Sampling & Non-Sampling errors

 SAMPLING AND NON-SAMPLING ERRORS

The errors involved in the collection, processing and analysis of data may be broadly classified under the following heads.

Sampling ErrorsNon-sampling errors

Sampling Errors

Sampling errors have their origin in sampling arise due to fact that only a part of the population has been used to estimate population parameters and draw inferences about the population.

Sampling biases are primarily due to the following reasons.

1.    Faulty Selection of Sample: Some of the biases is introduced by the use of defective sampling technique for the selection of sample eg., purposive or judgment sampling in which the investigator usually selects a representative sample to obtain certain results. This bias can be overcome by strictly adhering simple random sample or select sample at random.

2.   Substitution: If difficulties arise in enumerating a particular sampling unit included in the random sample, the investigator usually substitute a convenient member of the population. This obviously leads to some bias because the substitute unit may not possess the same characteristics of original sample unit.

3.   Faulty demarcation of Sampling units: This type of bias arises due to defective demarcation of sampling units is particularly significant in areas survey such as agricultural experiments in the field or crop cutting survey. In such surveys, while dealing with boarder line case, it depends more or less on the discretion of investigator whether to include them in the sample or not.

4.  Constant Error due to improper choice of statistics for estimating population parameters: Suppose x1, x2, x3,…….xn is a sample of independent observations, then the sample variance

is an estimate of the population variance is biased where as the statistic 

is an unbiased estimate of σ2.

                             Sampling error

                     Sample Size

      

NON-Sampling errors

 Non-sampling errors can occur at every stage of the planning or execution of census or sample survey. The important non-sampling errors arise due to the following factors.

1. Faulty Planning or Definitions: The planning of a survey consists in explicitly stating the objectives of the survey. These objectives are then translated into (i) a set of definitions of the characteristics for which data are to be collected and (ii) into set of specifications for collecting, processing and publishing. The following are responsible for occurring non-sampling errors.

Ø data specification may be inadequate and inconsistent w.r.t. objectives of the survey.

Ø error due to location of the units and actual measurements of the characteristics, errors in recording measurements, error due to ill-designed questionnaire etc..

Ø lack of trained and qualified investigators and lack of adequate supervisory staff.

2.   Response Errors: These type of errors are introduced as a result of the responses furnished by the respondents and may be the following reasons:

 

ü Response errors may be accidental: Suppose the respondent may misunderstand a particular question and accordingly furnish improper information un-intentionally.

ü Prestige Bias: Sometimes the pride or prestige of person interviewed may introduce yet another kind of bias, called prestige bias. In this bias he/she may be upgrade his education, intelligence, occupation, income etc., or downgrade his/her age, thus resulting in wrong answers.

ü Self-interest:  Quite often, in order to safeguard one’s self interest, one may give incorrect information, e.g., a person may give under estimate of salary or production and over-statement of his expenses or requirements.

ü Bias due to interviewer: Sometimes the interviewer may effect the accuracy of the response by the way he/she asks questions or records them. The information obtained from the interviewer is likely to influence by interviewer’s beliefs and prejudices.

ü Failure of Respondent’s Memory: Common source of error occurred by asking information related too past (time).

 

3.   Non-response Biases: Non-response bias occurs if full information is not obtained on all the sampling units. In house-to-house survey, non-responses usually results if the respondent is not found at home even after repeated calls, he/she unable to furnish the information on all questions or if refuse to answer certain questions. Therefore, some bias is introduced as a consequence of the exclusion of a section of population with certain peculiar characteristics, due to non-response.

 

4.   Errors in Coverage: If the objectives of the survey are not precisely stated in clear cut terms, this may result in (i). the inclusion in the survey of certain units which are not to be included, or to exclusion of certain units which were to be included in the survey under the objectives.

 

5.   Compiling Errors: Various operations of data processing such as editing and coding of the responses, tabulation and summerising the original observations made in the survey are potential sources of error. Compilation errors are subject to control through verification, consistency check etc.,

 

6.   Publication Errors: Publication errors i.e., the errors committed during presentation and printings of tabulated results are basically due to two sources. The first refers to the machines of publication-the proof error and the like. The other, which is more serious in nature, lies in the failure of the survey organization to point out the limitations of the statistics.

Sources: Fundamentals of Applied Statistics, S.C.Gupta & V.K.Kapoor, Fundamentals of Mathematical Statistics, S.C.Gupta & V.K.Kapoor, Sampling Techniques, W.G.Cochran