comparison Factors Probability Sampling Non-probability Sampling List of Population Complete list necessary Complete list not necessary Information about Sampling Units Each unit identified Need detail on Habits, Activities, Traits etc Sampling skill Skill required Little skill required Time Time consuming Low time consuming Cost Moderate to high Low Estimates of population parameters Unbiased Biased Sample Representativeness Good, Assured Suspect, Undeterminable Accuracy & Reliability Computed with Confidence interval Unknown Measurement of Sampling error Statistical measures No true measures available
73. 73. How big should your sample be? • Rule of thumb: Bigger is better
74. 74. Factors affecting Sample Size • Size of population • Nature of study • Type of Sampling techniques • Homogeneity • Degree of Accuracy (or Errors) • Availability of time, money and resources • Effect size • Variability (SD) –Pilot study, Literature • Margin of error • Power of study • Level of Significance • Dropout Rate
75. 75. Common Methods for Determining Sample Size Common Methods: –Budget/time available –Executive decision –Statistical methods –Historical data/guidelines
76. 76. Qualitative studies – Sample size • Depends upon - purpose of study - quality of informants - type of sampling - Variety of characteristics • Thumb rule estimation (In ethnography studies -25-50 samples In phenomenology studies- minimum 10 samples In grounded theory – 20-30 samples)
77. 77. Quantitative studies – Sample size • Large sample chosen is good • Power analysis used to estimate accurate sample size • Thumb rule estimation (In health science, For small sized trial /PG research- atleast 30 subjects For medium sized trial /PG research- atleast 100 For Large sized trial /PG research- atleast 300 subjects Descriptive studies – 200 subjects) • Sample size determination using sample size calculation formula - using tables, through computer
78. 78. Determining Sample size • Used for estimating adequate number of samples to be included in the study • Part of designing a High Quality study • To allow appropriate analysis • Provide desired level of accuracy • To allow validity of significance test
79. 79. Sample Size for two Population Mean
80. 80. Sample Error How close the sample size is to the population size, or how well a sample of that size approximates a given population.
81. 81. Sampling Error Difference between a sample result and the true population result, such an error results From chance sampling fluctuations
82. 82. • The standard deviation of a sampling distribution is referred to as the standard error or sampling error. • It is the deviation of the selected sample from the true characteristics, traits, behaviours, qualities or figures of entire population • The greater your sample size, the smaller the standard error. Sampling Error
83. 83. Types of Sampling Errors Sampling Errors Non Sampling Errors Any type of bias that results from mistakes in either the selection process of sampling units, sampling techniques or in determining sample size Bias that occurs in a research study regardless of whether a sample or census is used. Bias caused by measurement errors, response errors, coding errors etc.
84. 84. Difference between sampling and non sampling errors Sampling Errors Non Sampling Errors Occurs in any project involving sampling Poorly worded Questions Because only a sample of the population is studied Inadequate responses Interviewer interview the wrong respondents Non response of individuals selected to the study – Behavioural effects Bias error, where only interested respondents respond Coding error Poor Sampling methods Bias in the selection of individuals for the study
85. 85. Sampling Bias The error resulting from taking a non-random sample of a population
86. 86. Sampling Bias • Based on sampling method used, some members of a population are less likely to be included in the sample. • Reduces the ability for results to be generalized to a larger population. • Some studies might deliberately take a biased sample in order to produce misleading results. • More often, sampling bias occurs because of difficulty in obtaining a truly representative sample of a complex population.
87. 87. Types of Sampling Bias • Self-selection bias- Selection from only a specific area of the population (intentional (“purposive”), or accidental “convenience sample”) • Information bias – due to systematic measurement error or misclassification of subjects on one or more variables, either risk factors or disease status • Confounding bias – results when the risk factor being studied is so mixed up with other possible risk factors that its single effect is very difficult to distinguish • Response bias- subjects gives an incorrect response or the question is misleading
88. 88. Avoid Bias • Select individuals for the sample at Random