Factor Reversal Test and Simple Aggregative Index Number

Factor Reversal Test
The factor reversal test is a statistical test used to determine whether an index number is reliable or not. The test involves reversing the base and current period for a particular item or group of items and then calculating the new index number. If the new index number is the reciprocal of the original index number, then the index is said to satisfy the factor reversal test.

Simple Aggregative Index Number
A simple aggregative index number is a type of index number that measures the change in the value of a group of items over time. The formula for calculating a simple aggregative index number is:

Index number = (current period value ÷ base period value) × 100

Where:
- current period value is the total value of the group of items in the current period
- base period value is the total value of the group of items in the base period

Factor Reversal Test and Simple Aggregative Index Number
A simple aggregative index number satisfies the factor reversal test because of the way it is calculated. When the current period and base period values are reversed, the index number is calculated as:

New index number = (base period value ÷ current period value) × 100

If we take the reciprocal of this, we get:

1 ÷ (base period value ÷ current period value) × 100

Simplifying this expression gives:

(current period value ÷ base period value) × 100

Which is the same as the original index number. Therefore, a simple aggregative index number satisfies the factor reversal test.

Conclusion
In conclusion, a simple aggregative index number satisfies the factor reversal test. This is because of the way it is calculated, which ensures that the index number is reliable and consistent when the current period and base period values are reversed.