Explain the law of inertia of large number. Point out the significance of this law in sampling investigation.
Explain the law of inertia of large number. Point out the significance of this law in sampling investigation.
Ans.
Principle of Inertia of Large Numbers
An immediate deduction from the Principle of Statistical Regularity is the Principle of Inertia of Large Numbers which 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 behaviour of a phenomenon masse, i.e., on a large scale is generally stable. By this we mean that if individual events are observed, their behaviour may be erratic and unpredictable but when a large number of events are considered they tend to behave in a stable pattern. This is because a number of forces operate on the given phenomenon and if the units are large, then the typical odd variations in one part of the universe in one direction will get neutralised by the variations in equally bigger part of the universe in the other direction. According to A.L. Bowley, “Great numbers and averages resulting from them, such as we always obtain in measuring social phenomena have a great inertia.” Thus in dealing with large numbers, the variations in the component parts tend to balance each other and consequently the variation in the aggregate result is likely to be insignificant. However, it should not be inferred that in case of large numbers, there is no variation at all. Large numbers are relatively more stable in their characteristics than the small numbers. They (large numbers) also exhibit variations but they are of very small magnitude and intensity and are not violent in nature. For example, if a coin is tossed, say, 20 times then nothing can be said with certainty about the proportion of heads. We may get 0, 1, 2…, or even all the 20 heads. But it is thrown at random a very large number of times, say, 5,000 times, then we may expect on the average 50% heads and 50% tails. As another illustration let us consider the production of a particular commodity, way, rice in two districts in a state for a number of years. The figures will show great variations due to favourable or unfavourable conditions in that particular region. However, the figures for the production of rice for the whole state over number of years will show relatively lesser variations because lower production in some of districts will be compensated by the excessive production in some other districts of the state. Arguing similarly we find that the production figures for the whole of India will show still lesser variation and for the entire world it would be more or less stable.
