Statistical Method and Demography
♦ Index :
- Sample Surveys
- Simple Random Sampling and Stratified Random Sampling
- Systematic Random Sampling and Cluster Sampling
In statistics, survey sampling describes the process of selecting a sample of elements from a target population to conduct a survey. The term “survey” may refer to many different types or techniques of observation.
The total count of all units of the population for a certain characteristic is known as complete enumeration, also termed as census survey.
When only a part, called a sample, is selected from the population and examined, it is called sample enumeration or sample survey.
Advantages of sample surveys over census surveys:
◊ Reduced cost survey : A census usually involves a huge expenditure while data can be collected at a much lesser cost only a sample is studied.
◊ Greater speed of getting results : The data can be collected and summarized more quickly with a sample than with complete count. Thus it is a vital point when the information is needed urgently.
◊ Greater accuracy of results : Information collected form a sample is often more accurate than that obtained form a census. This is due to the fact that in a sample survey trained person can be employed and greater control can be exercised over filed work.
Principle Steps in a Sample Survey
- Statement of objectives
- Definition of population to be studied
- Determination of sampling frame and sampling units
- Selection of proper sampling design
- Organization of field work
- Summary and analysis of data
Sampling frame : This is the actual list of sampling units from which the sample, or some stage of the sample, is selected. It is simply a list of the study population.
Sample size : The number of units included in the sample is known as the sample size.
Statistic : Any function of sample values is called statistic.
Estimator : Statistic is used to estimate any parameter, it will be called estimator.
Unbiased and biased : An estimator t is said to be unbiased estimator for the parameter b if E(t) = b.
Otherwise it will be biased. Thus biased is given by E(t-b) = B(t).
If t is an estimator for the parameter b, then the mean square error (MSE) of t is given by MSE (t) = E(t – b)2
And the sampling variance of t is given by v(t) = E[t – E(t)] 2
Questionnaires: A set of common questions laid out in a standard and logical form to record individual respondent’s attitudes and behavior. Instructions show the interviewer or the respondent how to move through the questions and complete the schedule. It could be printed on paper or on a computer screen.
The key Steps of effective questionnaire design:
Step 1 – Decide what information is required
Step 2 – Make a rough listing of the questions
Step 3 – Refine the question phrasing
Step 4 – Develop the response format
Step 5 – Put the questions into an appropriate sequence
Step 6 – Finalize the layout of the questionnaire
Step 7 – Pretest and revise
Example of Ranking Response Questions:
Rank the following brands according to how much you like them… Please place a 3 next to the brand you like most, a 2 in your next preferred brand and a 1 next to your least preferred brand.
Coke ____ Pepsi ____ Fanta ____
Example of Rating Response Questions:
How do you rate the following?
Non-Sampling error : Besides sampling error, the sample estimate may be subject to other errors which, grouped together, are termed non-sampling error.
- The census survey results may suffer form non-sampling errors although these may be free from sampling error.
The main sources of non-sampling errors are :
- Failure to measure some of the units in the selected sample.
- Observational errors due to defective measurement technique.
- Errors introduced in editing, coding and tabulating the results.
The non-sampling error is likely to increase with the increase in sample size, while sampling error decreases with increase in sample size.
A pilot survey, pilot study, or pilot experiment is a small scale preliminary study conducted in order to evaluate feasibility (conveniently done), time, cost, adverse events, and effect size (statistical variability) in an attempt to predict an appropriate sample size and improve upon the study design prior to performance of a full-scale research project.
Sample design : This refers to a set of rules or procedures that specify how a sample is to be selected. This can either be probability or non-probability.
Characteristics of a Good Sample Design
Following are the characteristics of good sample design:
- Sample design should be a representative sample: A researcher selects a relatively small number for a sample from an entire population. This sample needs to closely match all the characteristics of the entire population. If the sample used in an experiment is a representative sample then it will help generalize the results from a small group to large universe being studied.(Sample Surveys)
2. Sample design should have small sampling error: Sampling error is the error caused by taking a small sample instead of the whole population for study. Sampling error is reduced by selecting a large sample and by using efficient sample design and estimation strategies.
Characteristics of a Good Sample Design
- Sample design should be economically viable: Studies have a limited budget called the research budget. The sampling should be done in such a way that it is within the research budget and not too expensive to be replicated.(Sample Surveys)
4. Sample design should have marginal systematic bias: Systematic bias results from errors in the sampling procedures which cannot be reduced or eliminated by increasing the sample size. The best bet for researchers is to detect the causes and correct them.
5. Results obtained from the sample should be generalized and applicable to the whole universe: The sampling design should be created keeping in mind that samples that it covers the whole universe of the study and is not limited to a part.
Equal Probability Sampling : This is the method of selecting samples according to certain laws of probability in which each unit in the population has same (equal) probability of being selected in the sample. Let Pr(ui)=Pi , the probability of selecting the ith unit ui in the sample. If Pr(ui)=Pi=P, for all i, then it is called the equal probability sampling.(Sample Surveys)
Unequal Probability Sampling: When units vary in their sizes and the variate under study is highly correlated with the size of the unit, the probability of selection may be assigned in proportion to the size of the unit. This type of sampling procedure where the probability of selection is proportional to the size of the unit is known as unequal probability sampling or probability proportional to size sampling.
Simple Random Sampling (SRS): Simple random sampling involves selection of a sample by drawing the units with equal probability. The probability of selection of the units at each draw is always equal.
Simple random sampling is a method of selecting n units out of a population of size N, by giving equal probability all units.(Sample Surveys)
Simple random sampling is a sampling procedure in which all possible combinations of n units that may be formed from the population of N units have the same probability of selection.
Procedures of Selecting a Random Sample:
- Lottery Method
- Use of Random Number Tables
Inflation factor: The factor N/n by which the sample total is multiplied is called the expansion or raising or inflation factor. Its inverse n/N is called the sampling fraction and is denoted by the letter f.(Sample Surveys)
Finite Population Corrections (FPC): It can be easily seen that terms for the variance and for the standard error are introduced due to fitness of the population and these are called finite population correction (fpc).
The FPC factor is used to adjust a variance estimate for an estimated mean or total, so that this variance only applies to the portion of the population that is not in the sample. That is, variance is estimated from the sample, but through the fpc it is used to assess the error in estimating a mean or a total, which is due to the fact that not all data from the finite population are observed.Sample Surveys
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