Everybody is interested in sex, age, height, and weight. If all you know about a person is his(her) sex, age, height, and weight, you have a pretty good idea regarding what he(she) looks like [even without checking the Photographic Height/Weight Chart website.] Differences between males and females are discussed all of the time. (Vive la difference?!) Age is sometimes the only identifier in a news item. (Example: “57-year-old jumps from Golden Gate Bridge.”) Whole books have been written about height and weight, both collectively and separately. I can't think of any other variables that are both of general interest and have been studied so thoroughly. So what I have tried to do in this book is to share with you some of the information about sex, age, height, and weight that I have accumulated in the last 30 years or so. I hope you'll find it to be both enlightening and entertaining.
The first three chapters in what follows are devoted to sex (but not in the way that you’re thinking)--its measurement, the percentages of males and females in various populations, and a brief summary of the literature on sex differences. [The word “effect” appears in the title of Chapter 3 and some of the other chapters. It and the associated word “cause” will usually appear inside of quotation marks throughout this book. Sex, age, height, and weight are neither “manipulable” nor “randomly assignable”, so it is difficult if not impossible to determine whether or not they are “causes” of anything.]
The next seven chapters address age in most of its ramifications, including its measurement and the relationship between age and other variables.
Chapters 11-20 are devoted to height and weight--how to measure them, their frequency distributions in various populations, and lots of other things about those two variables.
The final chapter (21) is concerned with the “effect” of sex, age, height, and weight (in various combinations) on a number of interesting variables. That chapter includes some interesting real data for sex, age, height, and weight, plus one additional variable (cholesterol). Several analyses regarding those data are carried out and the results are summarized.
No special background is necessary for following the narrative. A modest familiarity with basic statistical concepts and a smattering of knowledge about research design and measurement should be sufficient.
I shall use the word SHAW as an acronym for sex, height, age, and weight. That’s not the right order, “covariately speaking”, since sex is more basic than age, which in turn is more basic than height, and weight is least basic, but SAHW is unpronouncible as are most of the other permutations of the letters S, A, H, and W. I also toyed with WASH, but that didn’t wash (bad pun), so SHAW it is. [I also am an admirer of the writings of George Bernard Shaw. If you haven’t yet read his marvelous essay, “The vice of gambling and the virtue of insurance”, please do so. You’ll have a real treat in store for yourself.]
TABLE OF CONTENTS
Chapter 1: THE MEASUREMENT OF SEX
Chapter 2: THE DISTRIBUTION OF SEX IN VARIOUS POPULATIONS
Chapter 3: THE “EFFECT” OF SEX
Chapter 4: THE MEASUREMENT OF AGE (FROM WOMB TO TOMB)
Chapter 5: THE USE OF COMPUTER PROGRAMS TO CALCULATE AGE
Chapter 6: THE DISTRIBUTION OF AGE IN VARIOUS POPULATIONS
Chapter 7: DIFFERENT KINDS OF AGES
Chapter 8: THE “EFFECT” OF AGE
Chapter 9: LIFE EXPECTANCY AS A FUNCTION OF AGE
Chapter 10: AGE ON OTHER WORLDS
Chapter 11: THE MEASUREMENT OF HEIGHT
Chapter 12: THE MEASUREMENT OF WEIGHT
Chapter 13: THE DISTRIBUTION OF HEIGHT IN VARIOUS POPULATIONS
Chapter 14: THE DISTRIBUTION OF WEIGHT IN VARIOUS POPULATIONS
Chapter 15: THE RELATIONSHIP BETWEEN HEIGHT AND WEIGHT
Chapter 16: ESTIMATING HEIGHTS AND WEIGHTS
Chapter 17: "IDEAL” WEIGHT
Chapter 18: BMI, BSA, BIA, and BMR
Chapter 19: THE “EFFECT” OF HEIGHT
Chapter 20: THE “EFFECT” OF WEIGHT
Chapter 21: THE COMBINED “EFFECT” OF VARIOUS SHAW SUBSETS
CHAPTER 1: THE MEASUREMENT OF SEX
For most purposes there are only two ways to measure the sex of a person:
Ask the person to self-report whether he(she) is male or female; or
Look at the person and make the judgment.
The first of these is by far the more commonly employed, especially on questionnaires, which typically have two boxes labelled M and F, with the respondent asked to check one. But in some studies, e.g., quota-type surveys conducted in shopping malls or other public places, the investigator seeks out so many males and so many females by “eyeballing” who is which sex.
Babies at birth present an interesting sex measurement situation exemplified by the second method. The obstetrician, nurse, or midwife takes a look and proclaims “It’s a boy!” or “It’s a girl!”. [See the opening paragraph of the book by Diane Halpern (2000).] Sex can of course also be determined pre-natally by amniocentesis or ultrasound, whereby the mother herself can do the proclaiming.
Reliability and validity of the measurement of sex But are these two methods reliable and valid? If a person reports himself (herself) as male (female) on a particular questionnaire on a given day, will he (she) also report himself (herself) as male (female) on a subsequent administration of that same questionnaire? Likewise for the eyeballer. And is the target person REALLY male (female)?
You may be tempted to say “Of course” to all of those questions. Why would a respondent not check the same box on both occasions? I can think of at least two reasons: (1) inattention (in hurrying through the questionnaire the person checks one of the boxes the first time and the other box the second time); and (2) orneriness (some people like to louse up researchers). How about the eyeballer? Again those same two reasons, plus a third one: The target person may have originally appeared to be of one sex but subsequently appeared to be of the opposite sex (perhaps due to a change of attire or hair style).
The preceding paragraph is concened with the reliability (consistency) of the measurement process. The “REALLY” question is one of validity. Would a female respondent check the male box (that’s a terrible pun) or a male respondent check the female box? Perhaps; and for the same reasons alluded to for unreliability, plus: if the time between the two administrations of the questionnaire is fairly long, an actual sex change may have occurred in the interim [unlikley, but possible]. And for the observational indication of sex there is the additional problem that things are occasionally not what they seem to be. Boys with long hair are often taken for girls, for example, and newborns’ genitalia are sometimes not perfectly differentiable.
Sex vs. “gender” That leads naturally to one of the most confusing (to me, at least) problems in the “measurement” of sex, viz., what do we call the variable? Up until the last 50 years or so the word “sex” was always used to designate the male/female distinction. The word “gender” was strictly a grammatical term that identified nouns in various languages (not English) as masculine, feminine, or (for Latin) neuter according to their endings. It is now frequently the case that the word “gender” has replaced “sex” not only on questionnaires but also in popular discourse. There are allegedly important differences between the two words, as specified in the following quotation:
“Researchers should specify in publications their use of the terms sex and gender. To clarify usage and bring some consistency to the literature, the committee recommends the following:
• In the study of human subjects, the term sex should be used as a classification, generally as male or female, according to the reproductive organs and functions that derive from the chromosomal complement.
• In the study of human subjects, the term gender should be used to refer to a person’s self-representation as male or female, or how that person is responded to by social institutions on the basis of the individual’s gender presentation.
• In most studies of nonhuman animals the term sex should be used.”
(Institute of Medicine, 2001, Recommendation 7, page 8)
[Leonard Sax (2005), author of the book Why gender matters, and advocate of single-sex public education, doesn’t like the IOM’s recommendation. I don’t either, especially the definition of gender, which is circular. But I never use the term “gender” anyhow.]
You would not be aware of the sometimes subtle distinctions between the terms “sex” and “gender” by perusing much of the literature, however. I’ve seen books and articles devoted to studies of the differences between the sexes (genders?) in which approximately half of the citations are to sources with “sex differences” in their titles and the other half have “gender differences” in theirs. In her 1998 book, The two sexes, Eleanor Maccoby, one of the world’s leading authorities on the psychological differences between males and females, used the words sex and gender completely interchangeably. (For some other “takes” on sex vs. gender, see Halpern, 2000, Bullough, 2005, and the chapters by Poston and by Riley in the 2005 Handbook of population.) Interestingly, the internet encyclopedia Wikipedia has separate long articles on sex differences and gender differences, with the entry on sex differences having been “tagged” in July, 2007 for alleged inaccuracies.
CHAPTER 2: THE DISTRIBUTION OF SEX IN VARIOUS POPULATIONS
A note regarding the word “distribution” When I use the word “distribution” in this chapter and throughout the rest of the book I am referring to the statistical frequency distribution of a variable and not to any of the other meanings of “distribution”.
The world (in the year 2000) The exact figures are not known, since some countries don’t conduct censuses or don’t carry them out very well, but the UN estimated that there were approximately 3 billion males (50%) and aproximately 3 billion females (50%) in 2000, with males slightly outnumbering females (primarily because of the 1.02 male-to-female sex ratio at birth). [At the time of the writing of this paragraph in July, 2007 the best approximation, provided by the CIA in The World Factbook, 2003, was 3.32 billion males and 3.28 billion females.]
The United States as a whole (2000 census) In the year 2000 there were approximately 138 million males (49.1%) and 143 million females (50.9%) [the actual numbers provided by the Census Bureau are 138,053,563 and 143,368,343, but some people are missed and others are double-counted, even in the most careful censuses]. The “sex breakdown” varies considerably with respect to age (that matter will be examined in Chapter 6) and other variables.
The United States as a whole (projection for the year 2050) Males: 193,234,000 (49.1%)
Females: 200,696,000 (50.9%)
Same “breakdown” as 2000, at least to the nearest tenth of a percent. How dull.
(Source: U.S. Department of Commerce, 1996, Middle Series, Table 2, page 88)
Police officers, U.S. 595,000 (88.4%) 78,000 (11.6%)
CHAPTER 3: THE “EFFECT” OF SEX
Certain differences between males and females are rather obvious, e.g., anatomical features, height and weight discrepancies, and the like, and such
differences will be given no more than a cursory mention in this chapter. But there is a vast literature regarding not-so-obvious differences, and it is to a brief summary of that literature to which I would now like to turn. The major emphasis will be on “big” differences, with passing references to “small” differences. The samples upon which the differences have been determined vary in both size and representativeness, so if you look up any of these sources please keep that in mind. Also keep in mind that certain claims regarding the presence or the absence of sex differences are politically controversial (see, for example, Eagly, 1995 and the comments regarding her article that appeared in a subsequent issue--February, 1996--of the American Psychologist).
Note 1: The discussion will be limited to differences between males and females as biologically identified. No attention will be given to “masculinity” and “femininity”. (See Maccoby, 1998 regarding various definitions of those terms---if you’re interested.) And although the terms “gender differences”, “sex-related differences”, and “gender-related differences” are used in the titles of some books and articles concerned with the differences between males and females, I will not use any of those terms. “Sex differences” will do just fine.
Note 2: If what follows strikes you as too extensive and/or too complicated, just read the dictionary of sex differences with the delightful title, Why Eve doesn’t have an Adam’s apple, by Carol Ann Rinzler, and you’ll get the picture. That book is a little outdated (1996) and was apparently written primarily for young adults (the copy that I borrowed from our local library has a YP before the Dewey Decimal System 612.6 designation). If you find that too “babyish” (which I doubt), go on to read science writer Robert Pool’s 1994 book with the equally intriguing title, Eve’s rib. He writes extremely well about sex differences and the studies upon which claims regarding such differences have been made. [There are at least three books with the title, Eve’s rib; the other two that I know of are by Nowak(1980) and by Legato (2002). All deal with sex differences.]
Big differences What is a “big” difference? It is a difference that (a) leaps out at you; and/or (b) equals eight-tenths or more of a standard deviation [Cohen’s (1988) “large” effect size]; and/or (c) is statistically significant yet not based upon a huge sample size for which statistical significance, but not necessarily practical significance, is almost guaranteed. Here are some of those differences:
Jumping from Golden Gate Bridge: In my Preface I gave jumping from that bridge as a hypothetical example of a news headline. There recently (August 1, 2007) appeared the following headline in USA TODAY: “Most Golden Gate jumpers are local”. The writer (John Ritter) goes on to say that of 203 people confirmed to have jumped in the ten-year period from July, 1997 to July, 2007, males outnumbered females by approximately 3 to 1 (i.e., 75% of the jumpers were males). [Please forgive me for starting with this one. I just found it to be extremely interesting.]
Users of the filler word “like”: Three teenagers at a Scarsdale, NY high school (Thomas Levine, Andrea Nehorayoff, & Ariel Millhauser, 2007) studied the use of that annoying (to many people) word by males and females at their school. They found that it was used statistically significantly more often by females than by males. [I also found this study to be extremely interesting, and particularly impressive in that it was apparently carried out by those three students under the guidance of, but with little or no other assistance by, their teachers.]
The senses: Females generally have much greater acuity in hearing (see Corso, 1959; 1963). There is some evidence that males have slightly better visual acuity (McGuinness, 1976). See also the section on perceptual and motor skills in Halpern (2000).
Finger lengths: The ring fingers of males are usually longer than their index fingers, whereas those two fingers are of approximately equal length for females. There is some evidence that the ratio of ring finger length to index finger length is predictive (but of course not necessarily causally) of several variables, including academic ability and aggression! (See Manning, 2002 and Eachus, 2007.)
Health: In the long chapter entitled “Sex affects health”, the contributors to the Institute of Medicine’s book on sex differences point out that males and females have different patterns of illnesses, and all are not necessarily attributable simply to their “maleness” or “femaleness”. For example, the prevalence of obesity is greater for females than for males, especially for certain ethnic groups (see their Table 5-4). And males and females differ considerably in their reactions to drugs and to drug dosages.
Pain: Females are more sensitive than males to pain, but seek more help to alleviate it and derive more relief from such help. (See, for example, Berkley, 1997a,b; Unruh, 1996; Unruh, Ritchie, & Merskey, 1999.)
Automobile accidents: Males are much more likely to be involved than females, with males constituting about 73% of all traffic fatalities. See Evans (2006) for this and much more regarding sex differences in driving behavior.
Infant mortality: Greater for males. In the United States the male-to-female sex ratio at birth of approximately 1.05 drops considerably to almost 1.0 by one year of age because of that, and stays fairly close to 1.0 until about age 65, where it becomes about .70, i.e., there are many more females than males in the older age groups. See, for example, The (CIA’s) World Factbook, 2003.
Life expectancy: Consistently higher for women, by approximately five or six years. Some claim that the difference has been largely attributable to the difference in smoking prevalence for the two sexes (see, for example, Gorman & Read, 2007 and the references cited therein), and, if so, the difference in life expectancy should narrow as the percentages of both male smokers and female smokers get smaller and closer together.
Mathematical ability: The seminal work was carried out by Benbow and Stanley (1980) and reported in a brief three-page article in the prestigious journal, Science. In their study of 9927 gifted junior high school students they found that the boys scored considerably higher than the girls on the quantitative section of the Scholastic Aptitude Test (SAT), which was and still is intended for high school students. Their findings caused an uproar in the research community, mainly by advocates of the nurture side of the nature vs. nurture controversy (see, for example, Schafer & Gray, 1981), but Benbow and Stanley held their ground (see Benbow & Stanley, 1981, 1983; and Benbow, 1988 for their rejoinders). [As Pool (1994) points out, there is a surprisingly small difference between males and females on the verbal section of the SAT, however. See Hyde & Linn, 1988 for a meta-analysis on that topic.]
Intelligence: As you can imagine, whether or not females are smarter than males or males are smarter than females is even more controversial than the reported findings of sex differences in mathematics. Two of the best sources for empirical evidence regarding sex differences in intelligence are Feingold (1988) and Halpern (1989, 1997, 2000)--see also Bennett (1996, 1997) for differences in how males and females estimate their own abilities. A complicating factor is that some psychologists claim there are different “intelligences”, with respect to which males excel on some (e.g., spatial visualization--see Sanders, Soares, & D’Aquila, 1982 and Masters & Sanders, 1993) and females excel on others (e.g., memory--see McGuiness, Olson, & Chapman, 1990). But this is what one psychologist had to say: “Are men smarter than women? The answer to the above burning question is: No, they are not. Data are now being laid on the table that show that, on average, men and women are equal in mental ability.”
[Seligman, 1998, p. 72, cited in Halpern, 2000, p. 81.]
Income, adults age 15+: Huge difference in favor of males in general (see, for example, Figure 3, page 11 in DeNavas-Walt, Proctor, & Lee, 2006), and for male psychiatrists in particular (see Weeks & Wallace, 2007), although the gap in earnings between males and females in most occupations and professions seems to be narrowing, if one takes into account welfare [in the general economic sense, not in the governmental-dependent sense] as well as income (see Murphy, 2003).
So what? Males and females differ in lots of respects. Is there anything we can do about it? Do we want to do anything about it? The answer to the first question is: Sometimes. The answer to the second question is: Yes, if that would help to minimize sex discrimination.
Some of the things we can’t and/or don’t want to do anything about are jumping off Golden Gate Bridge and finger length. Some of the things that we can and should do something about are differences in the use of “like” as a filler word and income. For most of those differences the best strategy is not to reverse the direction of the difference (nobody wants to make males use “like” more often than females do, for example) but to try to put in place some educational interventions that might help to equalize the sexes (better training in spatial visualization for females? sensitivity training for personnel decision-makers regarding salaries for females and males who perform the same jobs?) Most sex differences are likely to be with us for a long time, however.
CHAPTER 4: THE MEASUREMENT OF AGE (FROM WOMB TO TOMB)
Gestational age Let’s start at the very beginning. How do we measure the age of a newborn, i.e., gestational age? There are actually three or four competing approaches to that problem:
1. Subtract date of conception from date of birth.
2. Subtract date of last menstrual period from date of birth.
3. Use the Dubowitz/Ballard scale.
4. [Not recommended, by me anyhow.] Use clinical observation and experience, without incorporating any sort of scale or calculation.
It goes without saying that date of conception is very difficult to determine (how can we know?) but date of last menstrual period is easily approximated since most women are very conscious of the timing of their menstrual periods.
The Dubowitz/Ballard scale was originally two different scales, one due to Dubowitz and the other due to Ballard, but they have been combined into one:
The Dubowitz/Ballard Examination evaluates a baby's appearance, skin texture, motor function, and reflexes. The physical maturity part of the examination is done in the first two hours of birth. The neuromuscular maturity examination is completed within 24 hours after delivery.
The physical assessment part of the Dubowitz/Ballard Examination looks at physical characteristics that look different at different stages of a baby's gestational maturity. Babies who are physically mature usually have higher scores than premature babies.
Points are given for each area of assessment, with a low of -1 or -2 for extreme immaturity to as much as 4 or 5 for postmaturity. Areas of assessment include the following:
skin textures (i.e., sticky, smooth, peeling).
lanugo (the soft downy hair on a baby's body) - is absent in immature babies, then appears with maturity, and then disappears again with postmaturity.
plantar creases - these creases on the soles of the feet range from absent to covering the entire foot, depending on the maturity.
breast - the thickness and size of breast tissue and areola (the darkened ring around each nipple) are assessed.
eyes and ears - eyes fused or open and amount of cartilage and stiffness of the ear tissue.
genitals, male - presence of testes and appearance of scrotum, from smooth to wrinkled.
genitals, female - appearance and size of the clitoris and the labia.
Six evaluations of the baby's neuromuscular system are performed. These include:
posture - how does the baby hold his/her arms and legs.
square window - how far the baby's hands can be flexed toward the wrist.
arm recoil - how far the baby's arms "spring back" to a flexed position.
popliteal angle - how far the baby's knees extend.
scarf sign - how far the elbows can be moved across the baby's chest.
heel to ear - how close the baby's feet can be moved to the ears.
A score is assigned to each assessment area. Typically, the more neurologically mature the baby, the higher the score.
When the physical assessment score and the neuromuscular score are added together, the gestational age can be estimated. Scores range from very low for immature babies (less than 26 to 28 weeks) to very high scores for mature and postmature babies.
[Source: University of Virginia Health System website]
Traditional chronological age After birth has taken place the usual way to measure age is to subtract date of birth from date at which age is to be determined. That sounds straightforward enough, but it can be a bit tricky, primarily because three variables are involved (month, day, and year) and things can get complicated. For example, how old on June 6th, 2008 would a person be who was born on September 19th, 1969? Setting it up like a typical subtraction problem we have:
Month Day Year
6 6 2008
- 9 19 1969
Hmmm. We can’t subtract 9 from 6 or 19 from 6, but we can subtract 1969 from 2008. In order to do the Year subtraction, however, we must first convert the Month and the Day for the later year (2008) to the 17th month and the 36th day of 2007. (June 6th, 2008 is the sixth day of what would be the 18th month of 2007, but it would be the 37th day of the fifth month--May--of 2007.) That gives us:
Month Day Year
17 37 2007
- 9 19 1969
Carrying out the subtraction, this person would be 38 years, 8 months, and 18 days old on June 6th, 2008. One might want to round this down to 38 (years of life completed) or round up to 39 (since the person is closer to 39 years of age than to 38).
Age of skeletons If death has taken place, and the age of the decedent is unknown, age at death can be estimated by the use of various forensic methods. Samworth and Gowland (2005) have summarized some of those methods and the statistical assumptions upon which they are based. Most methods involve skull or teeth measurements, or, occasionally, both. A fascinating example of forensic identification is "Earl", a skeleton whose sex, age, height, and weight were estimated by Terrie Winson (Kutztown University, PA). See her website for all of the details; its address is www.anthro4n6.net/forensics. And see Chapter 16 for forensic estimation of the heights and weights of corpses.
CHAPTER 5: THE USE OF COMPUTER PROGRAMS TO CALCULATE AGE
In the previous chapter I referred to the traditional measurement of age by subtracting date of birth from current date (rounding down or up, as desired). That calculation is a rather difficult arithmetical exercise, as illustrated by the example in that chapter. Fortunately, computers (actually computer algorithms) have come to our rescue. There are five readily-available routines for calculating one’s age. In order of my preference (from most to least), they are:
1. The marvelous Age Calculation Machine (www.geocities.com/Athens/Troy/8697/agecalculator.html), whereby you enter only your date of birth (to the nearest year, month, day, hour, minute--however accurately you know it) and it returns your age as of the current date (it knows what that is) to the nearest millisecond (!) right before your eyes, as well as the time to your next birthday. Amazing.
2. Pete Russell’s “Your Age in Days” webpage (www.peterussell.com/age.html). Input date of birth; output age in days.
3. The AGS Publishing Age Calculator (www.agsnet.com/). Input date of birth, output age in years, months, and days.
4. The SAS command age = INT ( (today( ) - db) / 365.25 )
where today() is the function that calculates the number of days between October 15th,1582 and the current date; db is the person's date of birth; and INT is the function that subtracts the integer part of the result from the number of years.
where $jdate is the system variable that returns the number of days between that same date of October 15th, 1582 and the current date, using the Gregorian Calendar; xdate.year, xdate.month, xdate.mday are functions that extract year, month, day from db (date of birth); yrmoda is the function that calculates the number of days between October 15th,1582 and the date of birth; and trunc is the function that extracts years minus the integer part of the result.
CHAPTER 6: THE DISTRIBUTION OF AGE IN VARIOUS POPULATIONS
The U.S. in the year 2000
In the table that follows I have reproduced from the CensusScope website the distribution of age, by sex, in the United States in the year 2000. Here are the numbers and the corresponding percentages).
Age Distribution by Sex, 2000
As you can see, there were more men than women under age 34, due primarily to the well-known phenomenon that in any given year there are more male births than there are female births. But thereafter there were more women than men, and the difference was greatest at the older ages, with almost three times as many women as men in the 85+ age group.
Two unusual distributions
But those data are for the population of the entire country. Here are the age distributions for two places with quite different populations for that same year (the first is for Grant County, North Dakota; the second is for Orange County, Florida):
Age Distribution by Sex, 2000 Grant County
Age Distribution by Sex, 2000 Orange County
As you can see, the Grant County distribution has proportionally more people in the 85+ age group than for the entire country, whereas the Orange County distribution has proportionally more in the younger age groups. [Although the state of Florida as a whole has a fairly high concentration of retirees, such is not the case for Orange County.]