Demography Is the Scientific Study of Human Population

Population and Demographic Data Lecture - 22 Measurement of Age and Digit Preference

 Homework: Today’s Topics:  What do you mean by Zero Error?  Age Heaping  Write short notes on different types of digit preference.  Digit preference   Whipple’s Index  Myers’s Blended Method

Important Points:

Summary After the lecture, use this space to summarize the main points of this Lecture Topic.    Measurement of Age and Digit numeral 3 because it sounds like the Preference word or character for life. In some cultures certain numbers and digits are In the analysis of single years of age data, if avoided, e.g., 13 is frequently avoided in there are no irregularities, the counts for the West because it is considered adjacent ages should be similar. Examples of irregularities are digit preference and unlucky. The numeral 4 is avoided in avoidance. Korea and in China because it has the  The tendency of enumerators or same sound as the word or character for respondents to report certain ages at the death. expense of others is called age heaping,  Age heaping and digit preference may be age preference, or digit preference. ascertained more precisely with indices. Age Heaping, if a population tends to report Indices of digit preference assume that certain ages (say, those ending in 0 or 5) at the true figures are rectangularly the expense of other ages, this is known as distributed over an n-year age range that age heaping. is centered on the specific age being  Age heaping is most pronounced among examined. If the index equals 100, there populations or population subgroups is no age heaping on the age being having a low educational status. examined. The greater the value above Digit preference, an analogous concept, 100, the greater the concentration on this carries the added feature of respondents age. The lower the value from 100, the having a preference for various ages having greater the avoidance of the age being the same terminal digit. examined.  The causes and patterns of age or digit Heaping, i.e., digit preference, or the lack of preference vary from one culture to heaping, i.e., digit avoidance, are the major culture, but preference for ages ending in forms of error typically found in single- ‘0’ and in ‘5’ is quite widespread, year-of-age data. Irregularities in reporting especially in the Western world. In single years of age can be detected using Korea, China, and some other countries graphs and indices. Both will be considered. in East Asia, there is sometimes a Digit avoidance refers to the opposite. preference for ages ending in the 2 Whipple’s Index and old age are often excluded because they are more strongly affected by other types of Indexes have been developed to reflect errors of reporting than by preference for preference for or avoidance of a particular specific terminal digits and the assumption terminal digit or of each terminal digit. For of equal decrements from age to age is less example, employing again the assumption applicable. of rectangularity in a 10-year range, we may measure heaping on terminal digit “0” in the The procedure described can be extended range 23 to 62 very roughly by comparing theoretically to provide an index for each the sum of the populations at the ages terminal digit (0, 1, 2, etc.). The population ending in “0” in this range with one-tenth of ending in each digit over a given range, say the total population in the range: 23 to 82, or 10 to 89, may be compared with one-tenth of the total population in the  P30  P40  P50  P60  100 1 P  P  P  ...... P  P  P range, as was done for digit “0” earlier, or it 10   23 24 25 60 61 62  Similarly, employing either the assumption may be expressed as a percentage of the of rectangularity or of linearity in a 5-year total population in the range. In the latter range, we may measure heaping on case, an index of 10% is supposed to multiples of five (terminal digits “0” and indicate an unbiased distribution of terminal “5” combined) in the range 23 to 62 by digits and, hence, presumably accurate comparing the sum of the populations at the reporting of age. Indexes in excess of 10% ages in this range ending in “0” or “5” and indicate a tendency toward preference for a one-fifth of the total population in the range: particular digit, and indexes below 10% indicate a tendency toward avoidance of a  P25  P30  ...... P55  P60  100 particular digit. 1 P  P  P  ...... P  P  P 5   23 24 25 60 61 62   62 The tendency of respondents or  Pa  ending in  0 or 5 23 enumerators to report particular ages are 62 1 P 5  a known as age heapings. Age heapings 23 are usually found at ages ending in 0 and The choice of the range 23 to 62 is largely 5. The whipple's index has been 174 arbitrary (or arbitrary one). In computing developed to determine the amount of indexes of heaping, the ages of childhood age heapings. If there are no age 3 heapings at ages ending in 0 and 5, the population ending in a given digit is of the whipple's index is 100. If only digits 0 total population 10 times, by varying the and 5 are reported, then index is 500. particular starting age for any 10-year age The whipple's index for the total group. population of Nepal is 206.1 indicating The abbreviated (or shortened) procedure of that the population tabulated at these calculation calls for the following steps: ages is more by 106 percent than the Step 1. Sum the populations ending in each corresponding unbiased population. In digit over the whole range, starting with the fact, the quality of data is very rough. lower limit of the range (e.g., 10, 20, 30, . . . According to UN scale, the quality of 80; 11, 21, 31, . . . 81). data is very rough if the value is 175 or Step 2. Ascertain the sum excluding the first more. population combined in step 1 (e.g., 20, 30,  The values of whipple's index for males 40, . . . 80; 21, 31, 41, . . . 81). and females are 205.7 and 206.6 Step 3. Weight the sums in steps 1 and 2 respectively indicating that quality of and add the results to obtain a blended data are very rough for both sexes population (e.g., weights 1 and 9 for the 0 though it is a little bit better for males digit; weights 2 and 8 for the 1 digit). than for females. Step 4. Convert the distribution in step 3 Myers’s Blended Method into percentages. Myers (1940) developed a “blended” Step 5. Take the deviation of each method to avoid the bias in indexes percentage in step 4 from 10.0, the expected computed in the way just described that is value for each percentage. due to the fact that numbers ending in “0” The results in step 5 indicate the extent of would normally be larger than the following concentration on or avoidance of a numbers ending in “1” to “9” because of the particular digit. The weights in step 3 effect of mortality. The principle employed represent the number of times the is to begin the count at each of the 10 digits combination of ages in step 1 or 2 is in turn and then to average the results. included when the starting age is varied Specifically, the method involves from 10 to 19. Note that the weights for determining the proportion that the each terminal digit would differ if the lower

4 limit of the age range covered were the value is 18.7 for total population in different. contrast to 17.4 in 1991 census. 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 Myers’s 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,