In Statistics, the word ‘error’ is used to denote the difference between the true value and the estimated or approximated value. In other words ‘error’ refers to the difference between the true value of a population parameter and its estimate provided by an appropriate sample statistic computed by some statistical device.
Errors arise due to the following reasons:
(i) Approximations in measurements, e.g., the heights of individuals may be approximated to 10th of a centimeter, age may be measured correct to nearest month, weight may be measured correct to 10th of a kilogram, distance may be measured correct to the nearest metre and so on. Thus, in all such measurements there is bound to be a difference between the observed value and the true value.
(ii) Approximations in rounding of the figures to the nearest hundreds, thousands, millions, etc. or in the rounding of decimals.
(iii) The biases due to faulty collection and analysis of the data and biases in the presentation and interpretation of the results.
(iv) Personal biases of the investigators and so on.
The inaccuracies or errors in any statistical investigation, i.e. in the collection, processing, analysis and interpretation of the data may be broadly classified as follows:
(i) Sampling Errors and
(ii) Non-Sampling Errors.
In a sample survey, since, only a small portion of the population is studied, its results are bound to differ from the census results and thus, have a certain amount of error. This error would always be there no matter that the sample is drawn at random and that it is highly representative.
This error is attributed to fluctuations of sampling and is called sampling error. Sampling error is due to the fact that only a subset of the population (i.e. sample) has been used to estimate the population parameters and draw inferences about the population. Thus, sampling error is present only in a sample survey and is completely absent in census method.
Sampling errors are primarily due to the following reasons:
1. Faulty selection of the sample:
Some of the bias is introduced by the use of defective sampling technique for the selection of a sample e.g., purposive or judgement sampling in which the investigator deliberately selects a representative sample to obtain certain results. This bias can be overcome by strictly adhering to a simple random sample or by selecting a sample at random subject to restrictions which, while, improving the accuracy are of such nature that they do not introduce bias in the results.
If difficulties arise in enumerating a particular sampling unit included in the random sample, the investigators usually substitute a convenient member of the population. This obviously leads to some bias since; the characteristics possessed by the substituted unit will usually, be different from those possessed by the unit originally included in the sample.
3. Faulty demarcation of sampling units:
Bias due to defective demarcation of sampling units is particularly, significant in area surveys such as agricultural experiments in the field or crop cutting surveys, etc. In such surveys, while, dealing with border line cases, it depends more or less on the discretion of the investigator whether to include them in the sample or not.
4. Error due to bias in the estimation method:
Sampling method consists in estimating the parameters of the population by appropriate statistics computed from the sample. Improper choice of the estimation techniques might introduce the error.
5. Variability of the population:
Sampling error also depends on the variability or heterogeneity of the population to be sampled.