There are four tests:

(a) Unit Test
(b) Time Reversal Test
(c) Factor Reversal Test
(d) Circular Test

---

(a) Unit Test: In this the formula should be independent of the unit in which or for which prices and quantities are equal are quoted.
All formula of Index Number satisfy this test except simple unweighted aggregative Index Number.

---

(b) Time Reversal Test: This test was suggested by Prof. Irving Fisher.When the data for only two years are treated and will work in both ways in time, forward and backward. There are two ratios Such that, the current on the base and the base on the current should multiply into unity.

P₀₁ x P₁₀ = 1 or P₀₁ = 1/P₁₀

Where P₀₁ is the index for time 1 on 0 and P₁₀ is the index for time 0 on 1. Laspeyer's and Paasche's method do not satisfy this test. Fisher's, M-E, Walsch's, Kelly's, Simple aggregate index number satisfy this test.

---

(c) Factor Reversal Test: This test is suggested by Prof. Irving Fisher. According to this test the product of price index and the quantity index must be equal to the value index ,
i.e. ∑(P₁Q₁)/∑(P₀Q₀)

Symbolically :P₀₁ x Q₀₁ = V₀₁
Only Fisher's index number satisfies this test and no other index number satisfy this test.

---

(d) Cirular Test: This test is an extension of time reversal test(It is a generalisation of the time reversal test). The test of shiftability of base is called the circular test.

P₀₁ x P₁₂ x P₂₃ ------ P_n-1,n x P_n0 = 1.

Laspeyer's, Paasche's and Fisher's index number do not satisfy test. The simple aggregative method and the fixed weight aggregative method satisfy this test.