The Law of inertia of Large Numbers is an immediate deduction from the Principle of Statistical Regularity.
INERTIA OF LARGE NUMBERS
The Law of inertia of Large
Numbers is an immediate deduction from the Principle of Statistical Regularity.
Law of Inertia of Large Numbers states, “Other things being equal, as the
sample size increases, the results tend to be more reliable and accurate.” This
is based on the fact that the behavior or a phenomenon en masse. I.e., on a
large scale is generally stable. It implies that the total change is likely to
be very small, when a large number or items are taken in a sample. The law will
be true on an average. If sufficient large samples are taken from the patent
population, the reverse movements of different parts in the same will offset by
the corresponding movements of some other parts.
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. In statistics the
word error is used to denote the difference between the true value and the
estimated or approximated value. 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 exist due to the fact that only a sub set of the population 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.
errors occur primarily due to the following reasons:
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 judgment sampling in which the investigator deliberately selects a
representative sample to obtain certain results. This bias can be easily
overcome by adopting the technique of simple random sampling.
Substitution: When 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.
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 of 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.
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
Variability of the population: Sampling error also depends on the variability or heterogeneity of the
population to be sampled. Sampling errors are of two types: Biased
Errors and Unbiased Errors
Errors: The errors that occur due to a
bias of prejudice on the part of the informant or enumerator in selecting,
estimating measuring instruments are called biased errors. Suppose for example,
the enumerator uses the deliberate sampling method in the place of simple
random sampling method, then it is called biased errors. These errors are
cumulative in nature and increase when the sample size also increases. These
errors arise due to defect in the methods of collection of data, defect in the
method of organization of data and defect in the method of analysis of data.
Errors: Errors which occur in the normal
course of investigation or enumeration on account of chance are called unbiased
errors. They may arise accidentally without any bias or prejudice. These errors
occur due to faulty planning of statistical investigation.
To avoid these errors, the statistician must take
proper precaution and care in using the correct measuring instrument. He must
see that the enumerators are also not biased. Unbiased errors can be removed
with the proper planning of statistical investigations. Both these errors
should be avoided by the statisticians.
Sampling Errors: Errors in
sampling can be reduced if the size of sample is increased. This is
shown in the following diagram. From the above diagram it is
clear that when the size of the sample increases, sampling error decreases. And
by this process samples can be made more representatives to the population.
Tags : Research Methodology - Questionnaire & Sampling
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