Page 259 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

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

(ii) Factor reversal test Notes

505 530
P on = 425 × 470

470 530
Q on = 425 × 505

∑ p q
nn
P no × P on = ∑ p q
00
Hence, the data satisfies both time reversal and factor reversal tests.
Example 2: The following figures relate to the prices and quantities of certain commodities.
Construct an appropriate index number and find out whether it satisfies the time
reversal test.
Commodities 2004 2005
Price Quantity Price Quantity

A 30 50 32 50
B 25 40 30 35
C 18 50 16 55

Solution:
INDEX NUMBER BY FISHER’S IDEAL METHOD

Commodities 2004 2005
p 0 q 0 p 1 q 1 p q p q p q p q
10
01
00
11
A 30 50 32 50 1,600 1,500 1,600 1,500
B 25 40 30 35 1,200 1,000 1,050 875
C 18 50 16 55 800 900 880 990
∑ pq ∑ pq ∑ pq ∑ pq
11
00
10
01
= 3,600 = 3,400 = 3,530 = 3,365
∑ pq ∑ pq
1 1
10
P 01 = ∑ pq × ∑ p q × 100
00
0 1
3,600 3,530
= 3,400 × 3,365 × 100 = 1.111 100× = 1.054 × 100 = 105.4
Time reversal test is satisfied when

P × P 10 = 1
01
∑ p q ∑ p q 3,600 3,530
11
10
P 01 = ∑ p q × ∑ p q = 3,400 × 3,365
00
01
∑ p q ∑ p q 3,365 3,400
01
00
P 10 = ∑ p q × ∑ p q = 3,530 × 3,600
10
11
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