Demography is the scientific study of human population,

Population and Demographic Data

Lecture - 22

Measurement of Age and Digit Preference

Homework:

( What do you mean by Zero Error?

( Write short notes on different types of digit preference.

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Todays Topics:

Age Heaping

Digit preference

Whipples Index

Myerss Blended Method

Important Points:

Summary

After the lecture, use this space to summarize the main points of this Lecture Topic.

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Measurement of Age and Digit Preference

In the analysis of single years of age data, if there are no irregularities, the counts for adjacent ages should be similar. Examples of irregularities are digit preference and avoidance.

The tendency of enumerators or respondents to report certain ages at the expense of others is called age heaping, age preference, or digit preference.

Age Heaping, if a population tends to report certain ages (say, those ending in 0 or 5) at the expense of other ages, this is known as age heaping.

Age heaping is most pronounced among populations or population subgroups having a low educational status.

Digit preference, an analogous concept, carries the added feature of respondents having a preference for various ages having the same terminal digit.

The causes and patterns of age or digit preference vary from one culture to culture, but preference for ages ending in 0 and in 5 is quite widespread, especially in the Western world. In Korea, China, and some other countries in East Asia, there is sometimes a preference for ages ending in the numeral 3 because it sounds like the word or character for life. In some cultures certain numbers and digits are avoided, e.g., 13 is frequently avoided in the West because it is considered unlucky. The numeral 4 is avoided in Korea and in China because it has the same sound as the word or character for death.

Age heaping and digit preference may be ascertained more precisely with indices. Indices of digit preference assume that the true figures are rectangularly distributed over an n-year age range that is centered on the specific age being examined. If the index equals 100, there is no age heaping on the age being examined. The greater the value above 100, the greater the concentration on this age. The lower the value from 100, the greater the avoidance of the age being examined.

Heaping, i.e., digit preference, or the lack of heaping, i.e., digit avoidance, are the major forms of error typically found in single-year-of-age data. Irregularities in reporting single years of age can be detected using graphs and indices. Both will be considered.

Digit avoidance refers to the opposite.

Whipples Index

Indexes have been developed to reflect preference for or avoidance of a particular terminal digit or of each terminal digit. For example, employing again the assumption of rectangularity in a 10-year range, we may measure heaping on terminal digit 0 in the range 23 to 62 very roughly by comparing the sum of the populations at the ages ending in 0 in this range with one-tenth of the total population in the range:

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62

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100

Similarly, employing either the assumption of rectangularity or of linearity in a 5-year range, we may measure heaping on multiples of five (terminal digits 0 and 5 combined) in the range 23 to 62 by comparing the sum of the populations at the ages in this range ending in 0 or 5 and one-fifth of the total population in the range:

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EMBED Equation.3

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The choice of the range 23 to 62 is largely arbitrary (or arbitrary one). In computing indexes of heaping, the ages of childhood and old age are often excluded because they are more strongly affected by other types of errors of reporting than by preference for specific terminal digits and the assumption of equal decrements from age to age is less applicable.

The procedure described can be extended theoretically to provide an index for each terminal digit (0, 1, 2, etc.). The population ending in each digit over a given range, say 23 to 82, or 10 to 89, may be compared with one-tenth of the total population in the range, as was done for digit 0 earlier, or it may be expressed as a percentage of the total population in the range. In the latter case, an index of 10% is supposed to indicate an unbiased distribution of terminal digits and, hence, presumably accurate reporting of age. Indexes in excess of 10% indicate a tendency toward preference for a particular digit, and indexes below 10% indicate a tendency toward avoidance of a particular digit.

The tendency of respondents or enumerators to report particular ages are known as age heapings. Age heapings are usually found at ages ending in 0 and 5. The whipple's index has been 174 developed to determine the amount of age heapings. If there are no age heapings at ages ending in 0 and 5, the whipple's index is 100. If only digits 0 and 5 are reported, then index is 500. The whipple's index for the total population of Nepal is 206.1 indicating that the population tabulated at these ages is more by 106 percent than the corresponding unbiased population. In fact, the quality of data is very rough. According to UN scale, the quality of data is very rough if the value is 175 or more.

The values of whipple's index for males and females are 205.7 and 206.6 respectively indicating that quality of data are very rough for both sexes though it is a little bit better for males than for females.

Myerss Blended Method

Myers (1940) developed a blended method to avoid the bias in indexes computed in the way just described that is due to the fact that numbers ending in 0 would normally be larger than the following numbers ending in 1 to 9 because of the effect of mortality. The principle employed is to begin the count at each of the 10 digits in turn and then to average the results. Specifically, the method involves determining the proportion that the population ending in a given digit is of the total population 10 times, by varying the particular starting age for any 10-year age group.

The abbreviated (or shortened) procedure of calculation calls for the following steps:

Step 1. Sum the populations ending in each digit over the whole range, starting with the lower limit of the range (e.g., 10, 20, 30, . . . 80; 11, 21, 31, . . . 81).

Step 2. Ascertain the sum excluding the first population combined in step 1 (e.g., 20, 30, 40, . . . 80; 21, 31, 41, . . . 81).

Step 3. Weight the sums in steps 1 and 2 and add the results to obtain a blended population (e.g., weights 1 and 9 for the 0 digit; weights 2 and 8 for the 1 digit).

Step 4. Convert the distribution in step 3 into percentages.

Step 5. Take the deviation of each percentage in step 4 from 10.0, the expected value for each percentage.

The results in step 5 indicate the extent of concentration on or avoidance of a particular digit. The weights in step 3 represent the number of times the combination of ages in step 1 or 2 is included when the starting age is varied from 10 to 19. Note that the weights for each terminal digit would differ if the lower limit of the age range covered were different.

The method thus yields an index of preference for each terminal digit, representing the deviation, from 10.0%, of the proportion of the total population reporting ages with a given terminal digit. A summary index of preference for all terminal digits is derived as one-half the sum of the deviations from 10.0%, each taken without regard to sign. If age heaping is nonexistent, the index would approximate zero. This index is an estimate of the minimum proportion of persons in the population for whom an age with an incorrect final digit is reported. The theoretical range of Myerss index is 0, representing no heaping, to 90, which would result if all ages were reported at a single digit, say zero.

As there are more age heapings at ages ending in 0 than ending in other digits, Myer's blended method has been developed to determine the amount of heapings.

Values range from 0 to 90. If there are no age heapings, the value is zero. If there are maximum heapings, theoretically reporting all ages at a single digit only, the value is 90. In case of 2001 census, the value is 18.7 for total population in contrast to 17.4 in 1991 census.

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