Theory Of Sampling

VI. Types of Sampling The method of selecting samples from the population is called sampling. It is three types. They are i) Probability sampling or Random Sampling ii) Non Probability sampling or Non Random sampling. iii) Mixed Sampling i) Probability sampling: In this, there is always a fixed, pre assigned probability for each member of the population to be a part of the sample taken from that population. Examples for Probability sampling are 1. Simple random sampling 2. Stratified random sampling 3. Systematic random sampling 4. Two Stage random sampling 5. Multistage random sampling 6. Cluster sampling 7. Double sampling 8. Inverse sampling 9. P.P.S. Sampling 10. Area Sampling ii) Non Probability sampling: In this, no probability attached to the member of the population and as such it is based entirely on the judgment of the sampler. Examples for Non probability sampling or non random samplings are 1. Representative sampling 2. Purposive sampling 3. Judgment sampling 4. Quota sampling 5. Convenience sampling iii) Mixed sampling: It is based partly on some probabilistic law and partly on some pre decided rule. Example: Systematic random sampling. Sometimes the sampling technique such as two stage random sampling and Multistage random sampling etc are called mixed random sampling. Probability sampling: 1. Simple random sampling: S.R.S. is that “each and every unit of the population has equal and independent probabilities of being included in the sample”. The sample units are selected one by one from the population. This is two ways. i) Simple random sampling with replacement: The sample units are selected one by one from the population and once selected unit is replaced into the original population before coming to the next draw. Population size remains constant at every stage. The number of ways selecting samples from the population is Nn. ii) Simple random sampling without replacement: The sample units are selected one by one from the population and once selected unit is not replaced into the original population before coming to next draw. Population size gradually decreases at every stage. The number of ways selecting samples from population is Selection procedures for S.R.S: a. Lottery system b. Mechanical randomization method or Random numbers method 2. Stratified random sampling: Divide the heterogeneous population into homogeneous groups is Stratification. Each group is called Stratum. After dividing the population into to strata and then applying S.R.S.W.O.R on each and every strata, constitute of all sample units is called Stratified random sample. Allocation Methods 1. Proportional Allocations (Bowely’s) “Sample size directly proportional to strata (population) sizes”. 2. Optimum Allocations (Neyman) “Sample sizes vary jointly with population size and population standard deviation”. 3. Systematic random sampling: Select the first sample unit at random and the remaining units are selected based on predetermined formula. Let us suppose that N sampling units are serially numbered from 1 to N in some order and a sample of size n is to be drawn such that K = N/n, where k is called sampling interval, is an integer. First sample unit say ‘i’ (is called random start) which is i ≤ n, the remaining units are 4. Cluster Sampling: In many situations, the sampling frame for elementary units of the population is not available; moreover it is not easy to prepare it. But the information is available for groups of elements so called clusters. Dividing the population into various groups and select the some groups, the selected groups are cluster sampling For example, we can divide a town into various blocks and their using random sampling technique for each block for collection of information about their income groups. 5. Two stage or multistage sampling: Selection of a sample from each selected cluster is known as sub sampling under such a sampling procedure a sample is drawn in two stages. (i.e.) In the Ist stage a sample of cluster is selected and IInd stage a sample of elementary units is drawn from each selected cluster. This type is two stage sampling. The selection proceed can be extended to any number of stages then it is called multistage sampling. Ex: Select villages as Ist stage and farmers in the village as IInd stage. 6. Inverse sampling: The size of the sample ‘n’ is not fixed but selection process continuous until a predefined number of units possessing the rare character or attribute has been selected in the sample. 7. P.P.S: Probability proportion to size. Non probability sampling: 1. Representative sampling: The sample selected in general/represent a characteristic or variable and may not represent the population with respect to other variables. If we take a sample of school students the pupils in the First grade will not represent the school with respect to age, where as they may represent the school with respect to color of the eyes. Thus there is precise meaning to term “Representative Sampling”. 2. Judgment Sampling: In this method of sampling, the choice of sample items depends on the Judgment of the Investigator. It is also called opinion sampling. It is inevitable that bias will enter the sample and good estimates can’t be prepared. 3. Quota sampling: Developed by Gallup and Crossely and others. The population is divided into number of groups and total sample is allocated to these groups in proportional to their real size or estimated size. The investigators are fixed for each group and they are given the sample size fixed for that group. For admission to institutes, there may be quota fixed such as general category 50%, SC/ST category 40%, and NRI quota 10%. 4. Convenience sampling: A convenience sample is obtained by selecting ‘Convenient’ population units. A sample obtained from readily available lists such as automobile registrations, telephone directory etc, is a convenience sample and not a random sample even if the sample is drawn at random from the lists. Some Important Definitions: Complete Enumeration or Census: When complete information is collected for all the units belonging to a population, it is defined as census. Sample Survey: Sample survey is the study of the unknown population on the basis of a proper representative sample drawn from it. Some basic principles of sample survey: a) Law of Statistical regularity: If a sample of fairly large size is drawn from the population then on an average the sample would possess the characteristics of that population. b) Principle of Inertia: The results derived from a sample, according to the principle of inertial, are likely to be more reliable, accurate and precise as sample size increases, provided other factors are kept constant. This is a direct consequence of the first principle. c) Principle of Optimization: It ensures that an optimum level of efficiency at a minimum cost or the maximum efficiency at a given level of cost. d) Principle of validity: It states that a sampling design is valid only if it is possible to obtain valid estimates and valid tests about population parameters. Only a probability sampling ensures this validity. Errors: 1. Sampling Error: The error involved in taking the sample from the population is sampling error. The difference between the parameter and statistic is sampling error. As sample size increases the sampling error decreased and vice versa. Sampling error occurred in only sample survey. 2. Non Sampling Error: These errors are due to lapse of memory, calculation mistakes, non-responses on the part of the interviewees, wrong measurements, communication gap between investigator and respondent. As sample size increases the non sampling error increased and vice versa. Non sampling error occurred in both census and sample survey.