Unit 2 Sampling PDF

Unit 2 Sampling Concept of Sampling, Population and Sample:  The aggregate of units lying under the area of study is called population.  If all units under the field of inquiry are examined and information is obtained from them then it is called census inquiry of complete enumeration...

Unit 2 Sampling Concept of Sampling, Population and Sample:  The aggregate of units lying under the area of study is called population.  If all units under the field of inquiry are examined and information is obtained from them then it is called census inquiry of complete enumeration or population study.  The census of our country carried out at every ten year’s interval is the most familiar example of population survey.  If the population contains finite countable number of units then it is called finite population. For example in the study of economic condition of students of a university the respective population is called finite population.  On the other hand if the number of units in population is uncountable then the population is called the infinite population. For example, number of flowers in a city, a set of real numbers between 1 to 100 etc.  In a population study, each and every population units is to be examined and the observation is obtained hence it is quite obvious that it requires more time, money and labor. Moreover, the standard of accuracy can not be maintained, as many persons are involve in the survey work and all persons cannot be expected to be highly sincere and honest.  Also in certain survey, the nature of the test is destructive, for example, life testing of electric bulb, blood testing, etc.  In all these circumstances the population study is not advisable, in such cases, instead of studying each and every population unit, certain representative units are selected from the population and are studied and on the basis of it inferences regarding the population characteristics under study is derived.  The aggregate of the representative units drawn from the population by some scientific method for getting knowledge about the characteristics under study is called a sample study and the method of selecting such representative units is called sampling method.  In a sample study, as less number of units are to be examined, it saves time, money and labor. Also the standard of accuracy of the data value is maintained in the sample study, as less number of units are to be examined so the experts can be hired for the survey work. Also when the nature of test is destructive in that case the sample survey is the only way-out. In order to get accurate and reliable information about population, the sample must be true representative of the population.  Sampling frame and design:  By using the sampling method, the population units are selected in a sample these units are called sampling units.  A list containing all such sampling units is called sampling frame. i.e in short a list of population units from which a sample is to be drawn is called sampling frame.  For example, the researcher can use telephone directory for conducting opinion pole, here, telephone directory is sampling frame.  A well define technique or procedure by using which the sample units are selected from the population is called sampling design i.e it is a definite plan for drawing a sample from sampling frame. Sampling design is determined before any data collected, it involved several decisions of a broader nature.  Types of Sampling Methods:  The sample may be selected by using probability (random) sampling, or may be selected by using non- probability (non- random) sampling.  Non- Probability Sampling: It is totally depends on the discretion of the researcher, i.e. the researcher can arbitrarily or consciously decide what elements to include in the sample. A sample selected by using this method may yield good estimates of the population characteristic, but the precision of the sample results cannot be obtained from this method. Followings are the commonly used non-probability sampling techniques. (i) Convenience Sampling:  In this method, the sample units are selected at the convenience of the researcher. For example the public opinion surveys are conducted by any TV channel, bus stop etc.  Convenience sampling is the least expensive and least time consuming technique as compare to the other sampling techniques.  The main limitation of this method is that it is a bias sample hence is not a true representative of the population and hence it is not meaningful to derive any generalized conclusions from a convenience sample.  These samples are not to be used in descriptive or casual research, but they can be used in exploratory research for generating ideas or hypothesis. (ii) Judgemental Sampling:  The judgmental sampling is used when a limited number of respondents possess the required information and it involves the selection of respondents who are able to give required information.  Judgemental sampling is a particular form of convenience sampling in which the sample units are selected based on the judgement of the research.  The researcher is supposed to be an expert in choosing the sample units. For example to determine potential market of new product or department stores are selected to test a new merchandising display system etc.  The main advantage of this method is that this sampling is very quick, low cost consuming and is convenient; where as the main disadvantaged of this method is that it does not allow direct generalizations a population under consideration because the population is not defined explicitely.  Judgemental sampling is subjective and its value depends entirely on the researcher's judgement and creativity. (iii) Quota Sampling:  Quota sampling may be considered as two stage restricetd judgmental sampling.  The first stage consists of distributing the population characteristics into the relevant control categories, which may includes gender, age, race, identified on the basis of judgment.  In the second stage, sample elements are selected based on convenience or judgment.  In other words quota sampling is a form of proportionate stratified sampling in which a predetermined proportion of elements are sampled from different groups in the population but on the convenience basis.  For example, the investigator may choose to interview five men and ten women in such a way that one of them have annual income more than ten lakh rupees, eight of them have annual income between five to ten lakh rupees and rest of them may have income below five lakh rupees. Further more some of them should be in between 25 to 35 years of age some of them may be of 36 to 50 years of age and balanced are above 50 years of age. This means that the researcher's choice of respondent is partly dictated by these type of controls or categories of quotas.  The main advantages of quota sampling are the lower costs and greater convenience to the interviewers in selecting elements for each quota.  Where as it does not satisfy the fundamental requirement of sample, that is, it should be random hence it does not permit assessment sampling error. And consequently, it is not possible to achieve precision of result. (iv) Snowball Sampling:  In this sampling method, initially the respondents are selected at random. After interviewing respondents they are asked to identify others who belong to the area of study, i.e. the subsequent respondents are selected on the basis of the referrals.  This process can be carried out in waves by obtaining referrals from referrals.  A major objective of snow ball sampling is to estimate characteristics that are rare in the population. For example members of a scattered minority population or widowed makes below 30 years of age etc. The major advantages of this sampling method is that it gradually increases the likelihood of locating the desired characteristic in the  Probability Sampling Method :  In probability sampling population units are selected in a sample just chance. In this sample of known size that will be drawn from the population as well as the probability of selecting each sample.  There are number of probabilities sampling methods are available. All these method vary in terms of sampling efficiency.  The sampling efficiency can be measured in terms of sampling cost and precision. The efficiency of probability sampling may be assessed by comparing it to that of simple random sampling. (i) Simple Random Sampling:  In this method, each of the population unit has equal chance of probability to be selected in a sample. To draw a random sample, a complete list of all elements in the population is required and each element has given unique identification number. Such list is called sampling frame.  The sample is drawn by a random procedure from a sampling frame. This method is equivalent to a lottery system  The another method is that the random numbers may be generated by using computer or a table of random number is used to select a random sample. For example suppose a random sample of size 50 is selected from a sampling frame of 500 units by using random numbers table; then any page of a random number table is selected at random and from it any row and column is selected at random selecting only three digits, the first 50 numbers between 1 to 500 have been selected. Numbers outside this range are ignored.  This method is comparatively easy to understand and is most suitable for statistical inference because most of the statistical techniques assumes that the data have been collected by using simple random sampling. However, the main limitation of this method is that many ho time it is difficult to construct sampling frame. Also when the population units are hetrogeneous in nature then this method do not represent population correctly. Usually cost associated with simple random sample is more. ii) Systematic sampling:  In some instances the most practical way of sampling is to select every 15th name on a list, every 10th house on one side of a street and so on. Sampling of this type is known as systematic sampling. An element of randomness is usually introduced into this kind of sampling by using random numbers to pick up the unit with which to start. This procedure is useful when sampling frame is available in the form of a list. In such a design the selection process starts by picking some random point in the list and then every nth element is selected until the desired number is secured (iii) Stratified sampling:  If the population from which a sample is to be drawn does not constitute a homogeneous group, then stratified sampling technique is applied so as to obtain a representative sample. In this technique, the population is stratified into a number of non overlapping subpopulations or strata and sample items are selected from each stratum. If the items selected from each stratum is based on simple random sampling the entire procedure, first stratification and then simple random sampling, is known as stratified random sampling vi) Cluster sampling and area sampling:  Cluster sampling involves grouping the population and then selecting the groups or the clusters rather than individual elements for inclusion in the sample.  Suppose some departmental store wishes to sample its credit card holders. It has issued its cards to 15,000 customers. The sample size is to be kept say 450. For cluster sampling this list of 15,000 card holders could be formed into 100 clusters of 150 card holders each. Three clusters might then be selected for the sample randomly. The sample size must often be larger than the simple random sample to ensure the same level of accuracy because is cluster sampling procedural potential for order bias and other sources of error is usually accentuated. The clustering approach can, however, make the sampling procedure relatively easier and increase the efficiency of field work, specially in the case of personal interviews.  Area sampling is quite close to cluster sampling and is often talked about when the total geographical area of interest happens to be big one. Under area sampling we first divide the total area into a number of smaller non- overlapping areas, generally called geographical clusters, then a number of these smaller areas are randomly selected, and all units in these small areas are included in the sample. Area sampling is specially helpful where we do not have the list of the population concerned. It also makes the field interviewing more efficient since interviewer can do many interviews at each location