Friday, April 13, 2012

MEASUREMENT OF ERRORS IN DEMOGRAPHIC DATA

Methods of measurements of errors have been developed for census statistics; however can equally be used in vital statistics registration.
Response error is a broad term which includes both errors of coverage and error of content. The sampling theory assumed the census or survey or VSR records collected at time period are regarded as one of the series of trials, collection of responses which would vary from trial to trial. This hypothesis further assumed that the trials have been conducted under the same conditions and that they are independent of each other.
Various indices, measuring levels of errors can be calculated through this table:

 Count in Census(Ideal/ Standard) / Survey C O N T E N E V A L U T I O Survey Number of persons in count Number of Person not in count Total Number of person in class a b a+b Number of person not in class C d c+d Total a+c b+d

·         Then (a+c) represent count in a census/ sample survey/ VSR in relation to birth, death etc.
·         (a+b) is the corresponding count in CES
·          “a” is the number appearing in both
·         And on the other hand c would occur in actual
·         And “d” is the number without count characteristic and vital counts.

i.            Net difference rate (NDR).
ii.            Gross difference rate (GDR).
iii.            The index of net shift relative to ideal or standard count.
iv.            Index of stability.
v.            Index of inconsistency.

1)    NET DIFFERENCE RATE (NDR):
The net difference rate is defined as

NDR=(c-b)/n *100

It provides an estimate of the extent of the biased in the actually observed count (a+c). A positive value of the rate indicates an over statement, while a negative value indicates an under count in census survey or VSR. In case of no error the value would be zero.
2)    GROSS DIFFERENCE RATE:
GDR assumed in a hypothetical situation of repeated response from the same person in a large series of census/survey or VSR conducted under same conditions that a record is made of the response deviation for some person on each trial from the average of all responses. Hence the gross difference rate is defined as
g= b+c/n*100

And the simple response variance is approximated as;
SRV =1/2g

3)    The index of net shift relative to ideal standard count:
It is defined as the ratio of the differences in the count with the total in ideal count. Its positive indicates over estimate and negative indicates an under count.
s =c-b/a+b*100

4)    Index of stability:
The index of stability is a ratio which shows a number with specified characteristics which included in both, the census/ survey/ VSR with relation to those characteristics in the ideal or standard count. In terms of notation adopted this index is defined as:
Index of stability= a/a+b*100

This indicates the stability of response, the census survey or VSR relative to the ideal or standard count.

5)    Index of consistency:
The index of consistency which is also the measure of the stability of response is defined as;
I = g/2p(1-p)*100

Where p (1-p) is estimated by the average of sampling variance of the proportion having same characteristics such as specified occupation in census survey or VSR in the ideal situation or standard count.
Census/ Survey/ VSR

Generally I vary between   0 ≤ I ≤100
However values of I greater than 100 may arise occasionally when small sample are involved or if the assumption of estimation is completely not valid. A large value of I indicates a high degree of response error, an index of the stability of response “r” is more readily understood than I.
However it should be recognized that I and r are complementary in the sense that a large number of response error by a large value of I and by a small value of “r”.