Probability sampling
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The document provides an overview of probability sampling in agricultural statistics, outlining definitions, objectives, characteristics of good samples, and various methods including simple random sampling, stratified random sampling, systematic sampling, cluster sampling, and multistage sampling. It details the advantages and disadvantages of each sampling method as well as sampling errors and non-sampling errors. The document concludes with the principle steps involved in conducting a sample survey.
![Multistage Sampling
Multistage sampling is the compromise
between SRS and cluster sampling.
The entire population is classified into a
number of clusters .
Select a sample of clusters.[first stage]
From each of the selected cluster, select a
sample of specified number of elements.
[second stage]
The procedure is generalized to three or more
stages.This is called Multistage Sampling .](https://image.slidesharecdn.com/probabilitysampling-210621025404/85/Probability-sampling-29-320.jpg)
Probability sampling
- 1. PROBABILITY SAMPLING Presented by Tejendra Singh Id no. : 52674 Course : M.Sc.(Agricultural Statistics) Advisor : Dr. Haseen Ahmad
- 2. CONTENTS Sampling Population Objectives of sampling Characteristics of good sample Probability Sampling Types of Probability Sampling Sampling Errors Non Sampling Errors Principle Steps in Sample Survey Conclusion
- 3. Sampling Definition The process through which a sample is extracted from a population is called as sampling. Sample One or more sampling units are selected from the population according to some specified procedure. A sample consists only of a portion of the population units. Sampling Unit An element or a group of elements on which observations can be taken is called a sampling unit.
- 4. Population Definition The collection of similar units i.e. collection of similar objects or persons, plants, animals etc. is referred to as a Population. Population may be living or non living & it may be finite or infinite.
- 5. Objectives of Sampling To get a better representative of the population. To save resources i.e., time and money. To obtain the best possible estimates of the population parameters. Sampling Frame Sampling frame is the complete list of individuals in the population having names, addresses and any other identity details.
- 6. Characteristics of a good sample Representative of the population. Free from bias & errors. No substitution & incompleteness. Appropriate size.
- 7. Probability Sampling If each and every unit of a population have a definite probability of being included in the sample then the sampling is probability sampling. Probability sampling is also referred to as random sampling or representative sampling.
- 8. Types of Probability Sampling Simple Random Sampling SRSWOR SRSWR Stratified Random Sampling Equal allocation Proportional Allocation Optimum Allocation Systematic Sampling Linear Systematic Sampling Circular Systematic Sampling Cluster Sampling Multistage Sampling
- 9. Simple Random Sampling In simple random sampling, each member of the population has the same probability of being included in the sample. The larger the sample, more it represents the population. It is a fair type of sampling without any bias. Simple random sampling is also called equal probability sampling or random sampling. Here pi= N 1
- 10. Methods of Selection of Sample in Simple Random Sampling Lottery Method Random number table method
- 11. Procedure of selection by Random Number Table: Identify ‘N’ units in the population with numbers from 1 to N. Identify the number of digits in N. Suppose it is ‘k’. Select any ‘k’ consecutive columns from random number table. Start at random from any place. Discard if unit selected is ‘0’ or greater than N. In this way select n units and units so obtained will constitute the random sample. In case of SRSWR, all the random numbers are accepted even if repeated more than once. In case of SRSWOR, if any random number is repeated, then it is ignored and more numbers are drawn.
- 12. Types of Simple Random Sampling Simple Random Sampling Without Replacement Simple Random Sampling With Replacement
- 13. Simple Random Sampling Without Replacement (SRSWOR) In SRSWOR, the first member is chosen at random from the population of size N, and once the first member has been chosen, the second member is chosen at random from the remaining N −1 members and so on, till there are ‘n’ members in the sample. Here no unit of population may appear more than once in a sample. If n units are selected by SRSWOR, the total number of possible samples are ᴺСn. Each sample has a same probability of selection i.e., equal to n N C 1
- 14. Simple Random Sample 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 equal chance of being selected, i.e., 1/ N When n units are selected with SRSWR, the total number of possible samples are N n The sampling units are chosen with replacement in the sense that the chosen units are placed back in the population. The Probability of drawing a sample is n N 1
- 15. Advantages Easy method to use Sampling error can be easily measured. Disadvantages Need complete list of units. Cost of collecting geographically spread sampling units may be much in terms of time and money. For a given precision it usually requires larger sample size compared to stratified random sampling.
- 16. Stratified Random Sampling In stratified random sampling entire heterogeneous population divided into a number of homogeneous groups. These groups are termed as strata, which differs from one another but each of these groups homogeneous within itself. These strata must be mutually exclusive and exhaustive. Treat each stratum as separate population and draw a sample by SRS from each stratum.
- 17. Problem of Allocation Deciding the number of units to be taken from each stratum is called the problem of allocation. This can be done in three ways- Equal Allocation Optimum Allocation Proportional Allocation
- 18. Equal Allocation Choose the sample size ni to be the same for all the strata. Draw samples of equal size from each stratum. Let n be the sample size and k be the number of strata. Then, ni = n/k for all 1, 2,...,k. Optimum Allocation In this allocation we select larger number of units from a stratum whose size is larger and Variability is larger. ni ∝ Ni Si Or ni = C*Ni Si where C* is the constant of proportionality
- 19. Proportional Allocation We Select larger number of units from larger stratum and smaller number of units from smaller stratum. For fixed k, select ni such that it is proportional to stratum size Ni , i.e., ni ∝ Ni Or ni = CNi where C is the constant of proportionality.
- 20. Advantages Can acquire information about whole population and individual strata. Precision gets increased if variability within strata is smaller than between strata. Full cross-section of population can be obtained through stratified random sampling. Provides separate estimates for each stratum. Disadvantages Sampling error is difficult to measure. Different strata can be difficult to identify. Loss of precision if size of individual strata is small.
- 21. Systematic Sampling In this sampling we select 1st unit at random from the population and remaining units of the samples are selected automatically from the population at equal interval. Two types of Systematic Sampling : i. Linear Systematic Sampling ii. Circular Systematic Sampling
- 22. Linear Systematic Sampling Let k = N/n be a positive integer. k is the multiple of n. We select 1st unit of the sample from the 1st k units and remaining (n-1) units of the sample at equal interval of k.
- 23. Circular Systematic Sampling In this method we select 1st unit of the sample at random from N units of the population and then going round the circle. Subtract N if the number selected is greater than N. Example Let N =14 and n= 5 Then, k = nearest integer to 14/5=3. Let the first number selected at random from 1 to 14 be 7. Then, the circular systematic sample consists of units with serial numbers 7,10,13, 16-14=2, 19-14=5. This procedure is illustrated. diagrammatically in the figure
- 24. Advantages of Systematic Sampling It is easier to draw the systematic sample & it is easier to execute it without any mistakes especially when the drawing is done in the field. Suitable sampling frame can be identified easily. Sample evenly spread over entire reference population. Disadvantage Sample may be biased if hidden periodicity in population coincides with that of selection. Each element does not get equal chance. Ignorance of all element between two n element.
- 25. In terms of Intra class correlation The systematic sampling is : More efficient than the corresponding equivalent stratified sample when Less efficient than the corresponding equivalent stratified sample when Equally efficient than the corresponding equivalent stratified sample when ρwst = 0
- 26. Cluster Sampling In cluster sampling a given population is classified into a number of subgroups, each group being considered as a cluster. After classifying the population into a number of clusters, a sample of cluster is selected according to some sampling scheme (generally SRS) and each unit of the selected cluster is surveyed. In cluster sampling cost of survey is reduced.
- 27. Example The list of all the agricultural farms in a village or a district may not be easily available but the list of village or districts are generally available. In this case, every farm in sampling unit and every village or district is the cluster. In a city, the list of all the individual persons staying in the houses may be difficult to obtain or even may be not available but a list of all the houses in the city may be available. So every individual person will be treated as sampling unit and every house will be a cluster.
- 28. Difference between stratified and cluster sampling In stratified sampling, the strata are constructed such that they are • within homogeneous and • among heterogeneous. In cluster sampling, the clusters are constructed such that they are • within heterogeneous and • among homogeneous.
- 29. Multistage Sampling Multistage sampling is the compromise between SRS and cluster sampling. The entire population is classified into a number of clusters . Select a sample of clusters.[first stage] From each of the selected cluster, select a sample of specified number of elements. [second stage] The procedure is generalized to three or more stages.This is called Multistage Sampling .
- 31. Example In a crop survey - villages are the first stage units, - fields within the villages are the second stage units and - plots within the fields are the third stage units. In another example, to obtain a sample of fishes from a commercial fishery - first take a sample of boats and - then take a sample of fishes from each selected boat. Advantage The principle advantage of two stage sampling is that it is more flexible than the one stage sampling.
- 32. SAMPLING ERRORS Sampling errors are restricted to sample surveys only. They are measurable from the sample data in the case of probability sampling. The sampling errors decrease as the sample size increases. The data collected by complete enumeration in census is free from sampling error. Sample size and variability within the population are the factors affecting the sampling error.
- 33. NON SAMPLING ERRORS These are errors that arise during the course of all data collection activities. Occurs in complete enumeration as well as in sample surveys. Non-sampling error increases as the sample size increases.
- 34. Sources of non-sampling errors Lack of proper specification of the domain of study and scope of investigation. Incomplete coverage of the population or sample. Defective methods of data collection Tabulation errors
- 35. Principle Steps in Sample Survey Defining the objectives of the sample survey Defining the population Determination of the data to be collected Degree of precision desired Deciding on the method of collection of data Getting a sample frame Designing the Survey Drawing the sample Training of personnel Analysis of the collected data
- 36. Thank You