Page 255 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 20: Test of Consistency: Unit Test, Time Reversal Test, Factor Reversal Test and Circular Test
Dilfraz Singh, LPU

Unit 20: Test of Consistency: Unit Test, Time Reversal Test, Notes

Factor Reversal Test and Circular Test

CONTENTS
Objectives
Introduction
20.1 Unit Test
20.2 Time Reversal Test
20.3 Factor Reversal Test
20.4 Circular Test
20.5 Summary
20.6 Key-Words
20.7 Review Questions
20.8 Further Readings

Objectives

After reading this unit students will be able to:
• Define Unit Test and Time Reversal Test.
• Know Factor Reversal Test and Circular Test.
Introduction

We have read in previous unit 19 that the relatives have certain important properties. What is true
for an individual commodity should also be true for a group of commodities. The index number as
an aggregative relative should also satisfy the same set of properties.
A number of mathematical criteria for judging the adequacy of an Index Number formula have been
developed by statisticians. In fact, the problem is that of selecting the most appropriate one in a given
situation. The following test are suggested for selecting an appropriate index.
(i) Unit Test
(ii) Time Reversal Test
(iii) Factor Reversal Test
(iv) Circular Test.
20.1 Unit Test

This test requires that the formula for constructing an index should be independent of the units in
which the prices are quoted. All formulae of weighted aggregate method except simple aggregative
method satisfy this test.
20.2 Time Reversal Test

Prof. Fisher has stated Time Reversal Test. ‘The test is that the formula for calculating an Index
Number should be such that will give the same ratio between one point of comparison and the other,
no matter which of the two is taken as base. Time Reversal means that if we change the base year to
the current year and vice versa then the product of the indices should be equal to unity. In other

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