sampling design

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Chapter 4: Sampling Design 

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Population or Universe: » All items in any field of inquiry constitute a ‘Universe’ or ‘Population.’ >» The whole group of people, objects, events etc. having some common characteristic and which is being researched on is called 

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Census: < A complete enumeration of all items in the ‘population’ is known as a census. > In such an inquirv. no element of chance is left and highest accuracy is obta 

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But in practice census may not be true: »The slightest element of bias in such an inquiry will get larger and larger as the number of observation increases. ‎method is practically beyond the reach of ordinary‏ فیط[ ‎researchers.‏ ‎»This type of inquiry involygs a great deal of time, money and ‎energy. ‎ 

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» Many a time it is not possible to examine every item in the population. » Considerations of time and cost almost invariably lead to a selection of respondents i.e., selection of only a few items. » Sometimes it is possible to obtain sufficiently accurate results by studying only a part of total population. » The respondents selected should be as representative of the total population. » The selected respondents constitute what is technically called a ‘sample’ and the selection process is called ‘sampling technique.” 

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ample: A sample is a part of a population. ampling: The selection of a part of the population. ampling technique: The selection process of a part of population. Population 

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For Example: If there are 145 patients in a hospital and 40 of them are to be surveyed by the hospital administrator to assess their level of satisfaction with the treatment received, then these 40 members will be the sample. Sample survey: > Collects information from a sample of the pop » Survey can be conducted by anyone. ‏يب‎ > Survey can be done in a shorter periode of tir 

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CENSUS VERSUS SURVEY ‎tacoma sats‏ فاءعلام موی ‎information about | information from a‏ ع له فأمصمة ع که هطعه مه ‎populati 00000‏ ‏۱ دز زره نیرگ ۵ وز و ‎detailed and accurate or reliable‏ ‎urate asacensus,‏ ‏عم ‎Sapte‏ ‏۵۵۴ 5110۳۲۵۲ 2 و ۵2 4عتووصی مرا ‎eats‏ ‎fer ey een 3 ‎Census is generally ‏هی له تاک‎ 6 conducted bythe | conducted by anyone. ‏امس نوج‎ ‎Surveys can b fees ted frequent] ‏وه‎ ۰ ‎Sarat ‎ 

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IMPLICATIONS 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. = * 5 

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STEPS IN SAMPLE DESIGN: 1.Type of 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 ‏تخب‎ thit: May be a geographical one (state, district, village, etc.,) ora construction unit (house, flat, etc.,) or a social unit (family, club, school, etc.,) or an individual. 3. Source list: It is also known as ‘sampling frame’.Contains the list of all items of a universe(in case of finite universe only).Example:Telephone book, List of emails. 4. Size of sample: Refers to the number of items to be selected from the universe to 

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5. Parameters of interest: For instance, we may be interested in estimating the proportion of persons with some characteristic in the population, or we may be interested in knowing some average or the other measure concerning the population. There may also be important sub-groups in the population about whom we would like to make estimates. All this has a strong impact upon the sample design we would accept. 6. Budgetary constraint: Cost considerations.This case effects on not only the size of the sample but also to the type of sample. 7. Sampling procedure: Researcher must decide the type of sample he will use and technique to be used in selecting the items for the 

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11 1۳۲۸ 0۳ 5۳۲,۳۱ 1] ۸ SAMPLING PROCEDURE: < Researcher must keep in view the two causes of incorrect inferences viz., systematic bias and sampling error. » 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. » Sampling errors: This errors arises when a sample is not renrecentative of the nonulation 

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Usually a systematic bias is the result of one or more of the following factors: Inappropriate sampling frame. . Defective measuring device. Non-respondents. Indeterminancy principle. . Natural bias in the reporting of data. e 1, 

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1.Inappropriate sampling frame: >If the sampling frame is inappropriate i.e, a biased representation of the universe, it will result in a systematic bias. SAMPLE FRAME 

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2.Defective measuring device: >If the measuring device is constantly in error, »If the physical measuring device _is defective, » If the questionnaire or the interviewer Biased, » will result in systematic bias. 

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3.Non-respondents: » If we are unable to sample all the individuals initially included in the sample, there may arise a systematic bias. 

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4. Indeterminancy principle: >» Sometimes we find that individuals act differently when kept under observation , than what they do when kept in non-observed situations. >» Thus, the indeterminancy principle may also be a cause of a systematic bias. 

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5. Natural bias in the reporting of data: » Natural bias of respondents in the reporting of data is often the cause of a systematic bias in many inquiries. » Generally in psychological surveys, people tend to give what they think is the ‘correct’ answer rather than revealing their true feelings. > A 

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Sampling Errors: » 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 c Bola ole r sampling error for a given sample size 

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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 design should be such that the results of the < y can be applied, in general, for the universe with a reasonable level of co 

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JIFFERENT TYPES OF SAMPLE DESIGNS: - Probability sampling is based on the concept of random selection. * Non-probability sampling is ‘non-random’ sampling. 

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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 ‏سر‎ and characteristics as the univers » This is as the best techniq: vie 1 ۳ 1۱ ag ! ‏هي نالا‎ 1 Probability Sampling 

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Simple Random Sampling(SRS): » The Simple Random Sampling is taken by the following process: write names or codes each of the possible samples on the paper, mix these in a box/container and then draw as a lottery. » Simple random sampling (SRS) is a method of selection of a sample comprising of n number of sampling units out of the population having N number of sampling units such that every sampling unit has an equal chance of being chosen. 

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» There are many ways to do a random selection: For example, The use of computer programs such as excel, random number table, pulling out names or numbers from a helmet or spinner. The samples can be drawn in two possible ways: 1. The sampling units are chosen without replacement in the sense that the units once chosen are not placed back in the population . 2. The sampling units are chosen with replacement in the sense that the chosen units are placed back in the population. 

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1. Simple random sampling without replacement (SRSWOR): >» SRSWOR is a method of selection of n units out of the N units one by one such that at any stage of selection, anyone of the remaining units have same chance of being selected. رم ۶ ات ۱ 

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2. Simple random sampling with replacement (SRSWR): > SRSWR is a method of selection of n units out of the N units one by one such that at each stage of selection each unit has ممما ع ع 60101219 ب شنت 

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06 Part of a Table of Random 07 03 77 20 Numbers 

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COMPLEX RANDOM SAMPLING DESIGNS: 1. Systematic sampling 2. Stratified sampling 3. Cluster sampling 4. Area sampling 5. Multi-stage sampling . Sampling with probability proportional to size 7. Sequential sampling 

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1.Systematic sampling » Only the first unit is selected randomly and the remaining units of the sample are selected at fixed intervals. » Number the units in the population from 1 to N. » Decide on the n (sample size) that you want or need »k = N/n = the interval size » Randomly select an integer between 1 tok » Then take every unit 

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For example: N=100 WANT n=20 N/n=5 Select a random number from1-5: chose=4 Start with #4 and take every 5" unit. 

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Ex 2: N=9 WANT n=3 K=N/n=3 ۱1 ۳ Select a random number 3 from1-3: chose=3 Cc. Start with #3 and take every 3% unit. و« و . وم . ات 00 

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2.Stratified sampling: » Ifa population from which a sample is to be drawn does not constitute a homogeneous group , stratified sampling technique is generally applied in order to obtain a representative sample. » Stratified random sampling is a sampling method in which the population is first divided into strata (A stratum is a > rpamogenqesspubsebadihe panuledaibingeencensemdlte the gands@ sample is taken from each stratum. 

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>In the stratified sampling, it should be noted that the classification of classes is done based on the purpose of the problem and the subject matter under consideration. » So, for example, when it comes to health matters, it should be noted that the effective factor in this research and classification is the age of the individual. >» Because the health needs of schoolchildren, youth, and so on ... are different, and in this case, the classification of individuals based on religion is completely unconnected and meaningless. >» We can classify the sampling based on the following factors: 

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> 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? » Regarding the first question, we can say that the strata be formed on the basis of common characteristic(s) of the items to be put in each stratum. » This means that various strata be formed in such a way as to ensure elements being most homogeneous within each stratum and most heterogeneous between the different strata. 

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> In respect of the second question, we can say that the usual method,for selection of items for the sample from each stratum, resorted to is that of simple random sampling. >» Systematic sampling can be used if it is considered more appropriate in certain situations. » Regarding the third question, we usually follow the method of proportional allocation under which the sizes of the samples from the different strata are kept proportional to the sizes of the strata. 

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Proportional allocation: » If the subsets in each class have the same characteristics, » If the class difference is only in the size of the class, > In this case, the stratified sampling will be of a proportional allocation type and the probability of selection for all population units is equal. That is, the number of samples per class is proportional to the ratio of that class in the whole society. 

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We use the following formula to determine the sample size: » If N represents the size of population, » :The number of population included in stratum i, » represents the proportion of population included in stratum i to total population, > n represents the total sample size, » ni the number of elements selected from stratum i, =nx 

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For example: If N = 8000 which is divided into three strata of size N1 = 4000, N2 = 2400 and N3 = 1600. We want a sample of size n = 30 For strata with N1: _4000_1 _ _ _ P1~ 30002 , nl=nx Pi= 1/2 x 30= 

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Non-Proportional allocation: » When from the non-proportional allocation is used, the population does not have a specific fit, that is, some stratums very small , and some are very large, or when, although the classification has been done, it is thought that there are other influential variables, and There are some doubts about the variables within a particular stratum. >In condition of non-Proportional allocation , the researcher should have more insight and knowledge about the population. 

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» Therefore, in cases where there is a difference not only in the size of the class but in the variables, a parameter is defined as standard deviation or variance.() » In this case, the following formula is used to determine the ‏تین‎ ai 6 .رل . جر _ مرج جر رل +6 2 ni For example: If a population is divided into three strata so that N1 = 5000, N2 = 2000 and N3 = 3000. Respective standard deviations are: =15, =18 and 5. 84.5000.15 We want a sample of size n 2162000 1572000 15730005 =50 Sample size for strata with N1. 

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» In addition to differences in stratum size and differences in stratum variables, we may have differences in stratum sampling cost, then we can assess Cost of sampling in stratums. For this purpose, we will ysgthe following formula: ni= N,.6,/VC,+.Ny 6,1) Cy+...4+Ng- 6d V Ox ‏”ا‎ = Cost of sampling in stratum 1 ‏”ا‎ = Cost of sampling in stratum 2 ” = Cost of sampling in stratum k 

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3.Cluster sampling: >In cluster sampling the total population is divided into a number of relatively small subdivisions which are themselves clusters of still smaller units (called “clusters”) and then some of these clusters are randomly selected for inclusion in the overall sample. > Thelfisalsempbacgnaisésiné dhiaeais maébese ‏عه هتاه‎ random, not the individuals. >It is assumed that each cluster by itself is an unbiased representation of the population, which implies that each of the clusters is heterogeneous. 

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>» For examples, consider a survey for evaluating the involvement of high school students in extracurricular activities. Rather than selecting random students from the student population, selecting a class as the samples for the survey is cluster sampling. Then every member of the class is interviewed. In this case, classes are clusters of the student population. 

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1 11111 399 ۳ iff 

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Sampling - Stratified vs Cluster : >In stratified sampling, the population is divided into homogeneous groups called strata, Then a simple random sample is taken from each stratum. >In cluster sampling, the population is grouped into heterogeneous clusters, and then a cluster is selected at random. » Stratified sampling is slower while cluster sampling is relatively faster. » Stratified samples have less error due to similarity in each 

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4.Area sampling: » If clusters happen to be some geographic subdivisions, in that case cluster sampling is better known as area sampling. و ۳ 

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5.Multi-stage sampling: » Multi-stage sampling is an advanced or extended form of cluster sampling. For example: Step 1: Select a Country. Step 2: Select a section from that country. Step 3: Select a few homes from that section. Step 4: Choose a home from several homes and Selecting sample people. Step 5: Choose a person between that persons. 

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itage2- egments Stage1- Stage3-homes countries Stage4-sample persons Stage5- عم [دنزتتر د ع جا ددع 

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6.Sampling with probability proportional to size: » In case the cluster sampling units do not have the same number or approximately 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. 

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7.Sequential Sampling: » This method of sample selection is slightly different from other methods. » Here the sample size is not fixed. The investigator initially selects small sample & tries out to make inferences; if not able to draw results, he or she then adds more subjects until clear-cut inferences can be drawn. » When the conclusion is based on a single sample, it is called single sampling.when the decision is to be taken on the basis of two samples, it is known as double sampling and in case the decision rests on the basis of more than two samples , the 

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Non-probability Sampling ‎Non-probability sampling is also known by different names‏ خ ‎such as deliberate sampling or purposive sampling.‏ ‎>In this type of sampling, items for the sample are selected ‎deliberately by the researcher. ‎fe — ie ‎ ‎Non-probability Sampling ‎ 

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Types of non-probability sampling: 1.Convenient Sampling 2.Quota sampling 3.Snowball sampling 4 Judgement Sampling 

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1.Convenient Sampling: » In this design, the most accessible members are selected as subjects. » This plan is not exhaustive and is not suitable for scientific research, and may be used to obtain quick information and use results at times. » For example; In our example of the 1,000 university students, if we were only interested in achieving a sample size of say 100 students. » Or, a researcher who wants to measure people's viewpoint toward an shop, randomly selects a number of people who are present at 

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Convenient Sampling in the shop center. ۱۳۵ ۳( و۱۳۱ 

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2.Quota sampling: » In the quota sampling, the population is initially divided into distinct and homogeneous subgroups. This division can be based on age, gender or educational level. Then, considering the volume of subgroups studied, a quota is considered for each. » This type of sampling can not be generalized to the entire population and also has less scientific aspect. 

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> For example: The researcher wants to investigate people's awareness in a neighborhood of the city. If the number he needs is, for example, 100, he will select these people according to the number of literate and illiterate people out of reach.For example, if the population of the neighborhood is 1000 people, of which 800 are = and 200 are illiterate, the sample of the selected sample v people. Quota: 9 Male, Above 50 | 0 i i 

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3.Snowball sampling: » Snowball sampling is a non-probabilistic sampling method for cases where the studied units are not easily identifiable. » Especially when these units are very scarce or a small part of a very large society, it is also appropriate for rare populations where their location is unclear. » Elements from a population guide the researcher to other elements of this population. 

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» For example: Homeless people, illegal immigrants or children who have been sexually abused. ۱11 8 9*1] 02 00 ‎ng vie‏ کی ۵-2 ۲ 

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A.Judgement Sampling: » A researcher exerts some effort in selecting a sample that seems to be most appropriate for the study. » In this type of sampling, individuals are selected for the sample to provide the required information in the best position. » Sample members are selected based on investigator judgment. » This sampling plan because of the difficulty of assessing the validity of the judgment of the researcher criticized. 

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For example: Suppose we are going to look at the status of teenagers who have escaped from home. Since it is not possible to make a list of these people, the researcher tries to visit places like parks, terminals, etc., and deliberately identifies the people at a particular location. © ak Researcher a ak 

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Conclusion: Normally one should resort to simple random sampling because under it bias is generally eliminated and the samplind error can be estimated. but purpose sampling is more appropriate when the congo" universe ha]