Sampling Design PDF

Sampling Design Census and Sample Survey Implications of a Sample Design Steps in Sampling Design Criteria of Selecting a Sampling Procedure Characteristics of a Good Sample Design Different Types of Sample Designs How to Select a Random Sample? Random Sample from an...

Sampling Design Census and Sample Survey Implications of a Sample Design Steps in Sampling Design Criteria of Selecting a Sampling Procedure Characteristics of a Good Sample Design Different Types of Sample Designs How to Select a Random Sample? Random Sample from an Infinite Universe Complex Random Sampling Designs Conclusion  CENSUS AND SAMPLE SURVEY All items in any field of inquiry‘Universe’ or constitute a ‘Population.’ A complete enumeration of all items in the ‘population’ is known as a census inquiry. It can be presumed that in such an inquiry, when all items are covered, no element of chance is left and highest accuracy is obtained.  CENSUS AND SAMPLE SURVEY But when the field of inquiry is large, this method becomes diffi cult to adopt because of the resources involved. many a time it is not possible to examine every item in the population. it is possible to obtain sufficiently accurate results by studying only a part of total population called respondents  CENSUS AND SAMPLE SURVEY The selected respondents constitute what technically is called a ‘sample’. The selection process is called ‘sampling technique.’ The survey so conducted is known as ‘sample survey’.  IMPLICATION OF A SAMPLE DESIGN A sample design is a technique or the procedure that the researcher would adopt in selecting items for the sample from a given population. Sample design is determined before data are collected. Researcher must select/prepare a sample design which should be reliable and appropriate for his research study.  STEPS IN SAMPLE 1. DESIGN Type of universe The first step in developing any sample design is to clearly define the set of objects, technically called the Universe, to be studied. Universe can be finite (number of items is certain, eg : number of workers in a factory) or infinite (number of items is infinite, eg : number of stars in the sky). 2. Sampling unit A decision has to be taken concerning a sampling unit before selecting sample. may be a geographical one (state, district, village, etc.,) or a construction unit (house, flat, etc.,) or a social unit (family, club, school, etc.,) or an individual. STEPS IN SAMPLE DESIGN 3.Source list contains the names of all items of a universe 4. Size of sample refers to the number of items to be selected from the universe to constitute a sample. 5. Parameters of interest one must consider the specific population parameters which are of interest (proportion of persons with some characteristic in the population) 6. Budgetary constraint Cost considerations 7. Sampling procedure researcher must decide the type of sample he will use i.e., he must decide about the technique to be used in selecting the items for the sample.  CRITERIA OF SELECTING A SAMPLING PROCEDURE While selecting a sampling procedure, researcher must ensure that the procedure causes a relatively small sampling error and helps to control the systematic bias. Systematic bias results from errors in the sampling procedures. Eg: Election Polls: A polling agency conducts a survey via landline telephones. This might systematically exclude younger individuals who primarily use mobile phones, leading to biased results. Sampling errors are the random variations in the sample estimates around the true population parameters Eg:A researcher surveys 50 people randomly to determine the favorite food of a city. By chance, more pizza lovers are included in the sample, making the estimate slightly CRITERIA OF SELECTING A SAMPLING Sampling Errors PROCEDURE –Sampling error decreases with the increase in the size of the sample The measurement of sampling error is usually called the ‘precision of the sampling plan’. –If we increase the sample size, the precision can be improved. –But increasing the size of the sample has its own limitations viz., a large sized sample increases the cost of collecting data and also enhances the systematic bias. –Thus the effective way to increase precision is usually to select a better sampling design which has a smaller sampling error for a given sample size at a given cost.  1. Inappropriate Sampling Frame A sampling frame is a list or representation of the elements of the population. If it is biased or incomplete, it does not adequately represent the entire population 2. Defective Measuring Device Errors in measurement tools or procedures introduce consistent inaccuracies. Examples: A biased questionnaire (leading questions or incomplete options). A physical measuring device (e.g., a faulty scale) producing incorrect readings. An interviewer influencing responses through tone or demeanor 3. Non-Respondents When certain individuals in the sample do not respond, the final dataset may not reflect the population accurately. Reason for Bias: Non-responses are often correlated with the characteristic being measured. For example, wealthier individuals may be less likely to participate in income surveys, skewing results.  4. Indeterminacy Principle People may behave differently when they know they are being observed. Example: Workers may deliberately slow down in a time-study exercise if they suspect it will lead to increased work quotas. 5. Natural Bias in Data Reporting Respondents often consciously or unconsciously misreport data, depending on the context or perceived consequences. Examples: Downward bias in income data for tax purposes (to avoid scrutiny or higher taxes). Upward bias in income data for social status surveys (to appear affluent). In psychological surveys, respondents may give socially desirable answers rather than honest responses. CHARACTERISTICS OF A GOOD SAMPLE DESIGN a) Sample design must result in a truly representative sample. b) Sample design must be such which results in a small sampling error. c) Sample design must be viable in the context of funds available for the research study. d) Sample design must be such so that systematic bias can be controlled in a better way. e) Sample should be such that the results of the sample study can be applied, in general, for the universe with a reasonable level of confidence. DIFFERENT TYPES OF SAMPLE DESIGNS Probability sampling is based on the concept of random selection. Non-probability sampling is ‘non-random’ sampling. DIFFERENT TYPES OF SAMPLE DESIGNS Non-probability Sampling – Non-probability sampling is also known by different names such as deliberate sampling, purposive sampling and judgement sampling. – In this type of sampling, items for the sample are selected deliberately by the researcher; his choice concerning the items remains supreme. Types of Non-Probability Sampling: 1.Purposive or Judgment Sampling: The researcher selects specific items or units based on their judgment of what constitutes a representative sample. Example: Choosing certain towns and villages to study the economic conditions of a state. Advantages: 1. Quick and cost-effective for small studies. 2. Useful when domain expertise is available. Disadvantages: 3. High risk of personal bias affecting the results. 4. Limited reliability for large-scale or critical studies. 2.Quota Sampling: A subset of purposive sampling where the population is divided into strata (e.g., age, gender, income groups), and interviewers are assigned quotas to fill within each group. Advantages: 1. Convenient and inexpensive. 2. Ensures some representation from key subgroups. Disadvantages: 3. Final sample is often subjectively selected, not random. 4. Results lack statistical robustness and are not formally generalizable.  Advantages of Non-Probability Sampling: 1.Cost-Effectiveness: Requires fewer resources and is quicker to conduct. 2.Flexibility: Can be adapted to specific research needs. 3.Feasibility: Practical for exploratory or small-scale studies. Disadvantages of Non-Probability Sampling: 1. Risk of Bias: The personal judgment of the researcher can lead to skewed samples. 2. Lack of Generalizability: Results cannot be confidently applied to the entire population. 3. Non-Statistical Basis: Sampling errors and biases cannot be formally measured or corrected 4. Limited Use in Large Studies: Rarely adopted for significant inquiries where precision and reliability are critical. Applications: Small-Scale Studies: Ideal for pilot studies, exploratory research, or situations with limited resources. Preliminary Research: Useful for generating hypotheses and understanding trends before larger studies. Convenience Sampling: Situations where representative sampling is not feasible due to constraints of time, budget, or access. DIFFERENT TYPES OF SAMPLE DESIGNS Probability Sampling – Probability sampling is also known as ‘random sampling’ or ‘chance sampling’. – Under this, every item of the universe has an equal chance of inclusion in the sample. – Random sampling ensures the law of Statistical Regularity which states that if on an average the sample chosen is a random one, the sample will have the same composition and characteristics as the universe. – This is the reason why random sampling is considered as the best technique of selecting a representative sample. Types of Probability Sampling: 1.Simple Random Sampling: Each element in the population has an equal chance of selection. For example: Random selection of 20 students from class of 50 student. Each student has equal chance of getting selected. Here probability of selection is 1/50 2.Sampling With and Without Replacement: 1. Without Replacement: Once an item is selected, it is not returned to the population for further selection. 2. With Replacement: Selected items are returned to the population before subsequent selections, allowing the same item to be chosen more than once. 3.Stratified Random Sampling: Population is divided into subgroups (strata) based on certain characteristics, and random samples are taken from each stratum. 4.Systematic Sampling: Selecting every kth item from a list, where k is a fixed interval. 5.Cluster Sampling: Dividing the population into clusters and randomly selecting entire clusters for study. 6.Multi-Stage Sampling: A complex form of cluster sampling conducted in multiple stages.  How to Select a Random Sample?  Random sampling involves ensuring that each element in the population has an equal and independent chance of being selected. Below are methods and procedures for selecting a random sample in practice. a. Lottery Method Process: Write each element of the population on a slip of paper. Place all slips into a container. Mix thoroughly and draw slips one by one without looking until the required sample size is reached. Drawbacks: Impractical for large or complex populations. Limited utility in modern, large-scale sampling scenarios. b. Successive Drawing without Replacement c. Using Random Number Tables Random number tables (e.g., Tippett’s Table) are pre-constructed datasets of random digits. Each element of the population is assigned a unique number. Identify the range of population numbers (e.g., 3001 to 8000). Read the table sequentially to select numbers within the specified range For example, from Tippett’s table, selecting 10 random numbers: Numbers like 6641, 3992, 7979, etc., form the random sample.  RANDOM SAMPLE FROM AN INFINITE UNIVERSE An infinite population refers to a scenario where the population size is too large or indefinite to enumerate (e.g., all possible outcomes of a random experiment). A random sample from an infinite population ensures that: Each selection is controlled by the same probabilities. Successive selections are independent of each other. Examples of Random Sampling in Infinite Populations Rolling a Dice Imagine a hypothetically infinite population of outcomes from rolling a fair six-sided dice. We roll the dice 20 times, treating the results as a sample. The 20 dice rolls constitute a random sample from the infinite population of all possible dice rolls. COMPLEX RANDOM SAMPLING DESIGNS 1. Systematic sampling 2. Stratified sampling 3. Cluster sampling 4. Area sampling 5. Multi-stage sampling 6. Sampling with probability proportional to size 7. Sequential sampling  COMPLEX RANDOM SAMPLING DESIGNS Systematic sampling – Systematic sampling is a practical method of sampling where items are selected at regular intervals from a list or population. To introduce randomness, the starting point of the selection process is chosen randomly – Random Start: A random number is used to determine the starting point within the first k elements, where k is the interval determined by the desired sample size. – Fixed Intervals: After selecting the first item, every k-th item is included in the sample. For instance, if a 4% sample is needed, k will be 25 (as 4% of 100 is 1/25). The first item is selected randomly from the first 25, and then every 25th item is added to the sample. COMPLEX RANDOM SAMPLING DESIGNS Stratified sampling A sampling technique used when the population is not homogeneous. Ensures the sample is representative of the population. Divide the population into homogeneous sub-populations (strata). Select samples from each stratum. Example: A study on education levels may divide the population by age group, gender, or location. Stratified sampling – The following three questions are highly relevant in the context of stratified sampling: (a) How to form strata? (b) How should items be selected from each stratum? (c) How many items be selected from each stratum or how to allocate the sample size of each stratum?  How to form strata? Ensure homogeneity within each stratum and heterogeneity between different strata. Approach: Form strata based on common characteristics (e.g., age groups, income levels, geographic regions) that are relevant to the study. Leverage past experience and personal judgment for initial stratification. Consider the relationship between: Characteristics of the population. Characteristics to be estimated. Pilot Studies: Conduct small-scale surveys to test proposed strata. Evaluate variances within and between strata to refine the stratification plan. A careful stratification plan improves sampling efficiency by reducing sampling error.  How Should Items Be Selected From Each Stratum? The selection method within each stratum typically involves: Simple Random Sampling: Ensures every item in the stratum has an equal chance of selection. Systematic Sampling: Can be employed when it offers logistical or analytical advantages over random sampling. The choice depends on the research context, the nature of the population, and available resources.  How to Allocate the Sample Size to Each Stratum? This part wasn't covered in detail in your excerpt, but it typically involves: Proportional Allocation: The sample size for each stratum is proportional to its size in the population. Optimal Allocation: Factors in variability within strata and costs of sampling to allocate sample sizes efficiently. Optimal Allocation (Disproportionate Sampling):  COMPLEX RANDOM SAMPLING DESIGNS Cluster sampling – Thus in cluster sampling the total population is divided into a number of relatively small subdivisions which are themselves clusters of still smaller units and then some of these clusters are randomly selected for inclusion in the overall sample. Area sampling – If clusters happen to be some geographic subdivisions, in that case cluster sampling is better known as area sampling  COMPLEX RANDOM SAMPLING DESIGNS Multi-stage sampling – Multi-stage sampling is a further development of the principle of cluster sampling. Sampling with probability proportional to size – In case the cluster sampling units do not have the same number of elements, it is considered appropriate to use a random selection process where the probability of each cluster being included in the sample is proportional to the size of the cluster. COMPLEX RANDOM SAMPLING DESIGNS Sequential sampling – This sampling design is some what complex sample design. – The ultimate size of the sample under this technique is not fixed in advance, but is determined according to mathematical decision rules on the basis of information yielded as survey progresses  The following are the number of departmental stores in 15 cities: 35, 17, 10, 32, 70, 28, 26, 19, 26, 66, 37, 44, 33, 29 and 28. If we want to select a sample of 10 stores, using cities as clusters and selecting within clusters proportional to size, how many stores from each city should be chosen? (Use a starting point of 10). Step-by-Step Solution: 1. Total Number of Stores (N): The total number of stores in all cities combined is the sum of the stores in each city: 2.Total Sample Size (n): You need to select a sample of 10 stores from these 500 stores. 3.Sampling Interval (k): To select the sample proportional to the size of the cities, we need to calculate the sampling interval (k), which is the number of stores in the population divided by the sample size: This means we will select every 50th store.  4.Start Point: The starting point for the sampling is given as 10. 5. Cumulative Totals: First, calculate the cumulative total of stores for each city, which represents the running total of the number of stores as you move through the cities. 6. Selecting the Stores: Starting from 10, we add 50 each time (the sampling interval), and select the corresponding cities based on the cumulative total. The selected numbers are: 10: This corresponds to the first store in city 1. 60: This corresponds to the second store in city 3. 110: This corresponds to the third store in city 5. 160: This corresponds to the fourth store in city 5. 210: This corresponds to the fifth store in city 7. 260: This corresponds to the sixth store in city 9. 310: This corresponds to the seventh store in city 10. 360: This corresponds to the eighth store in city 11. 410: This corresponds to the ninth store in city 12. 460: This corresponds to the tenth store in city 14.  So, we have selected: 1 store from city 1 (35 stores). 1 store from city 3 (10 stores). 1 store from city 7 (26 stores). 1 store from city 9 (26 stores). 1 store from city 10 (66 stores). 1 store from city 11 (37 stores). 1 store from city 12 (44 stores). 1 store from city 13 (33 stores). 1 store from city 14 (29 stores). 2 stores from city 5 (70 stores). Using proportional sampling based on size, the sample of 10 stores is selected as follows:2 stores from city 5,1 store from each of the following cities: 1, 3, 7, 9, 10, 11, 12 and 14. This ensures that the number of stores selected from each city is proportional to the number of stores in the city.