Fundamental of sampling
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The document discusses the fundamentals of sampling in business research, emphasizing the importance of sampling for effective and accurate research outcomes. It covers key terminologies such as population, sample, sampling frame, and details characteristics of a good sample while explaining various sampling methods and associated errors, both sampling and non-sampling. Additionally, it highlights methods to reduce errors and determine optimum sample size using Slovin's formula.
Fundamental of sampling
- 1. FUNDAMENTALS OF SAMPLING PRESENTED BY :- Siddharth Gupta. Business research methods UNIT-IV
- 2. WHAT IS SAMPLING? NEED OF SAMPLING Saves time, money and effort More effective Faster More accurate Gives more comprehensive information To bring the population to a manageable number To help in minimizing error from the despondence due to large number in the population Sampling is the act, process, or technique of selecting a suitable sample, or a representative part of a population for the purpose of determining parameters or characteristics of the whole population.
- 3. BASIC TERMINOLOGIES • POPULATION A population is the total group of people about who you are researching and about which you want to draw conclusions. • SAMPLE A part of the population which is examined to estimate the characteristics of the population is called a sample. • SAMPLING FRAME The actual set of units and a list containing every member of the population from which a sample is drawn at random is called a sampling frame. • SAMPLE UNIT Every sample is made up of several members or components known as sampling units.
- 4. • SAMPLE DESIGN Designing a plan for effectively drawing out a sample from the sampling frame is called sample design. • SAMPLE SIZE The total number of elements of the population to be included in the sample for conducting the research study is known as sample size.
- 6. CHARACTERISTICS OF A GOOD SAMPLE True representative Free from bias Accurate Comprehensive Approachable Good size Feasible Goal orientation Practical and economical
- 7. True representative:- The true representative of the population and matching its properties is termed as good sample where aggregate of certain properties is the population and sample is the sub-total of the universe. Free from Bias:- A good sample does not allows prejudices , pre-conceptions ,and imaginations which affects its choice and it is unbiased. Accurate:- A sample is called good when it yields accurate estimates or statistics and free from errors. Comprehensive:- A sample that is true representative of the population is also comprehensive in nature which is controlled by definite purpose of investigation. Approachable:- The subjects of good sample is such are easily accessible where the tools of research are easily conducted and easy collection of data is possible .
- 8. Feasible:- A good sample creates the research work more feasible. Goal orientation :- Any sample which is selected by the researcher should be able to satisfy the objective of the research. The sample should be taken in proper number . It should be customized to fit the environment under which the research is going to be conducted. Practical :- It means that the concepts of sample selection should be applied properly while conducting the research .the researcher should be well experienced end well instructed. The instructions which are passed to observer should be clear ,complete and correct in all terms so avoid errors and biasness on their part .the sample should be selected on basis of the sample design. Economical :- It refers that the research should not incur huge costs ,time or efforts. One of the objectives of any research is to complete the research with
- 10. SAMPLING ERROR A sampling error is a statistical error that occurs when an analyst does not select a sample that represents the entire population of data and the results found in the sample do not represent the results that would be obtained from the entire population. EXAMPLE- Imagine that you want to know the average height of men on earth. This average height exists but obviously you will never be able to know it (unless you're able to measure several millions men...). What you can do is measure hundreds or thousands of people and calculate the average height of these people. The average height among these people is probably not exactly equal to the average height of men on earth (because they are particular men in the whole population) but, if you did a good job (use a representative sample of the population), it should be close enough. The difference between the quantity that you want to know (average height of men on earth) and its estimation through your sample
- 11. FIVE COMMON TYPES OF SAMPLING ERRORS Population Specification Error—This error occurs when the researcher does not understand who they should survey. For example, imagine a survey about breakfast cereal consumption. Who to survey? It might be the entire family, the mother, or the children. The mother might make the purchase decision, but the children influence her choice. Sample Frame Error—A frame error occurs when the wrong sub- population is used to select a sample. A classic frame error occurred in the 1936 presidential election between Roosevelt and Landon. The sample frame was from car registrations and telephone directories. In 1936, many Americans did not own cars or telephones, and those who did were largely Republicans. The results wrongly predicted a Republican victory.
- 12. Selection Error—This occurs when respondents self-select their participation in the study – only those that are interested respond. Selection error can be controlled by going extra lengths to get participation. A typical survey process includes initiating pre-survey contact requesting cooperation, actual surveying, and post-survey follow- up. If a response is not received, a second survey request follows, and perhaps interviews using alternate modes such as telephone or person- to-person. Non-Response—Non-response errors occur when respondents are different than those who do not respond. This may occur because either the potential respondent was not contacted or they refused to respond. The extent of this non-response error can be checked through follow-up surveys using alternate modes. Sampling Errors—These errors occur because of variation in the number or representativeness of the sample that responds. Sampling errors can be controlled by (1) careful sample designs, (2) large samples, and (3) multiple contacts to assure representative response.
- 14. NON SAMPLING ERROR Non -sampling error is the error that arises in data collection process as a result of factors other than taking a sample. Non- sampling errors have the potential to cause bias in polls, surveys or samples.
- 15. TYPE OF NON SAMPLING ERROR Coverage Error Response Error Non Response Error Measurement Error Data Processing Error Data Analysis Error
- 16. COVERAGE ERROR Coverage errors are non sampling errors and result in bias, affecting the representativity of the data. Coverage errors may occur in data collected through both censuses and sample surveys. In censuses, errors of coverage comprise the under enumeration or (less commonly) the over enumeration of individuals in the population.
- 17. RESPONSE ERROR Sometimes respondent do not provide pertinent information during the survey. Response errors may be accidental. They may arise due to self- interest or prestige bias of the respondents or due to the bias of the interviewer. Due to these factors respondents furnish wrong information.
- 18. NON –RESPONSE ERROR Non response errors occur when the respondent is not available at home or the researcher is not in a position to contact him due to some other reason. Non response errors also occur when respondents refuse to answer certain questions which are important from the researchers point of view. As a result, it becomes difficult to obtain complete information. Due to this very important part of the sample do not provide relevant and required information and this leads to non sampling errors.
- 19. MEASUREMENT ERROR The measurement error is defined as the difference between the true or actual value and the measured value. The true value is the average of the infinite number of measurements, and the measured value is the precise value.
- 20. DATA PROCESSING ERROR Data processing refers to the process of systematic categorization of data to make the process of analysis easier and more accurate. However, errors may occur at the time of categorizing data such as, drawing up of tables, coding response etc.
- 21. DATA ANALYSIS ERROR Data analysis errors may be defined as those errors that arise due to the application of incorrect statistical techniques or formulae that give the wrong result. These errors may be simple as well as complex.
- 22. METHODS TO REDUCE THE ERRORS
- 23. Reducing Sampling Errors 1.Increasing the size of the sample: The sampling error can be reduced by increasing the sample size. If the sample size n is equal to the population size , then the sampling error is zero. 2.Stratification: When the population contains homogeneous units, a simple random sample is likely to be representative of the population. But if the population contains dissimilar units, a simple random sample may fail to be representative of all kinds of units in the population. To improve the result of the sample, the sample design is modified. The population is divided into different groups containing similar units, and these groups are called strata. From each group (stratum), a sub-sample is selected in a random manner. Thus all groups are represented in the sample and the sampling error is reduced. This method is called stratified-random sampling. The size of the sub-sample from each stratum is frequently in proportion to the size of the stratum. METHODS TO REDUCE THE ERRORS
- 24. Stratum # Size of stratum Size of sample from each stratum 1 N1=600N1=600 n1=n×N1N=100×600 1000=60n1=n×N1N =100×6001000=6 0 2 N2=400N2=400 n2=n×N2N=100×400 1000=40n2=n×N2N =100×4001000=4 0 N1+N2=N=1000N 1+N2=N=1000 n1+n2=n=100n1+n2 =n=100 1. Suppose a population consists of 1000 students, out of which 600 are intelligent and 400 are unintelligent. We are assuming here that we do have much information about the population. A stratified sample of size n=100 is to be selected the size of stratum is denoted by N1 and N2 respectively and the size of sample from each stratum is denoted by n1 and n2 . It is written as : n=
- 25. - Introducing consistency checks - Performing sample check - Carrying out post-census and post-survey checks - Performing external record check -Introducing the scheme of interpenetrating sub- samples - Providing detailed guidelines for data collection and data processing - Imparting proper training to the field workers and data processing personnel REDUCING NON SAMPLING ERRORS
- 27. PROBABILITY SAMPLING Probability Sampling is a sampling technique in which sample from a larger population are chosen using a method based on the theory of probability. For a participant to be considered as a probability sample, he/she must be selected using a random selection. The most important requirement of probability sampling is that everyone in your population has a known and an equal chance of getting selected.
- 28. Let us take an example to understand this sampling technique. The population of the US alone is 330 million, it is practically impossible to send a survey to every individual to gather information but you can use probability sampling to get data which is as good even if it is collected from a smaller population.
- 29. TYPES OF PROBABILITY SAMPLING SIMPLE RANDOM SYSTEMATI C CLUSTER AREA STRATIFIED RANDOM
- 30. SIMPLE RANDOM SAMPLING:- Simple random sampling is the easiest form of probability sampling . All the researcher needs to do is assure that all the members of the population are included in the list and then randomly select the desired number of subjects. SYSTEMATIC SAMPLING:- Systematic random sampling can be likened to an arithmetic progression wherein the difference between any two consecutive numbers is the same. Say for example you are in a clinic and you have 100 patients.
- 31. The first thing you do is pick an integer that is less than the total number of the population; this will be your first subject e.g. (3). Select another integer which will be the number of individuals between subjects e.g. (5). You subjects will be patients 3, 8, 13, 18, 23, and so on. CLUSTER SAMPLING:- Cluster random sampling is a way to randomly select participants when they are geographically spread out. For example, if you wanted to choose 100 participants from the entire population of the U.S., it is likely impossible to get a complete list of everyone. Instead, the researcher randomly selects areas (i.e. cities or counties) and randomly selects from within those boundaries.
- 32. AREA SAMPLING A method in which an area to be sampled is sub-divided into smaller blocks that are then selected at random and then again sub-sampled or fully surveyed. This method is typically used when a complete frame of reference is not available to be used. STRATIFIED RANDOM:- Stratified random sampling is a method of sampling that involves the division of a population into smaller sub- groups known as strata. In stratified random sampling or stratification, the strata are formed based on members' shared attributes or characteristics such as income or educational attainment. Stratified random sampling is also called proportional random sampling or quota random sampling.
- 34. NON-PROBABILITY SAMPLING Non –probability sampling is the sampling procedure which does not have any ground for estimating the probability that whether or not each item in the population has been included in the sample. In simples words, non-probability sampling is a sampling technique where the samples are gathered in a process that does not give all the individuals in the population equal chances of being selected Types: 1. Convenience Sampling 2. Purposive Sampling 3. Panel Sampling
- 35. CONVENIENCE SAMPLING Advantage:- 1. Economical 2. Proper Representation 3. Avoid Irrelevant Items 4. Accurate Results Disadvantage:- 1. Personal Bias 2. No Equal Chance 3. No Degree of Accuracy 4. No Possibility of Sample Error A statistical method of drawing representative data by selecting people because of the ease of their volunteering or selecting units because of their availability or easy access.
- 36. PURPOSIVE SAMPLING Advantage :- Suitable for Small Sampling Units. Studying Unknown Traits of Population. Solving Everyday Business Problems. Disadvantage:- Non-Scientific. No Method To Calculate Sampling Error. A non-probability sampling which follows certain norms. It is of two types: Judgment Sampling:- Judgmental sampling is a non-probability sampling technique where the researcher selects units to be sampled based on their knowledge and professional judgment.
- 37. Quota Sampling:- Quota sampling is a non-probability sampling technique wherein the assembled sample has the same proportions of individuals as the entire population with respect to known characteristics, traits or focused phenomenon. Advantages:- Economical. Administratively Convenient. Minimum Memory Errors. Independent. Disadvantages:- Difficulty in Calculating Standard Error. Difficulty in Obtaining Representative Sample. Hampers Quality of Work.
- 38. SNOWBALL SAMPLING Snowball sampling is a popular business study method. The snowball sampling method is extensively used where a population is unknown and rare and it is tough to choose subjects to assemble them as samples for research Types of Snowball Sampling:- Linear Snowball Sampling: The formation of a sample group starts with one individual subject providing information about just one other subject and then the chain continues with only one referral from one subject. This pattern is continued until enough number of subjects are available for the sample. Exponential Non-Discriminative Snowball Sampling: In this type, the first subject is recruited and then he/she provides multiple referrals. Each new referral then provides with more data for referral and so on, until there is enough number of subjects for the sample. Exponential Discriminative Snowball Sampling: In this technique, each subject gives multiple referrals, however, only one subject is recruited from each referral. The choice of a new subject depends on the nature
- 39. ADVANTAGES:- Identifying and selecting prospective respondents. Useful in qualitative research. Needs little planning. Less costly. Disadvantage:- Biased. Limited Data Structure. Limited Control. Researcher has no Idea of Distribution.
- 40. PANEL SAMPLING In panel sampling a group of participants are selected initially by random sampling method and the same group is asked for the same information repeated no. of times during that period of time . This sample is semi-permanent where members are included repeatedly for iterative studies. Advantages:- Saves Cost and Time. Helps in Measuring Changes. Helps In Tracing Shift in Behavior. Disadvantages:- Not Representative. Members become Conditioned. Difficult to Preserve Representative Character of Panel.
- 42. WHAT IS SAMPLE SIZE? This is the sub-population to be studied in order to make an inference to a reference population(A broader population to which the findings from a study are to be generalized) In census, the sample size is equal to the population size. However, in research, because of time constraint and budget, a representative sample are normally used. The larger the sample size the more accurate the findings from a study. Availability of resources sets the upper limit of the sample size. While the required accuracy sets the lower limit of sample size Therefore, an optimum sample size is an essential component of any research.
- 43. WHAT IS SAMPLE SIZE DETERMINATION? Sample size determination is the mathematical estimation of the number of subjects/units to be included in a study. When a representative sample is taken from a population, the finding are generalized to the population. Optimum sample size determination is required for the following reasons: To allow for appropriate analysis To provide the desired level of accuracy To allow validity of significance test.
- 44. Slovin’s formula for finding the sample size of the population is n = ___N____ 1+Ne² Where: n = a sample size N = population size e = desired margin of error
- 45. For example, in your research, if the population is 9,000 and the margin of error you allow is 2%, what is your representative sample? Solution: n = 9000 1+9000 (0.02)² n = ___ 9000 __ 1+ 3.6 n = 1957