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Tests for Adequacy of Index Numbers

There are four tests to check for the adequacy of index numbers. They are as follows:

  1. Unit test
    This test suggests that the formula for constructing an index should be independent of the unit of measurement in which the prices and quantities are quoted.

    Note: Except unweighted aggregative index number, all other formulae satisfy this test.

  2. Time reversal test
    The time reversal test requires that the index number computed backwards should be the reciprocal of the index number computed forward, except for the constant of proportionality.
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    Where, P01 is the index for time 1 on 0 and P10 is the index for time 0 on 1.

    Note: Laspeyre’s and Paasche’s method do not satisfy this test, but Fisher’s ideal index does. 

  3. Factor reversal test
    According to this test the product of price index and quantity index must be equal to the value index.
    Description: 70302.png

    Note: 1. Only Fisher’s index number satisfies this test.
    2. Since Fisher’s index number satisfies both time reversal and factor reversal test, it is called an ideal index number.

  4. Circular test
    It is a generalization of the time reversal test. It is concerned with the measurement of price changes over a period of years, when it is desirable to shift to the base.

    Note: 1. The simple G.M. of price relatives and the weighted aggregative with fixed weights satisfies this test.


    2. Laspeyre’s, Paasche’s and Fisher’s index number do not satisfy this test.

Link Relative

Link relative is the ratio of current year’s price to previous year’s price


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Chain Index Number

In this method, the relative figures for each year are first converted into link relatives and these link relatives are then chained together by successive multiplication to form a chain index.


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Note: For the base period, the link relatives and the chain indices may be taken as 100.


Calculate the link relatives and chain indices for the given data:
Years 1995 1996 1997 1998 1999
Price of Wheat (₹) 20 25 30 45 63
Let us take the link relative and chain index for the base period as 100.

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