# Tests for Adequacy of Index Numbers

There are four tests to check for the adequacy of index numbers. They are as follows:**Unit test****Note:**Except unweighted aggregative index number, all other formulae satisfy this test.**Time reversal test***P*_{01 }is the index for time 1 on 0 and*P*_{10 }is the index for time 0 on 1.**Note:**Laspeyreâ€™s and Paascheâ€™s method do not satisfy this test, but Fisherâ€™s ideal index does.**Factor reversal test****Note:**1. Only Fisherâ€™s index number satisfies this test.

2. Since Fisherâ€™s index number satisfies both time reversal and factor reversal test, it is called an ideal index number.**Circular test****Note:**1. The simple G.M. of price relatives and the weighted aggregative with fixed weights satisfies this test.2. Laspeyreâ€™s, Paascheâ€™s and Fisherâ€™s index number do not satisfy this test.

*Link relative is the ratio of current yearâ€™s price to previous yearâ€™s price*

# Link Relative

*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.*

# Chain Index Number

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

Example

Calculate the link relatives and chain indices for the given data:

Years |
1995 |
1996 |
1997 |
1998 |
1999 |

Price of Wheat (â‚¹) |
20 | 25 | 30 | 45 | 63 |

Solution

Let us take the link relative and chain index for the base period as 100.