differential contribution of stature phenotypes to assortative mating in parents of philadelphia...

Differential Contribution of Stature Phenotypes to Assortative Mating in Parents of Philadelphia Black and White School Children

WILLIAM H MUELLER AND ROBERT M MALINA I Center for Demographic a n d Population Genet ics , Universi ty of T e x ( ~ s Health Science Cen te i , Hoiislon, T e x a s 77025 rrnd Anthropology, Universi ly o j Tenas, Az i s t in , Texas 78712

Depar tmen t of

KEY U'ORDS Assortative mating . Stature . Weight . Ponderal index . Quetelet's index . Race Blacks . Whites.

ABSTRACT Assortative mating for stature, weight, and the ponderal and Quetelet's indices is considered in a large sample of Philadelphia Blacks and Whites. The husband-wife correlation for stature is positive and significant in Whites (r = 0.34, d.f. = 382), but negligible in Blacks (r = 0.06, d.f. = 420). Correlations for weight and the body indices are positive and significant i n both samples, those for body indices showing some dependency on the husband-wife correlations for stature and weight. When couples are grouped into statural mating combinations on the basis of short (S), medium (M) and tall (T), White spouses' statures show an approximately linear relationship to one another. The distribution of Black spouses' statures, however, is not completely independent, even though the husband-wife correlation is close to zero. There are elements of both positive and negative assortative mating among Blacks, resulting in a n excess of certain mating types over that expected on the basis of chance. These mating types are usually those in which the husband is shorter than the wife, except at the heterogeneous extremes of the bivariate array.

Various studies have reported on assortative mating for body size in samples of European ancestry. Low to moderate positive husband-wife correlations have been observed in these samples (Susanne, '67; Spuhler, '68). Similar correlations have been reported for a peasant-farming com- munity of the Colombian Andes of Spanish- Indian ancestry (Mueller, '75). Although data are scarce for samples of non-Euro- pean ancestry, husband-wife correlations for body size are effectively zero among the Japanese, American Indians and Solomon Islanders (Johnston, '70; Baldwin and Da- mon, '73). Except for Schull et al. ('70), to our knowledge there has not been a report on husband-wife similarity for body size in American Blacks. Schull et al. ('70) report husband-wife correlations for height, skin color and blood pressure among 56 Detroit Black couples. Our report considers assortative mating for s;ature, weight, and the ponderal (height/ V'weight) and Quetelet's (weight/height') indices, in a large sample

of Philadelphia Blacks and Whites. Sub- jects used in this study are parents of school children 6 through 12 years of age. The children were participants in a broader study of growth of Philadelphia children (Malina, '68; Malina et al., '70).

METHODS

Parental heights and weights were reported to the nearest one-half inch and nearest pound respectively on a question- naire circulated to all parents of children participating in the growth study. White children were enrolled in a public elementary school, while the Black children were from a parochial school. The White sample was from a middle to upper middle socio- economic background, while the Blacks were from a lower level, probably in the lower middle and upper lower socio-economic brackets. These socio-economic esti- mates are based on observations of neigh- borhoods and parental occupations, though not directly measured. Children for whom

269 AM. J . PHYS. ANTHROP.. 45: 269-276.

2 70 WILLIAM H. MUELLER AND ROBERT M. MALINA

heights and weights of both parents were not available (e.g., adopted or foster children. deceascd parent, separated parent, children living with relatives) were omitted from the sample.

Although reported heights and weights have inherent limitations, they are used in growth studies (Wingerd et al., ’73) and surveys (Schull et al., ’70; Perry et al., ’69; Frisancho and Borkan, ’74). Reported and measured heights and weights generally correlate well. Wingerd et al. (’73) reported a correlation of 0.92 between fathers’ measured and estimated heights, while Perry et al. (’69) reported a correlation “greater than 0.90” between self-reported weight and measured weight. In a large sample of Air Force women, Clauser et al. (’72) reported correlations of 0.96 and 0.97 between reported and measured heights and weights respectively. However, women tend to overestimate their stature by an average of 2.5 cm, and to underestimate their weights by an average of 0.83 kg. Within the series, heavy women tended to underestimate their weights more than light ones, and younger women did so more than older women. No such trend was apparent for stature.

Only the husband-wife correlation for stature differs significantly between the Black and White samples. To take a closer look at assortative mating for stature, parental statures were categorized on the basis of race and sex into percentile groups. Separate analyses were done using 2 x 2 , 3 X 3, and 4 x 4 formats to check con- sistency of results. For the 2 X 2 format, division into tall (T) and short (S) was made at the median. Since there are an even number of Black and White couples, the median is equal to the value of the mean of the scores of the two middle cases. This is the way the SPSS packaged program computes a median (Nie et al., ’70). None of the values for stature fall at any of the four race and sex-specific medi- ans so defined. Thus, there is only one way to make the 2 X 2 division in both samples. The limits of the other percentile divisions were made in the following way: For the 3 x 3 format, the shortest third (S) ranged from lowest stature to the value of stature at which the cumulative frequency came closest to one-third N; the middle third (M), as statures exceeding the first category up

to the stature at which the cumulative frequency came closest to two-thirds N; the remainder being the tallest third (T). Like- wise for the 4 X 4 format, the shortest quartile encompassed the lowest stature up to the value of stature at which the cumulative frequency came closest to one-fourth N; middle to short, statures exceeding the first category up to the stature at which the cumulative frequency came closest to one-half N, middle to tall, as statures exceeding the preceding categories up to the stature at which the cumulative frequency came closest to three-fourths N; with the remainder being the tallest quartile. This method of assignment comes closest to al- locating an equal number of husband-wife pairs to each of the percentiles. Of course in practice, not all categories will have equal numbers within a given format, because of sampling variability in the actual distributions of stature.

Using this procedure, husband-wife pairs may be classified into mating combinations: homogeneous (T X T, S X S, M X M) and heterogeneous (T X S, M X S, T X M), and the distribution of mating combinations in the two races compared. Although it may seem arbitrary to class a continu- ously distributed variable like stature into discrete categories, the technique has been used in studies on the genetics of growth (Garn, ’62; Malina et al., ’70) to illustrate offspring trends with respect to parental stature. Here, we hope to clarify how husband-wife pairs distribute within and between the two samples.

Sample sizes, means and standard deviations for stature, weight and the body indices are shown in table 1. Height and weight were converted to their metric equiv- alents. The ponderal index, however, is calculated on the basis of inches and pounds, while Quetelet’s index is based on height in centimeters and weight in grams. In spite of stature and weight being reported data, their distributions follow bio- logical expectations. Stature is distributed in an approximately normal (Gaussian) way. Only stature of Black wives approached significant skewness ( p = 0.05), while stature of White husbands showed slight kurtosis ( p = 0.01). However, the coeffi- cients of skewness and kurtosis in both in- stances were very small compared to those for weight or Quetelet’s index, measure-

ASSORTATIVE MATING I N BLACKS A N D WHITES 271

TABLE 1

Sample size^, m e a n s a n d s tandard deviations for s ta ture , weight , a n d ponderal a n d QueteZrt’P ind ice5 among Ph i lade lphm Blrtrlz a n d Whzte couple5

Males Females

N x S D N x S D

B1 ac k Stature (cm) 422 174.8 8.1 422 162.8 7.4 Weight (kg) 418 78.1 11.1 420 67.8 13.9 Panderal index 1 418 12.4 0.6 420 12.2 0.8 Quetelet’s index 2 418 2.6 0.3 420 2.6 0.5

White Stature (cm) 384 177.4 6.7 384 162.7 6.1 Weight (kg) 381 78.9 9.3 38 1 57.5 7.3 Ponderal index 1 381 12.5 0.4 38 1 12.8 0.5 Quetelet’s index 2 38 1 2.5 0.3 38 1 2.2 0.3

1 (Height = in/-t = lbs) 2 (Weight = g/Heirht = cm2).

ments expected to show some departure from normality. Ponderal index had only slight and occasional departures from normality, usually indicating a leptokurtic distribution. Average stature, weight and ponderal index for Black and While males compare favorably with data from the U.S. Health Examination Survey for the age ranges 25-34 and 35-44 years (Stoudt et al., ’65, ’70). Average stature for females agrees well with the Health Examination Survey data, but weights of Black women are slightly above, and those of White women are slightly below the health survey values. There was, however, almost twice as much variation in the weight of Black women as compared to White women. A trend similar to that noted for weight is apparent for the ponderal index in Black and White women.

Product-moment correlations between measurements of spouses were computed for each variable. Black-White differences

in assortative mating were tested by trans- forming the husband-wife correlations into normalized z’s according to the method described by Fisher (’58). Because of the before-mentioned departures from normality and unequal variances between races for some of the measurements, nonpara- metric husband-wife correlations were also computed as a check. For this, Spearman’s rank-order correlation ( T , ~ ) was used. This statistic assumes a continuous distribution, but does not require the variables to be normally distributed (Siegel, ’56).

RESULTS AND DISCUSSION

Husband-wife correlations for stature, weight and body indices are shown in table 2. Rank-order correlations give results similar to those of the product-moment correlation. Stature correlations for White married couples agree well with data for samples of European ancestry (Susanne, ’67; Spuhler, ’68), while the husband-wife

TABLE 2

Hucband-wife co~relatzons f o r ~ t a t u ~ e , u3ezqht, poridrrnl a n d Quetelet’s indzces amonq

T S , Spearmiin m n k - o r d e r t o r ~ e l a t ~ o n Phrlndelphia Black a n d Whi te couples r, product-moment correlation

Black-white B1 ac k White difference

r r t P Measurement

N N r S

Stature 422 0.06 0.03 384 0.34 1 0.34 1 4.15 0.001 Weight 418 0.23 1 0.22 1 381 0.17 1 0.17 1 0.85 n.s. Ponderal index 418 0.14 1 0.08 381 0.20 1 0.22 1 0.85 n.s. Quetelet’s index 418 0.19 1 0.14 1 381 0.15 1 0.18 1 0.56 n.s.

2 72 WILLIAM H. MUELLER AND ROBERT M. MALINA

correlation for Black married couples is not significantly different from zero. Results for Blacks agree with the general lack of assortative mating for body size among samples of non-European ancestry (Bald- win and Damon, ’73). Harburg (personal communication) has reported to us lower husband-wife correlations for stature among Detroit Black couples as compared to Whites (for details see: Schull et al., ’70; Harburg et al., ’73). The authors work with four samples, and their data are based on reported heights: a Black and White sample from each of two socio-economic areas of the city termed “high” and “low-stress” areas. Their husband-wife correlations are almost identical to ours for high-stress Blacks (corresponding to lower socio-economic conditions) and low-stress Whites (better socio-economic conditions). A4ver- aging Harburg’s correlations, we get r = 0.08 for 112 “high-stress” Black couples. and r = 0.34 for 115 “low-stress’’ Whites. However, husband-wife correlations for stature are virtually identical among “low- stress” Blacks and “high-stress” Whites ( r = 0.20). Hence. there seems to be some socio-economic effect on assortative mating for stature.

Husband-wife correlations for weight, ponderal and Quetelet’s indices are significant in both Blacks and Whites and do not differ significantly between the two races. Since the spouses have school aged children, co-habitation tirne of the spouses must have been considerable. This could account for the husband-wife similarity in weight in both Blacks and Whites. Corre-

lations for ponderal index are intermediate to those for stature and weight in both races, probably reflecting the dependency of’the ponderal index on the other two measurements. Spouse correlations for Quete- let’s index are less like those for height but more like those for weight in both samples. This reflects the lesser dependence of Quetelet’s index on stature (Billewicz et al., ’62). Indeed, in our sample correlations of’ the ponderal index with stature ranged from 0.32 to 0.50, whereas Correlations of Quetelet’s index with stature ranged from -0.08 to -0.22 depending on race and sex. These correlations are in general agree- ment with those reported by Billewicz et al. (’62).

Husband-wife statures by percentile are presented in tables 3 through 5. Tau-B is the husband-wife correlation based on the rows and columns of the contingency tables (Kendall, ’70: p. 45). It is notable that irrespective of how groupings are made, the husband-wife correlation in Blacks is consistently close to zero, while in Whites it is consistently positive. The chi-square is a measure of the independence of the distribution of spouses’ statures. For Whites, chi-squares are consistently highly significant. However, in Blacks, the chi-square is also highly significant for the 3 X 3 and 4 X 4 tables, but not the 2 X 2 table. Al- though Black spouses are uncorrelated with respect to height, spouses’ statures are not distributed independently. This seems to have some dependence on how the classification into percentiles is made.

The numbers in parentheses in tables

TABLE 3

Nztmher of husband-zti l fc p u i r s of rliflerrnt stature m a t i n g combinut ions -2 X 2 . Expected nuinhers are in pnrentheses . IS, Short ibpiow m e d i a n ) ; T , Tall (ribour m e d i a n ) 1

Black White

W1fe Wife S T Tot a1 S T Tot a1

S 111 85 196 115 53 168 (106) (90) (90) (78)

Hiisb. T 118 108 226 90 126 216

(123) (103) (115) (101)

Tot a1 229 193 422 205 179 384

T R U B = 0.04 Chi Square = 0.66

(d.f. = 1)

Tau B = 0.27 Chi Square = 26.20

(d.f. = 1)

ASSORTATIVE MATING I N BLACKS AND WHITES 273

TABLE 4

NllVlbfV o f h ~ b ~ i i ~ ~ L - w i f e p n r n of dif ferent s ta tur r -ma t ing Lombzncitiona - 3 X 3 Expectcd nirmbers (ire in paren theses . ( S , short , M , mediitnt, T. ta l l )

Black White

Wife Wife S M T Total S M T Total

S 47 72 38 157 51 (49) (60) (48) (30)

Hu sb . M 44 33 53 130 26 (41) (50) (39) (31)

Total

T 42 56 37 135 27 (43) (51) (41) (43)

133 161 128 422 104

TauB = 0.01 Chi Square = 15.74 1

(d.f. = 4)

46 15 112 (51) (30)

(52) (31)

67 65 159 (73) (43)

176 104 384

63 24 113

Tau B = 0.28 Chi Square = 44.60 2

(d.f. = 4)

~ 0 0 1 > p > 0 0 0 1 ' p < 0001

TABLE 5

Number of h u s b a n d w f e puirs of d i f f e ren t staticre mcct iny c o m b m u t i o n & - 4 X 4 Lxpec ted iiumberc are i i i paren theses is, ahort, M , medium, T, ta l l )

Black Whitr

Wife Wife S M T Total S ILI T Total

S 17 42 17 10 86 51 26 20 15 112 (16) (30) (21) (18) (30) (30) (23) (29)

13 39 38 20 110 16 22 8 10 56 (21) (39) (28) 123) (15) (15) (11) (15)

Hu sb M 17 20 25 29 91 26 30 36 33 125

(17) (32) (23) (19) (34) (33) (25) (33)

T 34 47 26 28 135 11 23 14 43 91 (261 (47) (34) (28) (25) (24) (18) (24)

Total 81 148 106 87 422 104 101 78 101 384

Tau B = 0.02 Chi Square = 30.96 1

(d.f. = 9)

Tau B = 0.28 Chi Square = 58.44 1

(d.f. = 9)

' p < 0.001

3 through 5 are those expected on the assumption of randomness of' spouses' statures. Expected numbers are the product of the marginal frequencies divided by the total N. Matings in which the number of observed couples deviates substantially from the expected, will be those contributing most to the chi-square. Among Whites there are consistently more homogeneous matings (S X S, M X M, T X T, etc.) than expected, and a deficit of heterogeneous matings (S X T, S X M, T X M, etc.), no

matter how the percentile assignments are made. Thus in this case, the chi-square undoubtedly reflects the positive correlation between spouses. But what about Blacks in which there is no correlation?

The number of Black homogeneous matings are notably close to those expected on the basis of chance in all three tables (3 through 5). An exception is a deficit of the M X M type in table 4 ( 3 X 3) . This is apparently due to short husbands who are more often in association with medium

2 74 WILLIAM H. MUELLER AND ROBERT M . MALINA

wives, and medium husbands who are more often with tall wives. This tendency paral- lels the "homogenous" diagonal (from upper left to lower right) in tables 4 and 5, and results in a deficit of the more extreme heterogenous matings of very short husbands with very tall wives. This deficit is the only thing which comes close to a ho- mogamous trend among Blacks. A similar deficit of short husbands with tall wives is apparent in assortatively mated Whites. However, among White couples there is a corresponding lack of the reciprocal type, i.e., tall husbands and short wives, whereas in Blacks there is an excess of tall husbands with short wives, especially apparent in the 4 X 4 format (table 5).

These results show that even though there is no correlation between Black spouses for stature, there is some assort- ment for this character. Black husbands are more often found in association with wives who are taller than themselves, except the extreme type S X T. This results in an excess of heterogeneous matings. No similar pattern obtains for White couples in which all heterogeneous matings are less than their expected values. A preference for one spouse to be taller than the other will lead to heterogamy and in the extreme to negative assortative mating. The tendency to negative assortative mating in Blacks is countered in this case by the lack of very short husbands with very tall wives. Hence, the Black spouse correlation is close to zero, but the distribution of husband-wife statures is not independent.

Other factors may influence the different degrees of assortative mating for stature in Blacks and Whites. As noted earlier the economic backgrounds of the two samples are different. Less assortative mating for body size among Blacks may reflect other priorities in mate selection in the lower economic situation. On the other hand, other physical characteristics, such as skin color, may take precedent over body size in Blacks (Taeuber, '34, cited by Spuh- ler, '68). Other groups of non-European descent do not practice assortative mating for body size, but do consistently practice mate selection on the basis of skin color (Pollitzer , Rucknagel, Tashian, Schreffler , Leyshon, Namboodiri and Elston, '70; Pol- litzer, Namboodiri, Elston, Brown and Ley- shon, '70; Baldwin and Damon, '73).

Traditionally, the husband-wife correlation coefficient has been used as a measure of assortative mating in human populations, the assumption being that all phenotypes are contributing proportion- ally the sam.e to a general trend of similarity. The husband-wife correlation, for exam- ple, is the parameter used in adjustments of estimated heritabilities of traits with assortative mating (Crow and Felsenstein, '68). Although statures of White couples appear to have a linear relationship to each other, assortative mating seems to be more complex in the Black sample. The effect of different levels of assortative mating for stature in Blacks and Whites on the value of the parent-child correlations for height in these samples, is considered else- where (Malina et al., '76).

ACKNOWLEDGMENT

The data upon which this study is based was supported by Public Health Service Grant 5TlDE109.

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differential contribution of stature phenotypes to assortative mating in parents of philadelphia...

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