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Appendix: Calculation of linear and quadratic contrasts

The following formulae were used to calculate the contrasts (L) and their variance (V) and confidence intervals (Cl) [22] used in estimating secular trends in the length of the three-year-old Guatemalan children studied:

where

c = coefficients (see below)
X = mean length at three years of age
n = sample size
i = time of measurement (= 7)
s² = estimated variance

The coefficients were obtained by the method proposed by Robson [15] for the construction of polynomials for unequally spaced data (table A1).

TABLE A1. Coefficients for linear and quadratic contrasts

As an example of the use of the methodology, we show the calculation of the linear contrast and its confidence interval for the atole group. Table A2 gives the calculation of the summations and . From this:

Then, using s² = 19.78,

and

Cl = 0.61

Thus, the contrast = 1.85 ± 0.61 (1.24, 2.46).

TABLE A2. Calculation of and

	ciXi	ci2/ni
1968	85.14 x -0.435801	-0.43582/196
1969-70	85.53 x -0.311286	-0.31132/82
1971-72	86.58 x -0.186772	-0.18682/100
1973-74	86.09 x -0.062257	-0.06222/117
1975-76	86.86 x +0.062257	0.06222/117
1977	86.55 x +0.124515	0.12452/35
1988-89	87.62 x +0.809345	0.80932/344
	1.85	0.0049

Acknowledgements

Data collection and analyses were supported by NIH grant HD22440. The study was a collaborative effort involving investigators at several institutions: R. Martorell (principal investigator, originally at Stanford University, now at Cornell University), J. Rivera (INCAP, Guatemala), E. Pollitt (University of California at Davis), and J. Haas (Cornell University).

References

1. Tanner JM. The secular trend towards earlier physical maturation. T Soc Geneesk 1966;44:524-39.
2. Van Wieringen JC. Secular growth changes. In: Falkner F. Tanner JM, eds. Human growth: a comprehensive treatise. 2nd ed. Vol 3. Postnatal growth. New York: Plenum Press, 1978:307-31.
3. Himes JH, Mueller WH. Aging and secular change in adult stature in rural Colombia. Am J Phys Anthro 1917;46:275-79.
4. Himes JH, Malina RM. Age and secular factors in the stature of adult Zapotec males. Am J Phys Anthro 1975;43:367-69.
5. Malina RM, Buschang PH, Aronson WL, Selby HA. Aging in selected anthropometric dimensions in a rural Zapotec-speaking community in the valley of Oaxaca, Mexico. Soc Sci Med 1982;16:217-22.
6. Eveleth PB, Salzano FM, de Lima PE. Child growth and adult physique in Brazilian Xingu Indians. Am J Phys Anthro 1974;41:95-102.
7. Miall WE, Ashcroft MT, Lovell HG, Moore F. A longitudinal study of the decline of adult height with age in two Welsh communities. Hum Biol 1967;39:445-54.
8. Cline MG, Meredith KE, Boyer JT, Burrows B. Decline of height with age in adults in a general population sample: estimating maximum height and distinguishing birth cohort effects from actual loss of stature with aging. Hum Biol 1989;61:415-25.
9. Chumlea WMC, Garry PJ, Hunt WC, Rhyne RL. Distributions of serial changes in stature and weight in a healthy elderly population. Hum Biol 1988;60:917-25.
10. Hertzog KP, Garn SM, Hempy HO. Partitioning the effects of secular trend and aging in adult stature. Am J Phys Anthro 1969;31:111-15.
11. Klein RE, Habicht JP, Yarbrough C. Some methodological problems in field studies of nutrition and intelligence. In: Kallen DJ, ed. Nutrition, development and social behavior: proceedings of the conference on the assessment of tests of bebavior from studies on nutrition in the western hemisphere. Washington, DC: Government Printing Office, 1973:61-73.
12. Rivera J. Martorell R. Habicht JP, Ruel MT, Haas J. Long-term effects of supplementary feeding in early childhood on body size and composition. J Nutr (in press).
13. Relethford JH, Lees FC. The effects of aging and secular trend on adult stature in rural western Ireland. Am J Phys Anthro 1981;55:81-88.
14. Draper NR, Smith H. Applied regression analysis. 2nd ed. Wiley Series in Probability and Mathematical Statistics. New York: John Wiley, 1981.
15. Robson D. A simple method for constructing orthogonal polynomials when the independent variable is unequally spaced. Biometrics 1959;15:187-91.
16. Borkan GA, Hults DE, Glynn RJ. Role of longitudinal change and secular trend in age differences in male body dimensions. Hum Biol 1983;55:629-41.
17. Himes JH, Mueller WH. Age-associated statural loss and socioeconomic status. J Am Geriatr Soc 1977;25: 171-74.
18. Galloway A. Estimating actual height in the older individual. J Forensic Sci 1988;33:126-36.
19. Bergeron G. Social and economic development in four Ladino communities of eastern Guatemala: a comparative description. Food Nutr Bull 1992;14(3):221-36.
20. Hamill PVV, Drizd TA, Johnson CL, Reed RB, Roche AF, Moore WM. Physical growth: National Center for Health Statistics percentiles. Am J Clin Nutr 1979; 32:607-97.
21. World Health Organization. Energy and protein requirements. Geneva: WHO, 1985.
22. J. Wasserman W. Kutner MH. Applied linear statistical models: regression, analysis of variance, and experimental design. 2nd ed. Homewood, Ill, USA: Irwin, 1985.

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