The statistical relationship between human height and weight is of especial importance to clinical medicine, epidemiology, and the biology of human development. Yet, after more than a century of anthropometric measure...The statistical relationship between human height and weight is of especial importance to clinical medicine, epidemiology, and the biology of human development. Yet, after more than a century of anthropometric measurements and analyses, there has been no consensus on this relationship. The purpose of this article is to provide a definitive statistical distribution function from which all desired statistics (probabilities, moments, and correlation functions) can be determined. The statistical analysis reported in this article provides strong evidence that height and weight in a diverse population of healthy adults constitute correlated bivariate lognormal random variables. This conclusion is supported by a battery of independent tests comparing empirical values of 1) probability density patterns, 2) linear and higher order correlation coefficients, 3) statistical and hyperstatistics moments up to 6th order, and 4) distance correlation (dCor) values to corresponding theoretical quantities: 1) predicted by the lognormal distribution and 2) simulated by use of appropriate random number generators. Furthermore, calculation of the conditional expectation of weight, given height, yields a theoretical power law that specifies conditions under which body mass index (BMI) can be a valid proxy of obesity. The consistency of the empirical data from a large, diverse anthropometric survey partitioned by gender with the predictions of a correlated bivariate lognormal distribution was found to be so extensive and close as to suggest that this outcome is not coincidental or approximate, but may be a consequence of some underlying biophysical mechanism.展开更多
The purpose of the study was to evaluate the BMI （body-mass index） and NAR （nutrient adequacy ratio） of intercollegiate and all India Interuniversity male volleyball players. The players who had reached the semi-f...The purpose of the study was to evaluate the BMI （body-mass index） and NAR （nutrient adequacy ratio） of intercollegiate and all India Interuniversity male volleyball players. The players who had reached the semi-final level in their respective tournaments were selected at both intercollegiate （N = 48） and interuniversity level （N = 48）. The BMI was computed using the standard formula weight in kg/height （in m） squared. The NAR was derived by 3-day dietary recall. In the case of BMI both the interuniversity level and intercollegiate level male volleyball players are observed to be normal and also there is no significant difference in their BMI scores. On comparing the NAR, it was observed that none of the players were consuming adequate RDA （recommended dietary allowances） as per the levels recommended by national institute of nutrition for volleyball players. The all India interuniversity players had a higher NAR for energy （0.89）, protein （1.05）, fat （0.76） and carbohydrate （0.91） than intercollegiate players who had a lower NAR for energy （0.64）, protein （0.71）, fat （0.58） and carbohydrates （0.66）, which could be probably due to the fact that training strategies and nutritional intervention of players are more focused at interuniversity level as compared to intercollegiate level.展开更多
文摘The statistical relationship between human height and weight is of especial importance to clinical medicine, epidemiology, and the biology of human development. Yet, after more than a century of anthropometric measurements and analyses, there has been no consensus on this relationship. The purpose of this article is to provide a definitive statistical distribution function from which all desired statistics (probabilities, moments, and correlation functions) can be determined. The statistical analysis reported in this article provides strong evidence that height and weight in a diverse population of healthy adults constitute correlated bivariate lognormal random variables. This conclusion is supported by a battery of independent tests comparing empirical values of 1) probability density patterns, 2) linear and higher order correlation coefficients, 3) statistical and hyperstatistics moments up to 6th order, and 4) distance correlation (dCor) values to corresponding theoretical quantities: 1) predicted by the lognormal distribution and 2) simulated by use of appropriate random number generators. Furthermore, calculation of the conditional expectation of weight, given height, yields a theoretical power law that specifies conditions under which body mass index (BMI) can be a valid proxy of obesity. The consistency of the empirical data from a large, diverse anthropometric survey partitioned by gender with the predictions of a correlated bivariate lognormal distribution was found to be so extensive and close as to suggest that this outcome is not coincidental or approximate, but may be a consequence of some underlying biophysical mechanism.
文摘The purpose of the study was to evaluate the BMI （body-mass index） and NAR （nutrient adequacy ratio） of intercollegiate and all India Interuniversity male volleyball players. The players who had reached the semi-final level in their respective tournaments were selected at both intercollegiate （N = 48） and interuniversity level （N = 48）. The BMI was computed using the standard formula weight in kg/height （in m） squared. The NAR was derived by 3-day dietary recall. In the case of BMI both the interuniversity level and intercollegiate level male volleyball players are observed to be normal and also there is no significant difference in their BMI scores. On comparing the NAR, it was observed that none of the players were consuming adequate RDA （recommended dietary allowances） as per the levels recommended by national institute of nutrition for volleyball players. The all India interuniversity players had a higher NAR for energy （0.89）, protein （1.05）, fat （0.76） and carbohydrate （0.91） than intercollegiate players who had a lower NAR for energy （0.64）, protein （0.71）, fat （0.58） and carbohydrates （0.66）, which could be probably due to the fact that training strategies and nutritional intervention of players are more focused at interuniversity level as compared to intercollegiate level.
