Statistical data can be collected by two methods i. e.
census method and sample method.
(1) Census method. Statistics deals with large number. It does not study a single figure. All the items under consideration in any field enquiry constitute a universe of population. A complete enumeration of all the items in the pupulation is known as census method of collecting data. Census method is that method in which data is collected about every item of the universe or population relating to the problem under investigation. Suitability of Census Method. The method is suitable under
certain conditions:
1. Where the area of inquiry is not vast.
2. Where the time is too much. '
3 Where more degree of accuracy is required.
4. Where too much finance is available.
(2) Sample Method. In the census enquiry all the items are taken into consideration On the other hand, in sample enquiry, only a part of population is studied and from the results given by the sample,conclusions are drawn for the whole population. In the words of Snedecor, “A car load of coal is accepted or , rejected on the evidence gained from testing only a few pounds. The physician makes inferences about a patient’s blood through examinations of a single drop. Samples are devices for learning about large masses by observing a few individuals.” Sampling i,e. the selection of a part of an aggregate of material to represent the whole aggregate is a long established practice.Thus, sampling is that survey in which data are collected about the sample or a group of items taken from the population for investigation.But the size of the sample should be sufhcient so as to be representative of the universe.
3 ERRORS IN SAMPLING
The word ‘error’ is used in a specialised sense in statistics. It does not mean the same thing as a ‘mistake’. Mistake in statistics means wrong calculation or use of inappropriate method in the collection or analysis of data. Error, on the other hand, means “the difference between the true value and the estimated value. " Errors in statistics may arise due to various reasons.Statistical errors arise due to a large number of factors. They may be due to inappropriate definitions of statistical units, bias of the investigator or the inherent instability of the collected data.‘ Such errors are called Errors of Origin. Errors may also arise on account ofmanipulation in counting,‘measurement, description or approximation.Such errors are known as Errors of Manipulation. Yet another cause of statistical errors may be the use of incomplete data, errors may also arise on account of inadequacy of the size of the sample and all sucherrors are called Errors of inadequacy.
SAMPLING AND NON-SAMPLING ERRORS ,
Errors in statistics are classed in two categories, namely,
(l) Sampling errors, and (2) Non-sainpling errors.
I. Sampling Errors
Sampling errors have their origin in sampling and they arise on account of the fact that sample has been used to estimate parameters or population values. Such errors are not found In census enquiry where the whole universe is investigated. Sampling errors are attributed to fluctuation of sampling and that is why they are called sampling errors.Such errors would always be there in sample studies, not withstanding the fact that the sample has been properly chosen and it is of adequate size. Samples always give estimated figures about the Universe and the difference between the actual and estimated figures would always remain and the differences are called sampling errors.Generally, sampling errors are due to the following
reasons :
(I) Improper Selecllon of the Sample : If the sample has not been properly selected, it would lead to Sampling error. For example. if the sample has been selected on the basis of personal judgement or convenience’ it may not be the representative of the universe and the sampling error in such a case can be substantial. This bias can be overcome if the selection of the sample is on the basis of random sampling.
(ll) Substitution : If a sample unit is absent or any information from it is not available, and if this unit is substituted by another unit, the sample will lose its representative character and this can also introduce an element of error in the sampling.
(ii!) Faulty demarcation of statistical units : lf statistical units are not properly demarcated, the sample will become unrepresentative or give faulty conclusions. It is true, particularly ,in crop cutting experiments where sample fields have to be demarcated to ensure precision. If there is a mistake in demarcation, results of the experiment would be faulty. '
(iv) Errors due to variability of population and wrong method of estimation : Sometimes, a population is highly heterogeneous and in such a case a sampling result may be very much different from the actual value of the parameter. This would also be so if the parameter or population values are not properly estimated on the basis of sampling results.
Measurement of Sampling Error
A measure of sampling error is provided by the standard error of the estimate. Estimation of sampling error can reduce the element of uncertainty associated with interpretation of data. In most cases, the degree of precision or the opposite of error, would depend on the size of the sample. The standard error of estimate is inversely proportional to the square root of the sample size. In other words, as the sample size increases, element of error is reduced.
2. Non sampling Errors ‘ As distinct from sampling errors (which are due to drawing inferences about the universe on the basis of the sample studies) non-sampling errors generally arise when data are not properly observed, approximated and processed. These are not chance errors. Such errors are present in both Census as well as Sample methods of survey. in the Census method, although the data are free from sampling errors, yet there could be non sampling errors in them. The data obtained from sample surveys are subject both to sampling and non-sampling errors. Non-sampling errors, generally, arise due to the following reasons :
(t) Improper or ambiguous definition of the various terms : If the different terms used in a survey are not properly defined and cannot be easily identified, mistakes would creep in and the element of non sampling errors would go up.
(ii) Incomplete questionnaire and defective methods of Interviewing : These may also give rise to non-sampling errors.
(iii) Personal bias of the investigaror is also responsible for nonsampling errors as the data collected in such a situation would not be
representative.
(iv) Lack of trained and qualified investigators and failure of respondents to give correct answers and leads to such errors.
(v) Improper coverage and inadequate or incomplete response also result in non-sampling errors.
(vi) Errors in compilation and tabulation : Very often, mistakes are committed in the tabulation and classification of data which result in non-sampling errors. Such errors may also arise on account of defective printing of the tabulated results.
