Question

Explain factor reversal test

Answer 1

This is another test for testing the consistency of a good index number.

The product of price index number and quantity index number from the base year to the current year should be equal to the true value ratio.

That is, the ratio between the total value of current period and total value of the base period is known as true value ratio.

Factor Reversal Test is given by

`"P"_01 xx "Q"_01 = (sum"p"_1"q"_1)/(sum"p"_0"q"_0)`

Where, `"P"_01 = sqrt((sum"p"_1"q"_0 xx sum"p"_1"q"_1)/(sum"p"_0"q"_0 xx sum"p"_0"q"_1))`

Now interchanging P by Q, we get

`"Q"_01 = sqrt((sum"p"_1"p"_0 xx sum"q"_1"p"_1)/(sum"q"_0"p"_0 xx sum"p"_0"p"_1))`

Where P₀₁ is the relative change in price

Q₀₁ is the relative change in quantity.