Electronic book on sampling in finite populations

The Selection Process

Between the Sampling Probabilities Plans

An article on line about the main features of a research made using POSDEM

In this page you could find the index of an electronic book on sampling in finite populations. This book is distributed free like help to the POSDEM program. They are also included some of the main features and examples and a specific bibliography on systematic sampling and sampling with unequals probabilities.

We recommend to read the introduccion, of a essay "About the definitón of Statistic"

The same paper translate to:

French.

Italian.

German.

PRINCIPLES OF SAMPLING

1.- Introduction

1.1.- Estimation 1.2.- Sampling distribution 1.3.- Sampling theory 1.4.- Probabilistic sampling

2.- Sampling aleatory simple

2.1.- With and without reposition 2.2.- Variability and estimators2.3.- Sampling size

3.- Unequal probabilities

3.1.- Advantages 3.2.- Disvantages 3.3.- With y without reposition 3.4.- Partial reposición

4.- Superpopulation aproach

4.1.- Evaluation of methods 4.2.- Models used4.3.- Aplication of the models

5.- Stratified sampling

5.1.- Concept 5.2.- One and two sample size

6.- Systematic sampling

6.1.- Concept 6.2.- Types of systematic sampling

7.- Two examples

7.1.- Data and models 7.2.- Results

¿ Useful for …?

A program of computer directed professors and students of a course of statistics in order to evaluate different technical of selection and methods of estimate based on probabilistics samples. I in the face of different classes of population mark, it is tried to answer questions of the type: what method of sampling choose? who is the size of sample for certain level of significance? what level of error could it be hoped? what units should they investigate?

It establish a protocol in order to solve the election between several methods of sampling, so that It improve the size of sample like the precision of the based on estimates the Design of Medibles Surveys so much.

A new pedagogic method in the field of the sampling in finite populations, so much for courses courses of introduction like advanced inside the field of the surveys.

POSDEM software allow:

Carrying out analysis of the population original objective and of the methods of sampling considered. It seek to help the students in the learning by means of guided examples and with questions of the type: what happen if ....?

Choosing that of old precision between alternative designs. It permit, before the work of field of an investigation for sampling, evaluate the results according to the type of sampling used and the characteristics of the population.

Key words :

For a basic course

With and without reposition and equal probabilities;
Estimator distribution;
Error level for diferents levels of trust;
Sampling size;
Systematic sampling;
Stratified sampling with one unit per stratum;

For an advanced course

Systematic sampling centered;
Balanced sampling y Modified sampling;
Systematic sampling con intervalo variable;
Probabilities proportional to size sampling;
Improved estimators;
Superpopulation models;
Correlogram;

References

Bellhouse,D.R.&Rao, J.N.K. (1975);Systematic sampling in the presence of a trend; Biometrika 62. P.694-697;
Biehler, R (1997); Software for learning and doing statistics. International Statistics Review
Cochran, W.G. (1977):«Sampling Techniques», 3rd edition, New York: Wiley. P.205
Murthy, M.N. (1967):«Sampling theory and Methods» Statistical Publishing Society,Calcutta. P.127
Krishnaiah, P.R.; Rao, C.R. (1988):«Sampling», Handbook of Statistics, North-Holland. P.131
Sánchez-Crespo, Jl. (1997) Journal Oficial Statistics, Vol. 13, Nº 4, Pg 327-339

A general example: Evaluation of procedures for the selection and estimate for mensurable sampling:

Enunciate Choose the method of sampling more appropriate for a population formed by 12,000 students. Fraction of sampling 10%. Calculate the absolute error for a level of significance of the 95%.

Protocol for the election of a method of sampling

Solution of the example of the example method sampling systematic balanced elect. Absolute relative error of the 4% to the 95% of significance.

Conclusion improves in precision using methods of sampling adapted the structure analyzed population.

Notes:

Types of the methods of considered [sampling], in function of their degree of difficulty and of the necessities of the survey.

Methods of type one Methods of type two Methods of type three
Calculation of the size of the sample and of the [absolute] given error the level of significance in the case of sampling aleatory without reposition

Evaluation of methods of sampling by means of models of superpopulation when the the order of the population is aleatory

Example with probabilities proportional to size:

Enunciate:: An agency that should inspect four files of expense, in order to know who it is the amount of money that has worn out witout control.

Comparison of methods: A comparison between methods of same and unequals probabilities.

Size of population and old sample: We are going to consider an outline of sampling estratified with sizes of sample two for stratum.

A model of simple superpopulation: It is tried to get that the analysis of the error due to the sampling is the most reliable possible thing.

Notes

Sampling With Proportional Probabilities to the Size: An introduction.
Sampling With reposition and PPS: The alternative first.
Sampling Without reposition and PPS: It is easy improve the previous outline
Sampling With Partial reposition and PPS: The better alternative.

Bibliography

This is a Bibliography on sampling in finite populations , it makes special reference to systematic sampling and to the sampling with unequal probabilities .

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HAJEK, J.; (1981); Sampling from a finite population; New York, Clav-Dupec:M.Dekker.
HANNAN, E.J.; (1962); Systematic sampling; Biometrika 49, 281-283.
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HARTLEY, H.O.; (1966); Systematic sampling with unequal probabilities and without replacement; Journal of the American Statistical Association 61, 739-748.
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HEILBRON, D.C.; (1978); Comparison of estimators of the variance of systematic sampling; Biometrika 65, 429-433.
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HORVITZ, D.G.; THOMPSON, D. J.; (1952); A generalization of sampling without replacement from a finite universe; Journal of the American Statistical Association 47, 663-685.
HOTELLING; SOLOMONS; (1932); Limits of a measure of skewness; Ann.Math.Stat.; Vol3, pp.141-142.
HYMAN, H.H.; (1954); Interviewing in Social Research; University of chicago Press, Chicago, III;1
IACHAN, R.; (1980); Topics in systematic sampling; University of california-Berkeley Ph.D.disertation.
IACHAN, R.; (1980); The weight scaling problem - Systematic sampling from a population of truckloads of trees; Univ. of Wisconsin Tech. Report No. 626.
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INDIAN COUNCIL OF AGRICULTURAL RESEARCH, NEW DELHI; (1950); Estimation of catch of marine fish in a sample of landing centres; Report on the pilot sample survey conducted on the Malabar coast for estimating the catch of marine fish (unpublished).;1.
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