I've always been fascinated by twins ("womb mates"; I stole that term from a 2004 article in The Economist). As far as I know, I am not one (my mother and father never told me so, anyhow), but my name, Thomas, does mean "twin".
I am particularly concerned about the frequency of twin births and about the non-independence of observations in studies in which some or all of the participants are twins. This chapter will address both matters.
Frequency
According to various sources on the internet (see for example, CDC, 2013;
Fierro, 2014):
1. Approximately 3.31% of all births are twin births, either monozygotic
("identical") or dizygotic ("fraternal"). Monozygotic births are necessarily same-sex; dizygotic births can be either same-sex or opposite-sex.
2. The rates are considerably lower for Hispanic mothers (approximately 2.26%).
3. The rates are much higher for older mothers (approximately 11% for mothers over 50 years of age).
4. The rate for a monozygotic twin birth (approximately 1/2%) is less than that for a dizygotic twin birth.
An interesting twin dataset
I recently obtained access to a large dataset consisting of adult male radiologic technicians. 187 of them were twins, but not of one another (at least there was no indication of same). It was tempting to see if any of their characteristics differed "significantly" from adult male twins in general, but that was not justifiable because although those twins represented a subset of a 50% random sample of the adult male radiologic technicians, they were not a random sample of US twins. Nevertheless, here are a few findings for those 187 people:
1, The correlation (Pearson product-moment) between their heights and their weights was approximately .43 for 175 of the 187. (There were some missing data.) That's fairly typical. [You can tell that I like to investigate the relationship between height and weight.]
2, For a very small subset (n = 17) of those twins who had died during the course of the study, the correlation between height and weight was
approximately .50, which again is fairly typical.
3. For that same small sample, the correlation between height and age at death was approximately -.14 (the taller ones had slightly shorter lives) and the
correlation between weight and age at death was approximately -.42 (the heavier persons also had shorter lives). Neither finding is surprising. Big dogs have shorter life expectancies, on the average (see, for example, the pets.ca website);
so do big people.
Another interesting set of twin data
In his book, Twins: Black and White, Osborne (1980) provided some data for the heights and weights of Black twin-pairs. In one of my previous articles (Knapp, 1984) I discussed some of the problems involved in the determination of the relationship between height and weight for twins. (I used a small sample of seven pairs of Osborne's 16-year-old Black female identical twins.) The problems ranged from plotting the data (how can you show who is the twin of whom?) to either non-independence of the observations if you treat "n" as 14 or the loss of important information if you sample one member of each pair for the analysis. 'tis a difficult situation to cope with methodologically. Here are the data. How would you proceed, dear reader (as Ann Landers used to say)?
Pair Heights (X) in inches Weights (Y) in pounds
1 (Aa) A: 68 a: 67 A: 148 a: 137
2 (Bb) B: 65 b: 67 B: 124 b: 126
3 (Cc) C: 63 c: 63 C: 118 c: 126
4 (Dd) D: 66 d: 64 D: 131 d: 120
5 (Ee) E: 66 e: 65 E: 123 e: 124
6 (Ff) F: 62 f: 63 F: 119 f: 130
7(Gg) G: 66 g: 66 G: 114 g: 104
Other good sources for research on twins and about twins in general
analysis (individual is "nested" within dyad); otherwise (and all too frequently) the observations are not independent and the analysis can produce very misleading results.
2. Kenny (2010). In this later discussion of the unit-of analysis problem, Kenny does not have a separate section on twins but he does have an example of children nested within classrooms and classrooms nested within schools, which is analogous to persons nested within twin-pairs and twin-pairs nested within families.
3. Rushton & Osborne (1995). In a follow-up article to Osborne's 1980 book, Rushton and Osborne used the same dataset for a sample of 236 twin-pairs (some male, some female; some Black, some White; some identical, some fraternal; all ranged in age from 12 to 18 years) to investigate the prediction of cranial capacity.
4. Segal (2011). In this piece Dr. Nancy Segal excoriates the author of a previous article for his misunderstandings of the results of twin research.
5. Twinsburg, Ohio. There is a Twins Festival held every August in this small town. Just google Twinsburg and you can get a lot of interesting information, pictures, etc. about twins and other multiples who attend those festivals
Note: The picture at the beginning of this paper is of the Bryan twins. To quote from the Wikipedia article about them:
"The Bryan brothers are identical twin brothers Robert Charles "Bob" Bryan and Michael Carl "Mike" Bryan, American professional doubles tennis players. They were born on April 29, 1978, with Mike being the elder by two minutes. The Bryans have won multiple Olympic medals, including the gold in 2012 and have won more professional games, matches, tournaments and Grand Slams than any other pairing. They have held the World No. 1 doubles ranking jointly for 380 weeks (as of September 8, 2014), which is longer than anyone else in doubles history."
References
Centers for Disease Control and Prevention (CDC) (December 30, 2013). Births:
Final data for 2012. National Vital Statistics Reports, 62 (9), 1-87.
Ferrio, P.P. (2014). What are the odds? What are my chances of having twins? Downloaded from the About Health website. (Pamela Prindle Ferrio is an expert on twins and other multiple births, but like so many other people she equates probabilities and odds. They are not the same thing.]
Kenny, D.A. (January 9, 2008). Dyadic analysis. Downloaded from David Kenny's website.
Kenny, D.A. (November 9, 2010). Unit of analysis. Downloaded from David Kenny's website.
Knapp, T.R. (1984). The unit of analysis and the independence of observations.
Undergraduate Mathematics and its Applications (UMAP) Journal, 5 (3), 107-128.
Osborne, R.T. (1980). Twins: Black and White. Athens, GA: Foundation for Human Understanding.
Rushton, J.P., & Osborne, R.T. (1995). Genetic and environmental contributions to cranial capacity in Black and White adolescents. Intelligence, 20, 1-13.
Segal, N.L. (2011). Twin research: Misperceptions. Downloaded from the Twofold website.
CHAPTER 6: VALIDITY? RELIABILITY? DIFFERENT TERMINOLOGY