Age, Time, and Fertility: Applications of Exploratory Data by Mary B. Breckenridge

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By Mary B. Breckenridge

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The number of large positive outliers at all age cuts except 44/45 and the pronounced asymmetry in the spread of the interquartile range of rates around the median rate at age cut 29/30 are clues to variability that remains to be described. 9798 This would result in period-independent age-cut effects and produce a set of residual rates with greatly reduced variability (Fig. 6). 9913 Fig. 3 Schematic plots of cumulated overall fertility rates by age cut for S w e d e n from 1751-1755 to 1966-1970.

Exploratory D a t a A n a l y s i s — T h e P h i l o s o p h y and t h e T o o l s 33 Least squares estimates of fit are taken as the departure point for the EHR procedures. Because ordinary least squares fitting gives equal weight to all residuals, it gives undue influence to extreme outliers that occur in data sets containing unusual observations or sizable errors. It often fails, therefore, to provide the best description of the bulk of the data. To downgrade the effect of outlying observations and provide better estimates, weighted least squares procedures rely on a priori assignment of a set of fixed weights that reflect judgments about the reliability of individual observations.

4. Total fertility rate is 5 2]=ifi(aj) in this case because w e are using rates for 5-year age groups. 5. A related procedure, trimmed mean polish, w a s used by Page (1977) in her investigation of the effects o f marriage duration o n marital fertility patterns. Instead of the median, the mean of the central two-thirds of a distribution w a s used in the s u c c e s s i v e approximations (see N o t e 6). 6. The E H R procedures also differ from these "polishing" procedures in another important regard—the weighting of the residuals in the iterative fitting procedure.

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