# Time And Factor Reversal Test Of Index Numbers Pdf

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*Time Reversal Test Prof.*

- Explain the various tests of adequacy of Index Number.
- Index Number MCQs | Multiple Choice Questions and Answers | B.Com-CA-CS-CMA Foundation Exam
- Properties and Tests
- INDEX NUMBERS Quantitative Aptitude & Business Statistics

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## Explain the various tests of adequacy of Index Number.

There are certain tests which are put to verify the consistency, or adequacy of an index number formula from different points of view. The most popular among these are the following tests:. At the outset, it should be noted that it is neither possible nor necessary for an index-number formula to satisfy all the tests mentioned above. But, an ideal formula should be such that it satisfies the maximum possible tests which are relevant to the matter under study. However, the various tests cited above are explained here as under:.

This test requires that a formula of Index number should be such that the value of the index number remains the same, even if, the order of arrangement of the items is reversed, or altered.

As a matter of fact, this test is satisfied by all the twelve methods of index number explained above. This test has been put forth by Prof. Irving Fisher, who proposes that a formula of index number should be such that it turns the value of the index number to its reciprocal when the time subscripts of the formula are reversed i. According to this proposition, if the index number of the current period on the basis of the current period i.

P 01 is , the index number of the base period on the basis of the current period i. P 10 would be As such, an index number formula, in order to satisfy this test must prove the following equation:. As a matter of fact, this test is satisfied by most of the formula of index number except those of Laspeyre and Paasche which is shown in the table as on the next page. Besides the seven methods shown in the table, both the simple and weighted geometric mean of piece relatives, also, satisfy this time reversal test.

This test has also been purforth by Prof. Irving Fisher, who proposes that a formula of index number should be such that it permits the interchange of the price, and the quantity factors without giving inconsistent result i. Thus, for the Factor Reversal test, a formula of index number should satisfy the following equation:.

Most of the formulae of index number discussed above fail to satisfy this acid test of consistency except that of Prof. Irving Fisher. This is the reason for which Prof. Fisher claims his formula to be an ideal one. The table displayed on page bears a testimony to the test mentioned above. This test has been purforts by Westergaard and recommended by C. Walsch in extension of the times reversal test purforth by Prof.

This test requires that an index number formula should be such that an index number formula should be such that it works in a circular fashion.

This means that if an index is computed for the period 1 on the base period 0, another index is computed for the period 2 on the base period 0 on the base period 2, the product of all these indices should be equal to 1. Thus, a formula to satisfy the test should comply with the following equation. An index formula which satisfies this test enjoys the advantage of reducing the computation work every time a change in the base year is made.

As it will be seen from the table exhibited on page , this test is not satisfied by most of the important index formula viz. This is a common test which requires that an index number formula should be such that it does not affect the value of the index number, even if, the units of the price quotations are altered viz. This test is satisfied by all the index formula except the simple aggregative method under which the value of the index number changes radically, if the units of price quotations of any of the items included in the index number are changed.

Live Chat. The most popular among these are the following tests: Order reversal test. Time reversal test. Factor reversal test. Circular test. Unit test. However, the various tests cited above are explained here as under: 1.

Order reversal test This test requires that a formula of Index number should be such that the value of the index number remains the same, even if, the order of arrangement of the items is reversed, or altered. Time reversal test This test has been put forth by Prof. Factor reversal test This test has also been purforth by Prof. Circular test This test has been purforts by Westergaard and recommended by C.

Unit test This is a common test which requires that an index number formula should be such that it does not affect the value of the index number, even if, the units of the price quotations are altered viz.

## Index Number MCQs | Multiple Choice Questions and Answers | B.Com-CA-CS-CMA Foundation Exam

Index number was first constructed in:. Index number is specialised average designed to measure the change in a group of related variables over a period of time. An index number calculated with a single variable is called univariate index. When an index number is constructed from a group of variables is considered a composite index. Most widely used weighted index is:. The best average for constructing an index number is:.

Several formulae have been suggested for constructing index numbers and the problem is that of selecting the most appropriate one in a given situation. The different tests are the unit test, time reversal test, factor reversal test, and circular test. This test states that the formula for constructing an index number should be independent of the units in which prices and quantities are expressed. All methods, except simple aggregative method, satisfy this test. Except for unweighted aggregative index number, all other indices satisfy this test.

There are certain tests which are put to verify the consistency, or adequacy of an index number formula from different points of view. The most popular among these are the following tests:. At the outset, it should be noted that it is neither possible nor necessary for an index-number formula to satisfy all the tests mentioned above. But, an ideal formula should be such that it satisfies the maximum possible tests which are relevant to the matter under study. However, the various tests cited above are explained here as under:. This test requires that a formula of Index number should be such that the value of the index number remains the same, even if, the order of arrangement of the items is reversed, or altered.

## Properties and Tests

Test of adequacy for an Index Number. Index numbers are studied to know the relative changes in price and quantity for any two years compared. There are two tests which are used to test the adequacy for an index number. The two tests are as follows,. The criterion for a good index number is to satisfy the above two tests.

### INDEX NUMBERS Quantitative Aptitude & Business Statistics

The new index numbers, which were introduced in Chapter 3, were designed not only to avoid the one-sidedness of the Laspeyres and Paasche measures of volume and price change, but also to meet the requirements of multiplicative as well as additive analysis of value changes of commodity aggregates into a volume and a price component. Having been designed with these objectives in mind, these index numbers have a number of properties which make them particularly suitable measures of volume and price change from an analytical point of view. In this chapter we aim to find out what these properties are, the extent to which they are shared by other index numbers and also whether by any chance the other index numbers have any useful properties which the new index numbers do not have. The method by which we establish whether or not a given type of index number possesses certain properties is the time-honoured one of applying appropriate tests to it. Unable to display preview. Download preview PDF.

However the problem still remains of selecting an appropriate method for the construction of an index number in a given situation. The following tests can be applied to find out the adequacy of an index number. Unit Test - This test requires that the index number formulae should be independent of the units in which prices or quantities of various commodities are quoted. For example in a group of commodities, while the price of wheat might be in kgs. Except for the simple unweighted aggregative index, all other formulae discussed above satisfy this test. The time reversal test may be stated more precisely as follows— If the time subscripts of a price or quantity index number formula be interchanged, the resulting price or quantity formula should be reciprocal of the original formula.

This paper presents the results of a pilot test performed on a real medium voltage distribution network in Switzerland with the aim of assessing the performance of a fault location system relying on the Electromagnetic Time Reversal EMTR method. Complete the form below to receive an email with the authorization code needed to reset your password. Please try again. Answer 1 of 1 : Time reversal test states that if the time subscripts that are o and n of a price or a quantity index number formula be interchanged, then the resulting price or quantity index formula should be the reciprocal of the original formula. Nuclear physics tests of parity- and time-reversal invariance have both shaped the development of the Standard Model and provided key tests of its predictions. Full Record; Other Related Research The email has already been used, in case you have forgotten the password.

(iv) It is the only formula which satisfies the two important tests i.e. The Time Reversal Test' and 'The Factor Reversal Test.' (5) Marshall—Edgeworth's Method.