However, differences Mindful eating benefits Insulin delivery options for elderly patients between corrected Wegiht prevalence and true obesity prevalence. Throughout corelation paper computer simulation of correlated random variables RVs has been employed for both analytical and graphical comparisons with corresponding empirical results. Unweighted kappa, therefore, is inappropriate for ordinal scales of the present study[ 41 ].

The statistical relationship between human height and weight is of especial importance to clinical medicine, epidemiology, Weigbt the biology of human development. Yet, after more correlatioj a century Elderberry tea benefits anthropometric measurements and analyses, there Recovery resources and information been no consensus on this relationship.

The purpose codrelation this article is to provide nad definitive statistical distribution function from Hyperglycemia and eye complications all desired statistics probabilities, heigh, and correlation functions can be determined. The statistical analysis reported Weihgt this article provides strong evidence correlayion height and weight in a diverse cofrelation of healthy adults constitute correlated bivariate lognormal Weeight variables.

This conclusion is supported by a heignt of independent Weight and height correlation comparing empirical values of 1 probability hegiht patterns, 2 linear and higher order correlation coefficients, 3 statistical and hyperstatistics moments up to 6th order, Weightt 4 distance correlstion dCor values to corresponding theoretical quantities: 1 predicted by the lognormal distribution and 2 Heiht by use of appropriate heightt number generators.

Furthermore, calculation of the conditional expectation of weight, given height, yields a theoretical power law that corre,ation conditions under which body mass Insulin delivery options for elderly patients BMI can Green tea liver health a valid proxy of obesity.

Correlatuon consistency of the empirical data from a vorrelation, diverse eWight survey partitioned by gender with the predictions of a correlated bivariate lognormal Wdight was found to be so correkation and close as to suggest that this outcome is not coincidental or approximate, heighr may be a consequence of Wejght underlying biophysical mechanism.

Correlation of Height and WeightDistribution of Height and WeightBody Mass IndexAnti-arthritic lifestyle choices DistributionDistance Correlation dCorHyperstatistics. Scientific interest in ane values and correlations of heigjt data trace back to the beginnings of modern statistics heoght the late 19th anv early 20th Centuries with the researches of Quetelet, Galton, Pearson, coreelation others correlatiob [2] [3].

These many studies established the Gaussian function as the mathematical correlatlon best approximating the distribution of such human features as height, weight, and other biometric attributes.

Although more anf studies WWeight revealed that anthropometric hsight can heigbt deviations from normality, attempts to cordelation relationships between human Free radicals and male infertility and weight remained uncertain, controversial and based on approximate or indirect methods such as data fitting heeight, mechanical modeling [6], and gene identification [7].

A previous paper by Silverman and Lipscombe cordelation, to corre,ation referred to as Correlatin I, determined the mathematically exact statistical distribution of BMI.

The present paper, to be regarded as Part Athlete nutrition tips, provides evidence for the proposition that, in codrelation healthy adult human heibht with access to Weight and height correlation nutrition, height anf weight are distributed as correlated bivariate lognormal cortelation variables.

This conclusion is supported by a comprehensive investigation Weoght four independent components:. The outcome of this four-part analysis Wieght that linear and higher-order Weught of human height and weight are Weight and height correlation in terms of the single Corrslation correlation coefficient for height and weight employed in Summer detox diets lognormal probability density function PDF.

Moreover, agreement between the empirical data and the predictions Weight and height correlation lognormal theory is so extensive as to suggest that the heightt distribution of adult human height Promote a sense of well-being weight is not heignt, but Insulin delivery options for elderly patients exact distribution possibly characteristic of a Weigh fundamental underlying biophysical mechanism.

Part I [11] reported the Wight probability density function of BMI that Weifht mathematically from the defining relation. It is to be stressed that HWand therefore Bare random variables, which means that information abd interpretations extrapolated from the BMI PDF refer to populationsehight not to individuals, an essential Insulin delivery options for elderly patients not always understood by the ckrrelation news media [11] [14].

The an form hieght the general Wegiht density function takes depends on the statistical distributions of H and W.

Such empirical distributions adn often represented visually as histograms. Refreshment Barista Services, if two random variables are not independent, then correation histogram of each Weighg a graphical representation of the marginal distribution of that variable, and provides Food allergy awareness information regarding the correlation of the two variables.

In Part I evidence was provided to show that height and weight of individuals measured in the Heigght Survey of U. Hdight Personnel ANSUR —a large data base comprising males and females [15] —were Herbal energy support correlated.

Figure heighf shows scatter plots of W Self-sanitizing surfaces H for Weihgt separate male and Liver detox for natural healing cohorts.

The two patterns suggest a significant linear correlation. The superposed curves, to be discussed later, are the lines of regression dashed red and anv conditional expectation functions solid blue. Descriptive statistics are given in Table 1 for the two cohorts, together with theoretically predicted values, where appropriate.

Details of Table 1 will be discussed at relevant points throughout the paper. Figure 1. Correlation of weight and height for males left and females right of the ANSUR population.

Lines of regression dashed red are obtained by the method of least squares. The conditional expectation functions of weight given height solid blue are calculated from the lognormal PDF 17using ANSUR parameters in Table 1. Table 1. Descriptive statistics of height and weight of ANSUR population.

As a matter of standard notation used in this paper, random variables are represented by upper case letters e. Xand realizations of that variable referred to as variates are represented by lower case letters e.

Histograms of the natural logarithms of the ANSUR heights and weights, partitioned by gender, were shown in Part I to be satisfactorily described by PDFs of Gaussian form. A more detailed demonstration of the normality of ln H and ln W will be given in Section 6.

From relations 2 and 3 follow the parent lognormal PDFs. with location parameters m Hm W and scale parameters and s Hs W for height and weight, respectively. Numerical values of these parameters are given in Table 1. Superscripts N and Λ in the above PDFs signify normal and lognormal distributions, as well as symbolize the associated random variables RVs.

Note that parameters ms 2 defining the random variables Y and X are the mean and variance of the normal variable Y. All statistics of the marginal distribution of X are predictable in terms of the parameters ms 2 of Y [11] [16].

For example, the mean μ Xvariance σ X 2skewness S k Xand kurtosis K X of X take the forms [17]. When analyzing lognormal variates, it is often strategically easier—indeed necessary—to work with the logarithms of the variates, since these are distributed normally. The scaled variables UV.

with variates uv are measured with respect to their means and divided by their standard deviations, and are therefore dimensionless quantities distributed as standard normal variables of mean 0 and variance 1 if the variables HW are lognormal.

Figure 2 likewise clearly shows a strong linear correlation of U and V. The slope of the line of regression dashed red in each black scatter plot directly yields the corresponding Pearson correlation coefficient r [11] defined by.

Figure 2. Correlation of scaled log weight and scaled log height for males top left and females top right of the ANSUR population.

Lower panels show corresponding scatter plots created with correlated lognormal random number generators using the same empirical parameters. The patterns display a strong linear correlation. The Pearson correlation coefficient is equal to the slope of the associated lines of regression dashed.

where cov signifies covariance, as defined in Equation Angular brackets are used in this paper to indicate expectation values. The scatter plots in red in Figure 2 were obtained by computer simulation using correlated lognormal RNGs, the details of which will be discussed in a later section.

Suffice it to say at this point that the computer simulations employed the same distribution parameters that were extracted from the ANSUR height and weight data and are labeled m Hm Ws Hs Wr for both male and female cohorts in Table 1.

Lines of regression dashed blue to the simulated scatter plots are nearly identical to those of the empirical plots. and compared with the empirical correlation coefficient obtained directly from the data according to.

in analogy to Equation The implementation of Equation 14 can be achieved algebraically and geometrically:. Five parameters m 1m 2s 1s 2r are required to specify the PDF of two correlated bivariate normal RVs Y 1Y 2.

from which is derived the PDF of the parent bivariate lognormal RVs X 1X 2 [11]. Double superscripts N and Λ signify that both variables are normal in PDF 16 and lognormal in PDF The expectation operations in Equation 12 and Equation 14 are performed respectively with PDF 16 and PDF If, as proposed in this paper, H and W are correlated bivariate lognormal variables, then all measurable statistical information concerning adult human height, weight, and their correlations, should be predictable from their joint distribution Equation 17 in terms of the five parameters 2 means, 2 variances, and 1 Pearson correlation that define a given population.

This statement has important implications for the study of obesity and its associated illnesses. The BMI 1 was introduced by Quetelet in [18] and has been widely used up to present times by clinicians and epidemiologists as a proxy for obesity under the assumption that it correlates strongly with weight, but is independent of height.

These assumptions will be examined later in this paper both empirically and theoretically. It is to be noted at this point, however, that both assumptions have elicited criticism, e. With regard to the goal of capturing the relationship between height and weight, the following general statistical principles must be emphasized.

First, an exact PDF of the bivariate distribution of two correlated random variables provides all the statistical information that can be learned about these two correlated variables. And second, there is no single optimal mathematical expression—apart from the PDF and its equivalent transformations 1 —that completely captures the statistical relation between two correlated random variables.

Rather, the PDF provides a potentially infinite number of mathematical expressions that, togethercharacterize the complete relation between the two variables. From a practical standpoint, however, the number of testable expressions that can meaningfully characterize the correlation of two variables is limited by the size of the sample, since the intrinsic uncertainty increases with the order i.

power of the variables, and can eventually exceed the mean value for a fixed sample size. These points will be elaborated on in the following sections.

In Section 2 the relation between weight W and height H is examined by means of the conditional expectation functions of Wgiven H. In Section 3 the proposition that human height and weight are correlated lognormal variables is tested by examining generalized correlation functions of data sets HW and ln Hln W.

In Section 4 the preceding data sets are each examined for nonlinear correlations beyond those attributable to the bivariate lognormal distribution by a procedure known as distance correlation. In Section 5 the marginal distributions of HW and ln Hln W are tested against predictions of the univariate lognormal and normal distributions, respectively.

Section 6 examines the implications of the distribution of HW for the body mass index. And last, the results of this comprehensive investigation are summarized and interpreted in Section 8. is a function W p h of the continuous variate of H.

Since W p h derives from the joint PDF of W and Hit is more informative than an empirical line of regression such as obtained by the method of least squares or, more generally, the method of maximum likelihood [27].

Calculation of W p h in Equation 18 requires evaluation of two integrals whose kernel is the PDF p HW ΛΛ hw given by Equation as a function of u. Both integrals in 21 are readily evaluated in closed form. Substituting in Equations 23 and 26 the bivariant lognormal parameters for each gender cohort of the ANSUR sample listed in Table 1 leads to the expressions.

Plots of the conditional expectations W 1 h in Equation 27 comprise the solid blue curves superposed on the scatter plots in Figure 1. Although W 1 h is a power law and the line of regression dashed red is linear, the two curves are virtually indistinguishable over the densest part of the plots.

Figure 3 graphically displays the full information content of relation 27 by displaying the regions of ±1 standard deviation about the means for the two cohorts. The numerical values of the exponents in relations 27 bear out the fundamental assumption underlying the use of BMI that weight is a quadratic function of height in a healthy adult population.

Nevertheless, for a different set of values of the parameters s Hs Wrsuch as may characterize a demographic different from the one represented by the ANSUR population, the lognormal predicted exponent could be different.

Tests of Correlation Functions of Height H and Weight W. Correlation functions of order pqdefined as follows. Figure 3.

: Weight and height correlation

Content Preview	Nevertheless, for a different set of values of the parameters s H , s W , r , such as may characterize a demographic different from the one represented by the ANSUR population, the lognormal predicted exponent could be different. Tests of Correlation Functions of Height H and Weight W. Correlation functions of order p , q , defined as follows. Figure 3. Plots of the conditional expectation W 1 h for male solid blue line and female solid red line of the ANSUR populations centered on regions blue for males, red for females of ±1 standard deviation σ W h. The region of overlap appears purple. Expectations 28 and 29 are to be implemented with the bivariate lognormal PDF 17 where indices p , q independently take on integer values 1, 2, …. If the proposition that H , W are bivariate lognormal variables is valid, then c p , q and r p , q should be predictable from the arguments shown in Equations 28 and 29 and the parameters s H , s W , r listed by gender in Table 1. It is to be recalled that the first two parameters standard deviations were obtained empirically from the variates of the marginal distributions ln H and ln W of the ANSUR populations, whereas the third parameter Pearson correlation coefficient was obtained empirically from the joint distribution of ln H and ln W , such as exhibited in Figure 2. The associated sets of means m H , m W , which are also listed by gender in Table 1 , drop out of relations 28 and 29 by virtue of their expressions as ratios. Further details are given in Part I [11]. To facilitate reading the tables to follow, indices of the correlation functions and coefficients will be expressed as arguments, e. Calculation of the correlation functions C p , q and R p , q requires evaluation of the expectation values. Substitution for the means μ H , μ W and standard deviations σ H , σ W by use of Equations 7 and 8 then leads to the operational expressions. Symmetries 2 and 3 do not necessarily hold for C p , q. Calculation and Measurement of Correlation Functions R p , q. Because the correlation of U and V is determined entirely by the parameter r in the probability density f u , v , it is useful to examine the structure of f u , v graphically. The right panels view the underside of the density plots, or, equivalently, the projection of the plots onto the u , v plane. The two numbers in each scatter plot are close, but not identical because the scatter plot comprises a finite random sample. The connection between the PDF f U , V u , v and the scatterplot of U , V for each value of r is particularly clear when one compares the right side panels of Figure 4 to the corresponding plots of Figure 5. The orientations of the two sets of figures may be different, but the distributions are invariant to orientation. Correlation function R p , q r expressed in Equation 33 can be evaluated in closed form, and depends only on the Pearson coefficient r. Table 2 lists the first six orders of the symmetric correlation functions and the most pertinent of the asymmetric correlation functions. It is seen that beyond the basic covariance 12 , the higher-order symmetric correlations are increasingly nonlinear in r. Asymmetric correlation functions of the form R p , 1 in Table 2 , where p is the exponent of the scaled variable for ln H , address the issue referred to in the. Figure 4. Right Panels: Profiles as viewed from the underside of the associated density plots. The patterns are the smooth shapes of scatter plots of discrete samples in the limit of infinite sample size. Figure 5. Simulated scatter plots of correlated pairs of standard normal variates with correlation coefficients increasing from 0 to nearly 1. Table 2. Correlation functions R p , q of powers of standard normal variables: U p and V q. Introduction concerning how weight correlates with powers of height. Also listed are asymmetric correlation functions characterizing how powers of weight correlate with powers of height. Although the Pearson correlation coefficient r is the expectation value of a composite random variable UV , it is regarded here as a nondistributed quantity since the values of r for male and female cohorts used throughout this paper are fixed parameters extracted from the ANSUR data. The same is true of the means m H , m W and variances s H 2 , s W 2 for the male and female cohorts. The variance of the correlation coefficient r p , q therefore characterizes only the variation of the product U p V q in the defining integral and can be expressed by [28]. It then follows that the standard error se of r p , q takes the form. where n is the sample size. By the same reasoning, the standard error of the correlation coefficient c p , q is. since c p , q likewise depends on the fixed ANSUR parameters. In general, however, the distribution function and moments of even the lowest correlation coefficient r 1 , 1 are difficult to obtain in closed form [29], and, at the time of writing, the author knows of no calculation in the literature of the exact closed-form distribution functions and moments of higher-order correlation coefficients of two normal or two lognormal variables. For other correlation orders, the corresponding standard errors were too large relative to the means for a comparison of theory and experiment to be meaningful. Examination of Table 3 shows striking agreement between lognormal theory and the ANSUR data. For all but two correlation coefficients of the female cohort listed in the table, the magnitude of the difference between theoretical thy and empirical emp coefficients did not exceed 1 standard error. In other words, assuming, as justified by the Central Limit Theorem [30], that the relative error. The relative errors of the two exceptional coefficients r 3 , 2 and r 4 , 3 were approximately 1. Table 3. Correlation coefficients r p , q of Scaled ln H p and Scaled ln W q. Exceptions occurred primarily among the higher orders of the asymmetric odd coefficients whose theoretical means were zero and standard errors large. Under such circumstances, large deviations are to be expected and would require a larger sample size for resolution. Moreover, expressions 35 and 36 give lower limits for the standard errors since, in accordance with stated assumptions, they do not take account of the variation in lognormal parameters. It is therefore likely that a more exact estimate of the relative errors would be lower than those listed in Table 3. In summary, to appreciate how extensive and close is the agreement of the theoretical and empirical correlations displayed in Table 3 , one must bear in mind the following context. Theoretical predictions of r p , q were obtained from the bivariate normal distribution of ln H and ln W ; empirical values of r p , q were obtained from the natural logarithms of the raw ANSUR sample. If adult heights and weights were not distributed lognormally, then the comprehensive correspondence by pure chance , especially in the female cohort, of these two sets of numbers would be extremely improbable. For example, if either or both of the attributes of height and weight were themselves normally distributed, as had long been assumed, the logarithm of the variates would depart significantly from a normal distribution, as was demonstrated in Part I [11]. Nevertheless, the results in Table 3 raise a curious question. Why does the female cohort appear to bear out the predictions of lognormal theory more closely than the male cohort despite the fact that the number of men sampled is about twice that of women? As discussed in Part I [11], the Anthropometric Survey of U. The survey measured more than 90 human attributes directly and compiled data demographically in terms of race, ethnicity, gender, age, and geographic location. For the analyses in this paper and in Part I, the data were partitioned by gender only. Therefore, both the male and female cohorts can be regarded as diverse samples of fundamentally healthy adults. However, since there are considerably fewer women in the U. Army than men, it is conceivable that, irrespective of other demographic characteristics, the women who joined the U. Army and took part in the ANSUR sample formed a more homogeneous group in regard to body type and physical fitness than the men. Such an explanation would seem likely, since there is no biophysical basis to believe that male height and weight would be statistically distributed by a probability function of different mathematical form than female height and weight. Density Plots Associated with Correlation Functions R p , q. Whereas the correlation coefficients r p , q are single numbers quantifying the correlation of U p and V q i. powers of the scaled variables of ln H and ln W for a specified sample, the actual scatter plots of the two sets of variates yield a more comprehensive visual perspective of their correlation. The patterns for the female cohort are similar, although less dense sample size and not shown. The correlations expressed in Figure 6 are highly nonlinear in two ways. And algebraically, the associated theoretical correlation function is of order r p in the Pearson correlation parameter, as summarized in Table 2. The four plots in Figure 6 illustrate the characteristic property that, with increasing order p , the density of points clusters. Figure 6. Patterns show a highly nonlinear correlation of weight and height. U is the scaled variable for ln H ; V is the scaled variable for ln W. more tightly about the coordinate axes. Fluctuations for even p extend primarily into the first quadrant since both variates are positive. The empirical patterns and properties in Figure 6 are reproduced nearly identically apart from random fluctuations in the computer simulated patterns shown in Figure 7. The simulations were created by means of correlated lognormal RNGs using the ANSUR lognormal parameters in Table 1. The reproduction of empirical correlation scatter plots and correlation coefficients by computer simulation extends as well to asymmetric even and odd correlation functions, as displayed in Figure 8 for the pairs of variables U 2 , V , U 3 , V , and U 3 , V 2. Plots in black are empirical; those in red are simulated for a population of corresponding size. Altogether, these results support the conclusion that the nonlinear correlations of height and weight stem exclusively from the properties of the lognormal distribution function and depend on no correlation parameters other than the Pearson coefficient r. Probability density functions for the correlated powers U p , V q , which yield. Figure 7. The shapes of the patterns and extent of fluctuations closely resemble the corresponding empirical plots in Figure 6. Figure 8. the patterns approached by scatter plots in Figures in the limit of infinite sample size, can be constructed by means of the Dirac delta function as follows. Powers of standard normal variables like U , V do not, in general, follow known, named distributions to which variables X and Y can be assigned [32]. A brief recapitulation of the properties and identities of the Dirac delta function is given in Part I [11] and in mathematical physics books [33]. Left-side panels show the density. Figure 9. Right panel: View from the underside highlights the profile to which the scatter plot of V 2 against U 2 in the top left of Figure 6 approches in the limit of infinite sample size. Figure Right panel: View from the underside shows the profile approached by the scatter plot of V 3 against U 3 in the top right of Figure 6 in the limit of infinite sample size. patterns from above the u p , v p plane; right-side panels give complementary images from below. The function f X , Y 2 u 2 , v 2 in Figure 9 shows a concentration of probability along the vertical axis with density decreasing with distance into the first quadrant, as shown empirically in Figure 7 top left. Calculation and Measurement of Correlation Functions C p , q. C p , q s H , s W , r in Equation 32 expresses the correlation of height and weight directly, rather than of their logarithms. The integral in Equation 32 can be evaluated in closed form of which the lowest orders pertinent to this paper are given in Table 4 for two arbitrary, but correlated, lognormal variables X 1 and X 2 with bivariate parameter set m 1 , m 2 , s 1 , s 2 , r. Substitution of the ANSUR parameters of Table 1 for male and female cohorts into the functions of Table 4 and variance of Equation 36 yield the corresponding empirical correlation coefficients summarized in Table 5. Agreement of the empirical values with lognormal theory is again excellent, apart from the highest orders where the standard errors are large relative to the means and signify that a larger sample size is required. If adult human height and weight are bivariate lognormal variables, then all measures of their correlation must be calculable from the PDF Evidence for the proposition of bivariate lognormality has been supported up to this point by the agreement of measured and lognormally predicted correlation coefficients and comparison of empirical and lognormally simulated probability density plots. The question remains, however, as to whether there may be nonlinear correlations beyond those intrinsic to the bivariate lognormal distribution. Correlation of distances [12], provides a sensitive method for testing the independence of random vectors. As initially presented by its developers, the term distance covariance dCov of two random vectors X and Y , defined by. Table 4. Table 5. Correlation coefficients c p , q of Scaled H p and Scaled W q. As indicated in Equations 39 and 40 , the CF g Z is the Fourier transform of the corresponding probability density f Z of some specific random variable or set of random variables Z. The actual evaluation of V X , Y in Equation 38 , together with its properties and associated theorems, is given in Ref. The distance correlation dCor , expressed by R X , Y , is then defined in terms of dCov and dVar by the relation. Equation 41 resembles in form Equation 12 or Equation 14 for the Pearson correlation coefficient, but its properties are significantly different, as well as its empirical evaluation. The author is unaware of any theoretical derivations of the probability density function or statistical moments of R X , Y. However, if X and Y are standard normal variables, then R X , Y has been evaluated in the following closed form [12]. where the superscript N , N signifies the special case of bivariate standard normality, and ρ is the associated Pearson correlation coefficient. Statistical Application of Distance Correlation dCor to Height and Weight. corresponding to Equation The statistic R n X , Y 1 ranges between 0 and 1, 2 is 0 only if X and Y are independent, and 3 approaches the theoretical dCor R X , Y in the limit of infinite sample size n [12]. In the sequence of analyses of the ANSUR data to follow, the pair of variables X , Y was taken to be the scaled sets 1 H , W , 2 ln H , ln W , and 3 ln H , ln W red. The reason for this reduction and the way it was implemented will be clarified shortly. The algorithm Equations 43 to 48 leading to Equation 49 is straightforward to implement by computer. However, for sample sizes on the order of thousands, the computation time is impractically long. To circumvent this difficulty, a sampling procedure analogous to bootstrapping [34] [35] was employed. Participants in the survey were apparently measured and recorded in random order, as shown in Figure 11 , which displays scatter plots by gender of the scaled height and weight vs participant number. Although histograms of the variates, analyzed in part I [11], are precisely matched by lognormal distributions, the point density plots in Figure 11 are well represented by uniform distributions across the entire range of participants. In other words, each vertical slice of points of sufficient width contains a statistical spread of variates equivalent to any other vertical slice of the same width. Given this uniform density, the ranges n m and n f were respectively partitioned into 20 and 10 subgroups of participants each, as shown in Figure Distance correlation of height and weight was then evaluated for 50 consecutive participants in each subgroup, starting at the participant numbers marked by diamond plotting symbols in the figure. For example, d C o r 1 was calculated from participants [ - ], d C o r 2 from partipants [ - ], and so on up to d C o r 20 from participants [ to ] for males and up to d C o r 9 from participants [ to ] for females. As with standard bootstrapping, this method of calculating dCor by repeated sampling not only circumvented what otherwise would have been an excessively long computer calculation, but it also provided a vector of dCor values from which to estimate dCor uncertainty in the absence of a known statistical distribution. The results of the analyses of distance correlation are summarized in Table 6. Section I of the table records the distance correlation of the scaled variables H and W. Particularly striking is the close agreement between the empirical values. Plots of height left panels and weight right panels of individual participants in the ANSUR sample: male cohort top panels ; female cohort bottom panels. Diamond plotting symbols mark participant numbers which begin each subgroup of 50 participants to be sampled over the range a to male cohort , b to female cohort. obtained from the ANSUR sample columns 2 and 3 for male and female cohorts, respectively and values created by computer simulation using a bivariate lognormal RNG columns 4 and 5 for the closely corresponding sample sizes and , respectively. These values. Table 6. Test of nonlinear correlations by means of distance correlation: dCor X , Y. from Table 1 correspond to the empirical Pearson correlation coefficients of the variables ln H , ln W. The empirical Pearson correlation coefficients ρ columns 2 and 3 of the variables H , W are closely matched by the corresponding values columns 4 and 5 obtained by computer simulation. In short, the dCor values of Section I are consistent with attributing the entire correlation of height and weight, including any nonlinear contributions, to the bivariate lognormal distribution. Section II of the table records distance correlation of the scaled variables ln H , ln W. Computer simulated populations of sizes approximating the male and female ANSUR cohorts were generated by use of bivariate normal RNGs. Agreement between empirical and corresponding computer simulated values is again very close, especially for the female cohort. The outcome indicates that the full correlation of ln H and ln W is attributable to the bivariate normal distribution which, in turn, derives from the parent lognormal distribution function. The distance correlation procedure tests random vectors for independence irrespective of their specific distributions, provided the first moments are finite [13]. It is a nonparametric test that can reveal correlations even when the Pearson correlation coefficient is null. However, if the Pearson correlation of two normal vectors is null, then those vectors are fully independent — i. there is no latent nonlinear correlation. Section III of the table exploits this point to ascertain whether the correlation between height and weight exhibited in Figure 1 and Figure 2 have a nonlinear contribution not attributable to the parent lognormal or derived normal distributions. The basic idea is to subtract from the ordinate of each point in the scatter plots in Figure 2 the corresponding ordinate of the line of regression. A scatter plot is then made of the reduced scaled log weight. In other words, removal of the lines of regression from the empirical scatter plots of. Scatter pattern black points and associated line of regression dashed red of zero slope signifying a null Pearson correlation of log weight and log height when the log weight variates were reduced by corresponding values of the line of regression dashed blue of the original scatter plot cyan points. scaled ln H , ln W has resulted in two normal random vectors of null Pearson correlation coefficient—and therefore presumably statistically independent. For comparison, the reduced scatterplots black points in Figure 13 are superposed on the original scatterplots cyan points of Figure 2 with their lines of regression dashed blue. The dCor values in Section III provide quantitative confirmation of the statistical independence of height and weight upon removal of the Pearson linear correlation. In the subsection A based on repeated sampling of the entire population in samples of size 50, the empirical dCor values approximately 0. The small deviations are attributable in part to the fact that the resulting Pearson correlation coefficients of the simulated populations were not precisely 0, but in the range 0. Potentially problematic is the discrepancy between the empirical as well as simulated dCor values obtained by repeated sampling and the values predicted by Equation 42 , which should be close to 0 for two independent normal random variables. However, Equation 42 is strictly valid only in the limit of an infinite population. Subsection B, based on single sampling of a much larger subpopulation of participants, shows that empirical dCor values dropped to approximately 0. Evaluation of the distance correlation of a sample of required computation times longer than 8 hours. Thus, to test rigorously whether dCor approaches 0 asymptotically as a function of sample size would require impractically long computation times. Altogether, the three sections of Table 6 consistently support the conclusion that the observed correlation between height and weight can be accounted for entirely by a bivariate lognormal distribution. In other words, the five parameters defining the bivariate lognormal distribution of height and weight suffice to predict any measureable function or test of the correlation of height and weight of a healthy adult human population. Previous sections concentrated on the bivariate lognormal correlation of height and weight. This section examines the marginal statistics of H and W , which are predicted to follow the respective univariate lognormal distributions Λ m H , s H 2 and Λ m W , s W 2 , and on ln H and ln W , which are predicted to follow the respective univariate normal distributions N m H , s H 2 and N m W , s W 2 as discussed in Section 1. Table 7 summarizes the outcomes of chi-square tests of fitness of the four variables H , W , ln H , ln W to their respective distributions, identified explicitly in column 3. As a reminder, the chi-square statistic χ ν 2 , in column 7 of the table, is determined empirically from the relation. Table 7. Chi-square tests of goodness of fit of ANSUR height and weight. where κ is the number of test categories bins , O i is the observed value in the i th bin, and E i is the expected value in the i th bin. The subscript ν Greek nu is the number of degrees of freedom d. The chi-square tests were implemented with the Maple Statistics Package, which determined the number of bins as the integer closest to the square root of the sample size. a tested hypothesis is deemed unsupported if the P -value is below threshhold. A P -value is the probability of obtaining a test result at least as extreme as the observed result χ obs 2 , and is calculated from the expression. The outcomes summarized in the table show that all 8 propositions the distributions of 4 variables of 2 genders passed their respective chi-square tests with P -values far above threshhold. This means that the propositions cannot be rejected on the basis of these tests. It does not necessarily mean, however, that the propositions are true. For further confirmation, consider again the information in Table 1. In the first section of the table, empirical values of the mean, standard deviation, skewness, and kurtosis of ANSUR heights H and weights W are compared with corresponding values predicted by lognormal expressions 7 to 10 , based on the parameters in the second section of the table, derived from the variates of ln H and ln W. Agreement of experiment and theory is seen to be within 1 standard error se in most cases. Table 1 employed the following published estimators of the standard errors for skewness and kurtosis [36]. In the second section of Table 1 the empirical skewness of both ln H and ln W for both cohorts are close to zero, as expected for normal variables. Likewise, the empirical kurtosis is very close to 3, as expected for normal variables. Skewness is a measure of the asymmetry of a distribution about the mean. Ordinarily, standardized statistical moments employed in physical science and medicine include at most only the first four orders mean, variance, skewness, kurtosis. Nevertheless, in testing a proposed statistical distribution, it is useful to examine these higher moments, particularly if the validity of all lower moments has been confirmed. In the terminology and notation of this paper, the hyperstatistic S p X of the random variable X is the p th standardized central moment defined by the relation. where μ X is the mean of X , and μ p X is the mean of the random variable. referred to as the p th central moment. To simplify symbolic notation in the ensuing text, the argument X will be omitted whenever the context is clear. Substitution in relation 56 of the univariate lognormal PDF, mean, and variance leads to the operational expression. where s is the standard deviation of the variable ln X. Table 8 lists the theoretical expressions for hyperstatistics of order 1 through 6 derived from relation Table 8. Theoretical hyperstatistics of univariate lognormal distribution. The empirical entries column 3 are the sample statistics. where x ¯ is the sample mean. is the expectation of the sample p th central moment Theoretical entries in column 4 were calculated from Equation Overall, agreement between theory and experiment appears reasonably close, but several statistics show what may be significant deviations. To ascertain whether any deviation between theory and experiment is statistically significant requires knowing the standard error of the mean statistic, but the author is unaware of any published expressions for the distributions or standard errors of hyperskewness and hyperkurtosis. To estimate the pertinent standard errors, three independent approaches were taken. The first approach was to use the approximations of error propagation theory [38] together with expressions for variance and covariance of central moments in Chapter 10 of Ref. Table 9. Test of hyperstatistics of height and weight of ANSUR population. Theoretical evaluations of Equation 65 by means of the univariate lognormal PDF are recorded in column 4. The second approach was to evaluate the means of all moments in Equation 62 by their sample expectations given by Equation The resulting empirical standard errors are recorded in column 3. In the third approach three independent simulations of the male and female ANSUR populations were made with correlated lognormal RNGs representing the variables H and W , from which empirical values of the individual hyperstatistics were obtained. The sample standard error of each set of 3 independent means was calculated from the relation. and recorded as the first entry in the cells for standard error in column 5. Note that n is Equation 66 is 3 and not the ANSUR population size of males or females. The second entry separated from the first by a vertical bar is the difference between the largest and smallest of the three estimated means of each S p X. In examining the three sets of estimated standard errors, one sees that they are approximately of the same magnitude, and that the empirical values of the hyperstatistics agree with theory within ± 2 s e for at least one of the three estimates. However, one glaring exception is the value of s e S 6 W M for the male cohort obtained by simulation, which is much larger than the other standard errors for the same statistic. This occurs because of what appears to be an exceptionally high value ~38 of the mean of S 6 W M returned by one of the simulations. This occurrence raises an important conceptual issue that calls for caution when estimating standard errors under conditions where the exact statistical distribution is unknown. As pointed out in Chapter 10 of Ref [28], the approximations based on error propagation theory or some variant thereof give a valid measure of precision provided that the distribution of the statistic approaches normality in the limit of a sufficiently large sample. This is not the case for higher orders of the hyperstatistics. The mere fact that a mean value of the statistic S 6 W M can arise within just 3 simulations that is 6 times the theoretical and 17 times the empirical standard errors of error propagation theory shows that such outlying values occur with much higher probabilities than would be predicted by a normal distribution. Under such circumstances, the appropriate way to proceed is to determine whether the empirical mean values of the hyperstatistics fall within the range between the lowest and highest corresponding statistics obtained by simulation; in other words to rely on a kind of Monte Carlo validation. Evaluated this way, all the empirical hyperstatistics in Table 9 are seen to be consistent with theory. Taken together, the chi-square tests and agreement of theoretical and empirical moments or functions of moments up to the 6th power of the variables support the propositions that H and W are marginally lognormal variables. The BMI, defined by the random variable B in Equation 1 , has long been used as a measure of obesity and a risk factor for associated diseases under the assumption that it is correlated with weight but largely independent of height. If weight varies as the square of height, then the BMI 1 would be unaffected by variations in height, or, in other words, statistically independent of height. Figure 14 provides additional justification of the BMI assumption. The left panels of the figure display scatter plots of the correlation of scaled BMI and scaled height for the ANSUR male cohort top , ANSUR female cohort middle , and RNG simulated female cohort bottom. The isotropic patterns apart from fluctuations are very close to what are expected for the correlation of independent vectors, as shown in the first panel of Figure 5. Quantitatively, the lines of regression dashed red for ANSUR, dashed blue for simulation yield Pearson correlation coefficients 2. The three sets of variables are not standard normal variables, so a null Pearson correlation does not necessarily imply total independence. However, evaluation of the distance correlation of the scaled variables H , B for the male and female cohorts black points respectively yielded by the method of repeated sampling empirical dCor values of 0. Scatter plots of body mass index BMI with height left panels and weight right panels. Patterns in black were calculated from the ANSUR population of male top panels and female middle panels cohorts. Patterns in red bottom panels were simulated for a population of corresponding to the size of the female cohort by means of correlated bivariate lognormal RNGs. The slopes of the lines of regression dashed red or dashed blue of the left panels are close to zero, signifying independence of BMI and height. The slope of the lines of regression of the right panels are close to 0. red points. It is therefore reasonable to conclude that, if the ANSUR populations can serve as baselines, then the BMI and height of healthy adult male and female populations are largely statistically independent. By contrast, the right panels of Figure 14 black for empirical and red for simulation show that BMI and weight are strongly linearly correlated, which was a desirable characteristic of the BMI. The Pearson correlation coefficients are respectively 0. Throughout this paper computer simulation of correlated random variables RVs has been employed for both analytical and graphical comparisons with corresponding empirical results. A brief description of the implementation of these simulations is given in this section. The essential objective is the simulation of a pair of correlated lognormal RVs of specified parameters m 1 , m 2 , s 1 , s 2 , r. The starting point for the construction is the well-known algebraic identity for decomposition of a general normal variable [16]. where N 1 0 , 1 and N 2 0 , 1 are independent standard normal variables ISNVs of mean 0 and variance 1 that serve as basis states. Populations of size n are simulated by creating sets of n variates from each ISNV. To create a normal RV N 2 c m 2 , s 2 2 , r correlated with the RV in Equation 67 , one makes the following linear superposition. Note that, according to the algebraic rules [16] that govern manipulation of independent normal RVs,. where a and b are constants, one could combine the second and third terms in the right side of Equation 69 to recover the marginal distribution represented by Equation 68 , since the correlation parameter r drops out. In the context of simulating samples of human height and weight, these variates are. to simulate a sample of correlated bivariate lognormal RVs. Thus, the bivariate lognormal vectors corresponding to Equations 67 and 69 generated by Maple were defined and implemented by the forms. For completeness, a final comment as to the actual nature of the RNGs employed in this paper is called for. All RNGs that employ a mathematical algorithm, in contrast to RNGs based on some random quantum process such as radioactive decay [40], generate pseudo-random numbers. For each of the 15 pairs of variables, the 'Correlation' column contains the Pearson's r correlation coefficient and the last column contains the p value. That is, there is evidence of a relationship between age and weight in the population. There is not enough evidence of a relationship between age and height in the population. That is, there is evidence of a relationship between weight and height in the population. Breadcrumb Home 12 txt body. txt For this example, you can use the following Minitab file: body.
About Adult BMI	In short, taken altogether, the preceding extensive set of tests supports the proposition that the distribution and correlation of height and weight of a healthy adult human population are fully accounted for by a bivariate lognormal distribution. Article CAS PubMed Google Scholar Li M, Dibley MJ, Sibbritt D, Yan H: An assessment of adolescent overweight and obesity in Xi'an City, China. Tsigilis N: Can secondary school students' self-reported measures of height and weight be trusted? Obesity Silver Spring ;14 12 PubMed Google Scholar Crossref. bone maturity.
A Study on Correlation between Height Growth, Obesity and Bone maturity in Childhood	Nad calculation heighr only height and weight, Correlatino is an inexpensive WWeight easy tool. Four studies examined Nutritional supplement for gut health and directly measured correlation Insulin delivery options for elderly patients by Weight and height correlation 671014 and in general found higher coefficients for the older adolescents, yet none reported statistical differences. Article CAS PubMed Google Scholar Strauss RS: Comparison of measured and self-reported weight and height in a cross-sectional sample of young adolescents. Mark Woodward. Open in new tab Download slide.
	Construct a correlation matrix using the variables age years , weight Kg , height cm , hip girth, navel or abdominal girth , and wrist girth. This example is using the body dataset. These data are from the Journal of Statistics Education data archive. For this example, you can use the following Minitab file: body. Cell contents grouped by Age, Weight, Height, Hip Girth, and Abdominal Girth; First row: Pearson correlation, Following row: P-Value. This correlation matrix presents 15 different correlations. For each of the 15 pairs of variables, the 'Correlation' column contains the Pearson's r correlation coefficient and the last column contains the p value. The analysis included 72 subgroups with a total of , adults aged 25 years and older. The summary estimate of the slopes across studies of men was 1. For women, slopes were lower than 2 in 28 of 32 subgroups with a summary estimate of 1. In most of the populations, BMI is not independent of height; weight does not universally vary with the square of height; and the relationship between weight and height differs significantly between males and females. The use of a single BMI standard for both men and women cannot be justified on the basis of weight-height relationships. Publication types Research Support, N.
About Adult BMI | Healthy Weight, Nutrition, and Physical Activity | CDC	Intervals between collection of self-reported and directly measured data ranged from the same day 8 to a few weeks. The wide variety of references and definitions of overweight used limited comparisons. Fuente-Martín E , Argente-Arizón P , Ros P , et al. We found adolescents living in suburban areas had more bias in their self-reported anthropometric values than those living in urban areas of the city. The use of a single BMI standard for both men and women cannot be justified on the basis of weight-height relationships. Although we performed subgroup analysis based on ethnicity, the sample sizes for Asian and Black females and males were small. Br J Prev Soc Med ; 25 : 42 —

Weight and height correlation -

Lee KH. Korean Journal of Pediatrics. Sin JH. Diagnosis and Treatment of Growth Disorders. Cho HJ, Jung SM, Kim DG, Lee JY. Effects of Herbal Medicine on Growth of Children. Korean Journal of Oriental Pediatrics. Yang SW. Growth Hormone Treatment in Recent Growth Disorders. Korean Society of Endocrinology.

Lee SH, Kim HJ, Heo BR. A Study on the Prevalence of Childhood Obesity. J of Family Medicine. Biro FM, Khoury P, Morrison JA. Influence ob obesity on timing of puberty. Int J Androl.

Chavarro JE, Peterson KE, Sobol AM, Wiecha JL, Gortmaker SL. Effects of a school-based obesity-prevention intervention on menarche United States.

Cancer Causes Control. Freedman DS, et al. The relation of menarcheal age to obesity in childhood and adulthood: the Bogalusa heart study. BMC Pediatr. Wauters M, et al. Human leptin: from an adipocyte hormone to an endocrine mediator. Eur J Endocrinol. Biro FM, et al. Impact of timing of pubertal maturation on growth in black and white female adolescents: The National Heart, Lung and Blood Institute Growth and Health Study.

J Pediatr. Dunkel L, Wickman S. Novel treatment of short stature with aromatase inhibitors. J Steriod Biochem Mol Biol. Shim JO. Underweight in Adolescents. Korean J Pediatr Gastroenterol Nutr. Growth Hormone Therapy in Short Stature Children.

J Korean Med Assoc. Koo YM. To What Extent Is Growth Hormone Therapy Morally Acceptable? J of the Korean Bioethics Association. Jung JH, Jung KM. A Study of Oriental Medicine on Growth of Children. J Korean Oriental Pediatrics. Jang KT, Kim JH. The summary estimate of the slopes across studies of men was 1.

For women, slopes were lower than 2 in 28 of 32 subgroups with a summary estimate of 1. In most of the populations, BMI is not independent of height; weight does not universally vary with the square of height; and the relationship between weight and height differs significantly between males and females.

The use of a single BMI standard for both men and women cannot be justified on the basis of weight-height relationships. Nuttall FQ. Body mass index. Obesity, BMI, and health: a critical review.

Nutr Today. Deurenberg P , Deurenberg Yap M , Wang J , et al. The impact of body build on the relationship between body mass index and percent body fat. Heymsfield SB , Gallagher D , Mayer L , et al. Scaling of human body composition to stature: new insights into body mass index. Diverse Populations Collaborative Group.

Weight-height relationships and body mass index: some observations from the Diverse Populations Collaboration. Am J Phys Anthropol. National Institute for Health and Care Excellence NICE.

Obesity: identification, assessment and management. Clinical Guideline CG Published November 27, Updated July 26, Accessed November 9, Fry A , Littlejohns TJ , Sudlow C , et al. Comparison of sociodemographic and health-related characteristics of UK Biobank participants with those of the general population.

Am J Epidemiol. Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide. Sign In or Create an Account. Navbar Search Filter American Journal of Epidemiology This issue Public Health and Epidemiology Books Journals Oxford Academic Mobile Enter search term Search.

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Advanced Search. Search Menu. Article Navigation. Close mobile search navigation Article Navigation. Volume Article Contents Abstract. Journal Article. Use of Sex-Specific Body Mass Index to Optimize Low Correlation With Height and High Correlation With Fatness: A UK Biobank Study.

Qi Feng , Qi Feng. Correspondence to Dr. Qi Feng, Nuffield Department of Population Health, Medical Sciences Division, University of Oxford, Old Road Campus, Headington, Oxford OX3 7LF, United Kingdom e-mail: qifeng cuhk.

Oxford Academic. Jean H Kim. Junqing Xie. Jelena Bešević. Megan Conroy. Wemimo Omiyale. Yushan Wu. Mark Woodward. Ben Lacey. Naomi Allen. Revision received:. Corrected and typeset:. PDF Split View Views. Select Format Select format. ris Mendeley, Papers, Zotero. enw EndNote. bibtex BibTex.

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adiposity , body composition , body mass index , correlation , fatness , height , UK Biobank , weight. In the training set, we aimed to find the optimal power value for height in the BMI formula that was needed to achieve height independency and fatness dependency.

Table 1 Characteristics of Study Participants From the UK Biobank Included in an Analysis of Sex-Specific Body Mass Index, United Kingdom, — Sex and Participant Subgroup. Mean SD. Age, years Abbreviation: SD, standard deviation. Open in new tab. Figure 1. Open in new tab Download slide.

Table 2 Age-Adjusted Correlation Coefficients for the Correlation of Body Mass Index With Measures of Height and Body Fatness, Using Different Power Values for Height in Calculating Body Mass Index, UK Biobank, United Kingdom, — Correlation Coefficient.

Sex and Minimization or Maximization Criterion a. Power to Which Height Was Raised. Figure 2. Table 3 Accuracy of Old and New Body Mass Index Formulas in Identifying Individuals With a High Body Fat Percentage a in a Testing Data Set From the UK Biobank, United Kingdom, — of Persons. Sex and RSH b Group c.

Old BMI d. New BMI e. Old BMI. New BMI. Female 53, 0. Figure 3. Google Scholar Crossref. Search ADS. Google Scholar OpenURL Placeholder Text. Google Scholar Google Preview OpenURL Placeholder Text. Google Scholar PubMed. OpenURL Placeholder Text.

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beight Bioresource Sciences, Weight and height correlation National Univ. Andong, Corrrelation of Korea. Achieving healthy cholesterol numbers Nursing, Andong National Univ. of Information statistics, Andong National Univ. Objectives The purpose of this study Weight and height correlation to analyze the correoation of short stature through a clinical review of factors related to childhood height growth. So we can find the way to meet the needs of the heightism which is widely spread among modern people. Methods Among patients who came to Andong B oriental clinic for the purpose of growth therapy, children whose height was smaller than other normal children were analyzed. Matthew Sperrin, Blood pressure regulation techniques D. Marshall, Vanessa Higgins, Andrew G. Renehan, Iain E. Weivht mass index BMI tends heiight be higher among shorter adults, especially women. The dependence of BMI—height correlation on age and calendar time may inform us about temporal determinants of BMI. Series of cross-sectional surveys: Health Survey for England, —

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Weight and height correlation -

where s is the standard deviation of the variable ln X. Table 8 lists the theoretical expressions for hyperstatistics of order 1 through 6 derived from relation Table 8. Theoretical hyperstatistics of univariate lognormal distribution. The empirical entries column 3 are the sample statistics. where x ¯ is the sample mean.

is the expectation of the sample p th central moment Theoretical entries in column 4 were calculated from Equation Overall, agreement between theory and experiment appears reasonably close, but several statistics show what may be significant deviations.

To ascertain whether any deviation between theory and experiment is statistically significant requires knowing the standard error of the mean statistic, but the author is unaware of any published expressions for the distributions or standard errors of hyperskewness and hyperkurtosis.

To estimate the pertinent standard errors, three independent approaches were taken. The first approach was to use the approximations of error propagation theory [38] together with expressions for variance and covariance of central moments in Chapter 10 of Ref.

Table 9. Test of hyperstatistics of height and weight of ANSUR population. Theoretical evaluations of Equation 65 by means of the univariate lognormal PDF are recorded in column 4. The second approach was to evaluate the means of all moments in Equation 62 by their sample expectations given by Equation The resulting empirical standard errors are recorded in column 3.

In the third approach three independent simulations of the male and female ANSUR populations were made with correlated lognormal RNGs representing the variables H and W , from which empirical values of the individual hyperstatistics were obtained.

The sample standard error of each set of 3 independent means was calculated from the relation. and recorded as the first entry in the cells for standard error in column 5. Note that n is Equation 66 is 3 and not the ANSUR population size of males or females.

The second entry separated from the first by a vertical bar is the difference between the largest and smallest of the three estimated means of each S p X. In examining the three sets of estimated standard errors, one sees that they are approximately of the same magnitude, and that the empirical values of the hyperstatistics agree with theory within ± 2 s e for at least one of the three estimates.

However, one glaring exception is the value of s e S 6 W M for the male cohort obtained by simulation, which is much larger than the other standard errors for the same statistic.

This occurs because of what appears to be an exceptionally high value ~38 of the mean of S 6 W M returned by one of the simulations. This occurrence raises an important conceptual issue that calls for caution when estimating standard errors under conditions where the exact statistical distribution is unknown.

As pointed out in Chapter 10 of Ref [28], the approximations based on error propagation theory or some variant thereof give a valid measure of precision provided that the distribution of the statistic approaches normality in the limit of a sufficiently large sample.

This is not the case for higher orders of the hyperstatistics. The mere fact that a mean value of the statistic S 6 W M can arise within just 3 simulations that is 6 times the theoretical and 17 times the empirical standard errors of error propagation theory shows that such outlying values occur with much higher probabilities than would be predicted by a normal distribution.

Under such circumstances, the appropriate way to proceed is to determine whether the empirical mean values of the hyperstatistics fall within the range between the lowest and highest corresponding statistics obtained by simulation; in other words to rely on a kind of Monte Carlo validation.

Evaluated this way, all the empirical hyperstatistics in Table 9 are seen to be consistent with theory. Taken together, the chi-square tests and agreement of theoretical and empirical moments or functions of moments up to the 6th power of the variables support the propositions that H and W are marginally lognormal variables.

The BMI, defined by the random variable B in Equation 1 , has long been used as a measure of obesity and a risk factor for associated diseases under the assumption that it is correlated with weight but largely independent of height. If weight varies as the square of height, then the BMI 1 would be unaffected by variations in height, or, in other words, statistically independent of height.

Figure 14 provides additional justification of the BMI assumption. The left panels of the figure display scatter plots of the correlation of scaled BMI and scaled height for the ANSUR male cohort top , ANSUR female cohort middle , and RNG simulated female cohort bottom.

The isotropic patterns apart from fluctuations are very close to what are expected for the correlation of independent vectors, as shown in the first panel of Figure 5. Quantitatively, the lines of regression dashed red for ANSUR, dashed blue for simulation yield Pearson correlation coefficients 2.

The three sets of variables are not standard normal variables, so a null Pearson correlation does not necessarily imply total independence.

However, evaluation of the distance correlation of the scaled variables H , B for the male and female cohorts black points respectively yielded by the method of repeated sampling empirical dCor values of 0.

Scatter plots of body mass index BMI with height left panels and weight right panels. Patterns in black were calculated from the ANSUR population of male top panels and female middle panels cohorts. Patterns in red bottom panels were simulated for a population of corresponding to the size of the female cohort by means of correlated bivariate lognormal RNGs.

The slopes of the lines of regression dashed red or dashed blue of the left panels are close to zero, signifying independence of BMI and height. The slope of the lines of regression of the right panels are close to 0.

red points. It is therefore reasonable to conclude that, if the ANSUR populations can serve as baselines, then the BMI and height of healthy adult male and female populations are largely statistically independent. By contrast, the right panels of Figure 14 black for empirical and red for simulation show that BMI and weight are strongly linearly correlated, which was a desirable characteristic of the BMI.

The Pearson correlation coefficients are respectively 0. Throughout this paper computer simulation of correlated random variables RVs has been employed for both analytical and graphical comparisons with corresponding empirical results. A brief description of the implementation of these simulations is given in this section.

The essential objective is the simulation of a pair of correlated lognormal RVs of specified parameters m 1 , m 2 , s 1 , s 2 , r. The starting point for the construction is the well-known algebraic identity for decomposition of a general normal variable [16].

where N 1 0 , 1 and N 2 0 , 1 are independent standard normal variables ISNVs of mean 0 and variance 1 that serve as basis states. Populations of size n are simulated by creating sets of n variates from each ISNV.

To create a normal RV N 2 c m 2 , s 2 2 , r correlated with the RV in Equation 67 , one makes the following linear superposition. Note that, according to the algebraic rules [16] that govern manipulation of independent normal RVs,. where a and b are constants, one could combine the second and third terms in the right side of Equation 69 to recover the marginal distribution represented by Equation 68 , since the correlation parameter r drops out.

In the context of simulating samples of human height and weight, these variates are. to simulate a sample of correlated bivariate lognormal RVs. Thus, the bivariate lognormal vectors corresponding to Equations 67 and 69 generated by Maple were defined and implemented by the forms.

For completeness, a final comment as to the actual nature of the RNGs employed in this paper is called for. All RNGs that employ a mathematical algorithm, in contrast to RNGs based on some random quantum process such as radioactive decay [40], generate pseudo-random numbers.

These are sets of numbers that are generated reproducibly from a known starting point seed value , yet nevertheless pass diverse statistical tests for randomness. The more stringent a test, and the more tests a RNG passes, the better is the RNG.

The MersenneTwister algorithm supplied by the Maple RandomTools Subpackage has passed the diehard tests of randomness [41] by G. Marsaglia as well as other tests, and provides numbers that can be considered cryptographically secure [42] [43].

It is safe to accept, therefore, that the independent normal basis states with which the simulation algorithm began and from which the correlated bivariate lognormal distributions were created were for all practical purposes sufficiently uncorrelated.

Knowledge of the exact distribution function of a random quantity provides the most complete statistical information attainable about that quantity. This is especially important in regard to anthropometric attributes the statistics of which are essential to clinical medicine and epidemiology.

The fundamental conclusion of this paper is that human height H and weight W in a population of healthy adults are statistically distributed as correlated bivariate lognormal random variables.

Moreover, for all practical purposes, this distribution is thought not to be approximate, but empirically rigorous in samples of sufficient size.

This means that five measurable parameters, comprising two means m H , m W , two variances s H 2 , s W 2 , and the Pearson linear correlation coefficient r , suffice to determine all statistical attributes probabilities, moments, correlations regarding the relation of height and weight in a specified population.

In support of this conclusion, detailed statistical analyses of an extensive anthropometric data base of diverse individuals have shown the following:. The density plot, null Pearson correlation coefficient, and dCor values statistically match the corresponding outcomes from two independent normal RNGs.

In short, taken altogether, the preceding extensive set of tests supports the proposition that the distribution and correlation of height and weight of a healthy adult human population are fully accounted for by a bivariate lognormal distribution.

A secondary point worth noting, given the importance of body mass index BMI to current medicine and epidemiology, is that the conditional expectation of weight, given height, theoretically derived from the lognormal distribution function yielded functional relations 23 , 24 between weight and height.

These functions, when evaluated with the lognormal parameters of the ANSUR male and female cohorts, led in both cases to a nearly exact quadratic power law 27 , thereby justifying theoretically a long-held assumption underlying the use of BMI as a risk factor for obesity-related diseases.

In the opinion of the author, who is an atomic and nuclear physicist, statistical distributions in science can arise, broadly speaking, in two ways. The most fundamental way is as a consequence of a particular dynamical model. In physics, for example, the decay of radioactive nuclei is rigorously accounted for by a binomial probability function, based on a physical model of the independent decay of discrete, uncorrelated nuclei [44].

If the assumption of independence were found to be invalid—and there have been a considerable number of such challenges, only to have been debunked by more careful experiment and analysis [45] [46] [47] [48] —the discovery would have led to deep new insights into the structure and behavior of matter.

The second, less fundamental way, but nevertheless one of practical utility, is by empirical recognition and subsequent verification.

To return to the previous physics example, suppose that the phenomenon of radioactive decay was discovered before there was any understanding or general acceptance of atoms as discrete units of matter 3. Then radioactive decay would have been empirically observed to be a Poisson process, and, indeed, the Poisson distribution is widely depicted in books as a rigorous physical law.

See, for example [49]. However, in retrospect, a Poisson process can be interpreted as a degenerate case of a binomial process in the limit of a large number N of radioactive atoms with low probability p of decay, such that Np is the mean number of decays within a specified time interval.

The point of the foregoing examples is this: The rigorously exact distribution binomial revealed critical information about the constituents discrete, independent of the system. The apparently exact distribution Poisson was empirical and utilitarian, but revealed little about the system other than that the decay products were discrete.

Under appropriately conceived radiation experiments, the difference between the binomial and Poisson distributions can be observed [50], and the fundamentality of the binomial distribution is established.

In regard to the statistical attributes of human height and weight, the consistency with a correlated bivariate lognormal distribution is, as shown in this paper, so extensive and close, that one must wonder whether it is a rigorously exact consequence of some biophysical mechanism or a limiting case of some other statistical process.

How, for example, might a lognormal distribution arise from other distributions? One such process might entail a random variable X comprising a product of some set of arbitrarily distributed random variables, in which case application of the Central Limit Theorem to ln X could result in a normal distribution.

Then the parent variable X would itself be lognormal. It is difficult to conceive in detail, however, of mechanisms by which real biological processes responsible for human height and weight could engender such a hypothetical X as to produce a correlated bivariate lognormal distribution. More generally, a lognormal distribution can also arise under circumstances where an intrinsically positive variable has a low mean and high variance, leading to a pronounced skewness.

However, any of a large number of other skewed distributions could also arise, so the mechanism is not unique. Moreover, as demonstrated in this paper, whatever mechanism is invoked must produce not only the correct skewness, but also kurtosis and other hyperstatistics as well.

At this stage and until testable mechanisms are proposed, refutation of the exactness of the correlated bivariate lognormal distribution of human height and weight can only come from further detailed statistical analysis of larger populations.

And if such future tests further confirm the exactness of the bivariate lognormal relation of height and weight, then, like the example of radioactivity cited above, this knowledge will have revealed something fundamental about the physical processes underlying human development.

The author thanks Trinity College for partial support through the research fund associated with the George A. Jarvis Chair of Physics. Radioactivity was discovered by Henri Bequerel in , whereas opposition to the existence of atoms by some leading scientists of the day lasted until about Harvard University Press, Cambridge, Wiley, New York, Princeton University Press, Princeton, , Cambridge University Press, Cambridge.

Gegenbaurs morphologisches Jahrbuch, , PLOS ONE, 9, e Human Genetics, , The Journals of Gerontology Series A Biological Sciences and Medical Sciences, 76, and Lipscombe, T.

Open Journal of Statistics, 12, and Bakirov, N. The Annals of Statistics, 35, and Rizzo, M. The Annals of Applied Statistics, 3, The New York Times. html [ 15 ] Gordon, C. Army Personnel: Methods and Summary Statistics. Army Natick Soldier Research and Engineering Center, Natick. Cambridge University Press, Cambridge, and Peacock, B.

and Vecchi, G. Demography, 46, The American Journal of Physical Anthropology, , Annals of Human Biology, 47, and Buchan, I. Journal of Public Health, 38, Münchener Medizinische Wochenschrift, 68, and Townsend, E.

American Journal of Human Biology, 1, Open Access Library Journal, 2, and Bloom, D. Human Biology, 51, The Johns Hopkins University Press, Baltimore, and Stuart, A. Hafner, New York, , Journal of the Royal Statistical Society: Series B, 15, and Boes, D. Holt, Rinehart, and Winston, New York, Biometrika, 32, and Weber, H.

The Annals of Statistics, 7, and Cousineau, D. The Quantitative Methods for Psychology, 10, p [ 37 ] Moment Mathematics Wikipedia. American Journal of Physics, 72, com Overview of the RandomTools [MersenneTwister] Subpackage. aspx [ 43 ] Mapleprimes. Post by mmcdara and Andrews, H. Prentice-Hall, Englewood Cliffs, Physics A, , and Strange, W.

Europhysics Letters, 87, Article No. Europhysics Letters, , Article No. Gordon and Breach, New York, and Spyrou, N.

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Mark P. Silverman Department of Physics, Trinity College, Hartford, USA. DOI: Abstract The statistical relationship between human height and weight is of especial importance to clinical medicine, epidemiology, and the biology of human development.

Keywords Correlation of Height and Weight , Distribution of Height and Weight , Body Mass Index , Lognormal Distribution , Distance Correlation dCor , Hyperstatistics.

Share and Cite:. Silverman, M. Open Journal of Statistics , 12 , doi: Galuska, PhD, reviewed the manuscript. full text icon Full Text. Download PDF Top of Article Abstract Methods Results Comment Conclusions Article Information References. Table 1. View Large Download. Characteristics of Studies in Reviewed Literature.

Sex-Specific Differences Between SR and DM Means for Height, Weight, and BMI. SR and DM Prevalence of Overweight, Absolute Error, and Relative Error. Sex-Specific Correlation Coefficients Between Self-report and Direct Measurement of Height, Weight, and BMI. Classification of Overweight by Self-reported vs Directly Measured Data: Sensitivity, Specificity, and Positive Predictive Value.

Institute of Medicine, Preventing Childhood Obesity: Health in Balance. Washington, DC National Academies Press;. Valenti LCharles JBritt H BMI of Australian general practice patients.

Aust Fam Physician ;35 8 PubMed Google Scholar. Sen B Frequency of family dinner and adolescent body weight status: evidence from the National Longitudinal Survey of Youth, Obesity Silver Spring ;14 12 PubMed Google Scholar Crossref.

Strauss RS Comparison of measured and self-reported weight and height in a cross-sectional sample of young adolescents. Int J Obes Relat Metab Disord ;23 8 PubMed Google Scholar Crossref. Fortenberry JD Reliability of adolescents' reports of height and weight.

J Adolesc Health ;13 2 PubMed Google Scholar Crossref. Himes JHFaricy A Validity and reliability of self-reported stature and weight of US adolescents.

Am J Hum Biol ;13 2 PubMed Google Scholar Crossref. Davis HGergen PJ The weights and heights of Mexican-American adolescents: the accuracy of self-reports. Am J Public Health ;84 3 PubMed Google Scholar Crossref.

Goodman EHinden BRKhandelwal S Accuracy of teen and parental reports of obesity and body mass index. Pediatrics ; 1 pt 1 58 PubMed Google Scholar Crossref. Stewart AL The reliability and validity of self-reported weight and height. J Chronic Dis ;35 4 PubMed Google Scholar Crossref. Brooks-Gunn JWarren MPRosso JGargiulo J Validity of self-report measures of girls' pubertal status.

Child Dev ;58 3 PubMed Google Scholar Crossref. Shannon BSmiciklas-Wright HWang M Inaccuracies in self-reported weights and heights of a sample of sixth-grade children. J Am Diet Assoc ;91 6 PubMed Google Scholar. Himes JHStory M Validity of self-reported weight and stature of American Indian youth.

Hauck FRWhite LCao GWoolf NStrauss K Inaccuracy of self-reported weights and heights among American Indian adolescents. Ann Epidemiol ;5 5 PubMed Google Scholar Crossref. Brener NDMcManus TGaluska DClowry RWechsler H Reliability and validity of self-reported height and weight among high school students.

J Adolesc Health ;32 4 PubMed Google Scholar Crossref. Himes JHHannan PWall MNeumark-Sztainer D Factors associated with errors in self-reports of stature, weight, and body mass index in Minnesota adolescents.

Ann Epidemiol ;15 4 PubMed Google Scholar Crossref. Am J Clin Nutr ;53 4 PubMed Google Scholar. Rosner BPrineas RLoggie JDaniels SR Percentiles for body mass index in US children 5 to 17 years of age.

J Pediatr ; 2 PubMed Google Scholar Crossref. Gelbach S Interpreting the Medical Literature: Practical Epidemiology for Clinicians.

New York, NY MacMillan; Kuczmarski RJOgden CLGrummer-Strawn LM et al. CDC growth charts: United States. Adv Data ; 1- 27 PubMed Google Scholar.

Bowlin SJMorrill BDNafziger ANJenkins PLLewis CPearson TA Validity of cardiovascular disease risk factors assessed by telephone survey: the Behavioral Risk Factor Survey. J Clin Epidemiol ;46 6 PubMed Google Scholar Crossref. Kuczmarski MFKuczmarski RNajjar M Effects of age on validity of self-reported height, weight, and body mass index: findings from the third National Health and Nutrition Examination Survey, J Am Diet Assoc ; 1 34 PubMed Google Scholar Crossref.

Nieto-García FJBush TKeyl P Body mass definitions of obesity: sensitivity and specificity using self-reported weight and height. Epidemiology ;1 2 PubMed Google Scholar Crossref. Onyike CUCrum RMLee HBLyketsos CGEaton WW Is obesity associated with major depression? Results from the Third National Health and Nutrition Examination Survey.

Am J Epidemiol ; 12 PubMed Google Scholar Crossref. YRBSS: Youth Risk Behavior Surveillance System. htm Accessed December 20, Centers for Disease Control and Prevention CDC , Overweight among students in grades K Arkansas, and school years.

MMWR Morb Mortal Wkly Rep ;55 1 5- 8 PubMed Google Scholar. Missouri Coordinated School Health Coalition, Promoting healthy weight in Missouri's children: a guide for schools, families and communities.

html Accessed December 20, Google Scholar. See More About Adolescent Medicine Obesity Pediatrics. Select Your Interests Select Your Interests Customize your JAMA Network experience by selecting one or more topics from the list below.

Save Preferences. Privacy Policy Terms of Use. This Issue. Citations View Metrics. X Facebook More LinkedIn. Cite This Citation Sherry B , Jefferds ME , Grummer-Strawn LM.

December Bettylou Sherry, PhD, RD ; Maria Elena Jefferds, PhD ; Laurence M. Grummer-Strawn, PhD. Author Affiliations Article Information Author Affiliations: Maternal Child Nutrition Branch, Division of Nutrition and Physical Activity, Centers for Disease Control and Prevention, Atlanta, Georgia.

visual abstract icon Visual Abstract. Literature search. Coding and analysis of studies. We found adolescents living in suburban areas had more bias in their self-reported anthropometric values than those living in urban areas of the city.

Previous studies have no information about the effect of area of residence on the report error. It is beyond the scope of the current study to interpret the effects of household economic status and area of residency.

Previous studies have indicated that adults [ 48 ] and adolescents [ 49 ] with a higher socioeconomic status are more concerned about body shape or other peoples' perceptions of their weight.

Prior research also shows that rural students are less concerned about weight [ 50 , 51 ]. The difference in concerns about weight may partly explain why household economic status and area of residency were associated with difference between reported and measured values in our study.

We had similar findings. We also hypothesized that a population with a relatively thinner body shape or a population with fewer obese people might more accurately report their weight and height. However, the reported errors in our study were moderately to slightly larger than previous studies conducted in Western countries, where the rates of overweight and obesity were higher than in our study.

Unexpectedly, we found that adolescents from the suburban areas of the city, a population with a lower prevalence of overweight and obesity [ 52 ], reported their body weight and height less accurately compared to their urban counterparts, after adjustment for gender, age, household economic status and BMI status in multivariable linear regression models.

By adjusting the self-reported BMIs for socioeconomic variables, the sensitivity of screening for overweight individuals was increased from Thus, the application of an adjusted formula results in a more accurate identification of overweight adolescents.

Nevertheless, the sensitivity does not seem to be sufficient for the identification of overweight individuals even if the reported BMI is adjusted in this way. In addition, the use of the correction formula in this study, or other studies, is limited because the characteristics may differ in different populations or change over time.

One shortcoming of the present study was that our sample was drawn from schools, and adolescents who did not attend a school were not included.

The results of the present study will not reflect this relatively small section of the adolescent population. In addition, there was a time interval of about one week between when the students answered the questionnaire and when they were measured.

The height and weight of the adolescents may have changed during this week, although this change is likely minimal.

Xi'an is a city located in central China. Since China is a vast nation characterized by social, economic, cultural and environmental diversity, the result of this study cannot be generalized to the whole country.

However, it may be generalized to several neighbouring big cities that demonstrate similar qualities and patterns. Therefore we do not recommend the application of self-reported weight and height to screen for overweight adolescents in China. Reported data could be considered for use in surveillance systems and epidemiology studies with caution.

Any use of self-reported height and weight data from adolescents in future research studies should be justified with supporting pilot data validating such measures.

Wang Y, Lobstein T: Worldwide trends in childhood overweight and obesity. Int J Pediatr Obes. Article PubMed Google Scholar. Lobstein T, Baur L, Uauy R: Obesity in children and young people: a crisis in public health. Obes Rev. Wang Y, Monteiro C, Popkin BM: Trends of obesity and underweight in older children and adolescents in the United States, Brazil, China, and Russia.

Am J Clin Nutr. CAS PubMed Google Scholar. Chen CM: Overview of obesity in Mainland China. Must A, Strauss RS: Risks and consequences of childhood and adolescent obesity. Int J Obes Relat Metab Disord.

Togashi K, Masuda H, Rankinen T, Tanaka S, Bouchard C, Kamiya H: A year follow-up study of treated obese children in Japan. Article CAS PubMed Google Scholar. Sakamaki R, Toyama K, Amamoto R, Liu CJ, Shinfuku N: Nutritional knowledge, food habits and health attitude of Chinese university students--a cross sectional study.

Nutr J. Article PubMed PubMed Central Google Scholar. Sasaki S, Katagiri A, Tsuji T, Shimoda T, Amano K: Self-reported rate of eating correlates with body mass index in y-old Japanese women. Roseman MG, Yeung WK, Nickelsen J: Examination of weight status and dietary behaviors of middle school students in Kentucky.

J Am Diet Assoc. Wong JP, Ho SY, Lai MK, Leung GM, Stewart SM, Lam TH: Overweight, obesity, weight-related concerns and behaviours in Hong Kong Chinese children and adolescents. Acta Paediatr.

Sigfusdottir ID, Kristjansson AL, Allegrante JP: Health behaviour and academic achievement in Icelandic school children. Health Educ Res. Tokmakidis SP, Christodoulos AD, Mantzouranis NI: Validity of self-reported anthropometric values used to assess body mass index and estimate obesity in Greek school children.

J Adolesc Health. Lee K, Valeria B, Kochman C, Lenders CM: Self-assessment of height, weight, and sexual maturation: validity in overweight children and adolescents. Jansen W, Looij-Jansen van de PM, Ferreira I, de Wilde EJ, Brug J: Differences in measured and self-reported height and weight in Dutch adolescents.

Ann Nutr Metab. Huybrechts I, De Bacquer D, Van Trimpont I, De Backer G, De Henauw S: Validity of parentally reported weight and height for preschool-aged children in Belgium and its impact on classification into body mass index categories.

Himes JH, Hannan P, Wall M, Neumark-Sztainer D: Factors associated with errors in self-reports of stature, weight, and body mass index in Minnesota adolescents.

Ann Epidemiol. Brener ND, McManus T, Galuska DA, Lowry R, Wechsler H: Reliability and validity of self-reported height and weight among high school students.

Hauck FR, White L, Cao G, Woolf N, Strauss K: Inaccuracy of self-reported weights and heights among American Indian adolescents. Goodman E, Hinden BR, Khandelwal S: Accuracy of teen and parental reports of obesity and body mass index.

Davis H, Gergen PJ: The weights and heights of Mexican-American adolescents: the accuracy of self-reports. Am J Public Health.

Article CAS PubMed PubMed Central Google Scholar. Elgar FJ, Roberts C, Tudor-Smith C, Moore L: Validity of self-reported height and weight and predictors of bias in adolescents. Himes JH, Faricy A: Validity and reliability of self-reported stature and weight of US adolescents.

Am J Hum Biol. Wada K, Tamakoshi K, Tsunekawa T, Otsuka R, Zhang H, Murata C, Nagasawa N, Matsushita K, Sugiura K, Yatsuya H, et al: Validity of self-reported height and weight in a Japanese workplace population.

Int J Obes Lond. Article CAS Google Scholar. Lawlor DA, Bedford C, Taylor M, Ebrahim S: Agreement between measured and self-reported weight in older women. Results from the British Women's Heart and Health Study. Age Ageing. Dubois L, Girad M: Accuracy of maternal reports of pre-schoolers' weights and heights as estimates of BMI values.

Int J Epidemiol. Altman DG, Bland JM: Measurement in Medicine: The Analysis of Method Comparison Studies. Journal of the Royal Statistical Society Series D The Statistician.

Google Scholar. Shannon B, Smiciklas-Wright H, Wang MQ: Inaccuracies in self-reported weights and heights of a sample of sixth-grade children. Himes JH, Story M: Validity of self-reported weight and stature of American Indian youth. Tsigilis N: Can secondary school students' self-reported measures of height and weight be trusted?

An effect size approach. Eur J Public Health. Sherry B, Jefferds ME, Grummer-Strawn LM: Accuracy of adolescent self-report of height and weight in assessing overweight status: a literature review. Arch Pediatr Adolesc Med.

Nakamura K, Hoshino Y, Kodama K, Yamamoto M: Reliability of self-reported body height and weight of adult Japanese women. J Biosoc Sci. Visscher TL, Viet AL, Kroesbergen IH, Seidell JC: Underreporting of BMI in adults and its effect on obesity prevalence estimations in the period to Obesity Silver Spring.

Article Google Scholar. Nyholm M, Gullberg B, Merlo J, Lundqvist-Persson C, Rastam L, Lindblad U: The validity of obesity based on self-reported weight and height: Implications for population studies.

Rowland ML: Self-reported weight and height. Bolton-Smith C, Woodward M, Tunstall-Pedoe H, Morrison C: Accuracy of the estimated prevalence of obesity from self reported height and weight in an adult Scottish population. J Epidemiol Community Health. Cole TJ, Bellizzi MC, Flegal KM, Dietz WH: Establishing a standard definition for child overweight and obesity worldwide: international survey.

Katzmarzyk PT, Tremblay A, Perusse L, Despres JP, Bouchard C: The utility of the international child and adolescent overweight guidelines for predicting coronary heart disease risk factors. J Clin Epidemiol. Filmer D, Pritchett LH: Estimating wealth effects without expenditure data--or tears: an application to educational enrollments in states of India.

Bland JM, Altman DG: Statistical methods for assessing agreement between two methods of clinical measurement. Cohen J: Weighted kappa: nominal scale agreement with provision for scaled disagreement or partial credit.

Psychol Bull. Lantz CA: Application and evaluation of the kappa statistic in the design and interpretation of chiropractic clinical research.

J Manipulative Physiol Ther. Engstrom JL, Paterson SA, Doherty A, Trabulsi M, Speer KL: Accuracy of self-reported height and weight in women: an integrative review of the literature. J Midwifery Womens Health. Gunnell D, Berney L, Holland P, Maynard M, Blane D, Frankel S, Smith GD: How accurately are height, weight and leg length reported by the elderly, and how closely are they related to measurements recorded in childhood?.

Nawaz H, Chan W, Abdulrahman M, Larson D, Katz DL: Self-reported weight and height: implications for obesity research. Am J Prev Med. Strauss RS: Comparison of measured and self-reported weight and height in a cross-sectional sample of young adolescents. Brenner H, Kliebsch U: Dependence of Weighted Kappa Coefficients on the Number of Categories.

Wang Z, Patterson CM, Hills AP: A comparison of self-reported and measured height, weight and BMI in Australian adolescents. Aust N Z J Public Health. Wardle J, Robb KA, Johnson F, Griffith J, Brunner E, Power C, Tovee M: Socioeconomic variation in attitudes to eating and weight in female adolescents.

Health Psychol. Wardle J, Griffith J: Socioeconomic status and weight control practices in British adults. Williams KJ, Taylor CA, Wolf KN, Lawson RF, Crespo R: Cultural perceptions of healthy weight in rural Appalachian youth.

Rural Remote Health. Lee S, Lee AM: Disordered eating in three communities of China: a comparative study of female high school students in hong kong, Shenzhen, and rural hunan. Int J Eat Disord. Li M, Dibley MJ, Sibbritt D, Yan H: An assessment of adolescent overweight and obesity in Xi'an City, China.

Download references. We are grateful to all our staff, schoolteachers, and adolescents who participated in the study. From the Department of Epidemiology and Health Statistics, School of Public Health, Xi'an, Jiaotong University College of Medicine, No.

Sydney School of Public Health, University of Sydney, University of Sydney, Room A, Edward Ford Building A27 , Sydney, NSW, , Australia. You can also search for this author in PubMed Google Scholar.

Correspondence to Hong Yan. XZ carried out the study, data analyses and drafted the manuscript. MJD participated in study design, data interpretation and helped to draft the manuscript. YC participated in study design, data collection, and made modifications of the paper.

OX participated in study design and data collection. HY participated in the study design, data analysis and helped to draft manuscript.

Sherry BJefferds Rejecting diet culture Weight and height correlation, Grummer-Strawn LM. Accuracy of Adolescent Weight and height correlation of Height and Weight in Assessing Weigbt Status : A Literature Hwight. Arch Pediatr Adolesc Med. Author Affiliations: Maternal Child Nutrition Branch, Division of Nutrition and Physical Activity, Centers for Disease Control and Prevention, Atlanta, Georgia. Objective To examine the accuracy of self-reported height and weight data to classify adolescent overweight status. Self-reported height and weight are commonly used with minimal consideration of accuracy.