Maureen Dowd's love life: a statistical analysis 
navigational aids: News ticker:

02 February 06.
Ms MKW of Washington, DC, was the third reader to point out to me an article by Maureen Dowd of the New York Times, so it's evidently time to give Ms Dowd's thesis a closer look. She explains that educated women have a disadvantage on the marriage market because boys prefer girls who are nonthreatening, less smart, and less successful. She cites an article by John Schwartz, also of the NYT, that cites an article by Stephanie Brown of UMich. Ms Dowd explains that this study demonstrated that males have a genetic aversion to dominant females. You know I have no patience for 'they did a study' hearsay, so here's the data [1].
The experiment is pretty simple: researcher shows to subject a photo with a story attached. The key point of interest in the story is that the person in the photo is a subordinate, a coworker, or a superior. The subject is then asked if the person in the photo is attractive for a onetime sexual encounter, for an activity partner (“would you like to exercise with this person”), or for a longterm relationship. Nine means absolutely and zero means absolutely not. Generally, you can see that when the boys rated girls, the mean floats around 6.5; when girls rate boys, the mean floats around 3.5. For the “would you exercise with him” question, the girls' means went up about a point. So policy implication number one: boys, ask her out for frisbee. Looking a little more closely, we see the anomaly that the paper and two New York Times articles are based on: boys rating an assistant for a longterm relationship rated her at the usual mean of 6.4; boys rating a boss rated her at a mean of 4.2.
That's it: a 2.2 point difference. The number after the ±
I was a little surprised by the use of the Ftest here, because we're comparing two means, which just screams of ttest to me. I checked some undergrad readings, and yes, this is the correct procedure for ANOVA on a multiway hypothesis. Here's the summary: the ttest is generally preferable, but it can only test for a difference between two numbers. To compare three means, or to test the hypothesis 'all the numbers in this subset of the table are not equal', you'll need the Ftest. So to check how males rate subordinate, equal, or boss females would need an Ftest, but to compare males rating subordinate or boss females, you can take your pick. Evidently, you'll get different results with the data they gathered. Which is all just to say that it is valid to apply a ttest and it fails to reject the hypothesis that the means of the two treatments are identical. Part of this may come from the experiment's design. Ms Dowd is interested in the question 'do boys like smart and successful girls', but the narrative in the study was: Please imagine that you have just taken a job and that Jennifer/John is your immediate supervisor. She/he is the person you report to on a daily basis. She/he has the responsibility for disciplining absence or poor performance on your part, for rewarding reliable or creative performance...Firing power is a whole 'nother bundle of goods beyond generally successful. If you want to claim that the data above as showing a statistically significant difference, then you can just as easily take the results to mean that boys are more concerned about their careers, or that girls are more trusting of those who could help or hurt them. Finally, and this is the least of my issues here, this is a study of 120 male and 208 female UCLA undergrads. The sample size of a few hundred is normal to large for this sort of work; for example, this academic study of pickup lines had only 142 F and 63 M subjects. But to say that UCLA undergrads speak for all of homo sapiens seems a bit much. The discussion links this to evolutionary theories about boys trying to work out who the father of a baby is. Our NY Times correspondents confidently cited the evolutionary results as proven by this paper. Me, I will refrain from commenting, since I'm unfamiliar with the evolutionary lit. But the structure of the paper itself is that nothing about how boys evolved is proven. Instead, the researchers ran a survey, and stated that it supports a certain existing hypothesis in the lit. Appropriately modest. Unfortunately, Ms Brown is not so understated in the press, and in another Dowd editorial, Ms Brown is directly quoted as stating “Powerful women are at a disadvantage in the marriage market”, and of course, the press eats it up. I have no clue how to find the study Ms Dowd attributes to “researchers at four British universities”, so I can't comment on whether it correctly supports Ms Dowd's claims or not. An SF Chronicle article says that that study only surveyed people born in 1921(!?).
Assortative matchingSince the microlevel literature left us flat, let's look at the demographic regularities. These are all based on education, which we take as a proxy for intelligence and success and whathaveyou.
Educational attainment means less marriageWelleducated women marry less. They're too busy working at their highpaying careers. On a related note, motherhood also takes a dive with higher education. [See the tables in [4], but bear in mind that most of them have a truncated Yaxis.]
People in school often marry each otherYes, I know it's obvious. When people in (or just out of) school randomly float around and bump into each other, they are more likely to show a high correlation in spouses' education levels than older outofschools bumping into and then marrying random people of broader educational attainment. See Mare [2]. So Ms Dowd's problem is not that she's welleducated but that she didn't get somebody during or just after grad school. Now that she's in the real world, the number of boys she will meet in the upper tail of the educational distribution will take a nosedive relative to the number she was meeting in grad school. But notice again that one could explain this with statistical mechanics (particles bumping into each other) without any recourse to a `boys seek out dumb chicks' story.
Level of education given marriedMichael Kremer [3] looks at the aggregate scale: some quick math shows that the correlation between spouses' educations was 0.649 in 1940 and 0.620 in 1990, indicating more disparity in spouses' education levels. But I find this to be too broad to answer the question we have. Education rates are going up over this period, marriage rates are shifting, and our question is primarily about the welleducated: do they show more or less assortative matching? For this, we look at page 21 of Mare [2], who provides more direct, disaggregated numbers:
Here's what we're looking at: I took the column for boys and girls with >16 years of education (i.e., a college education) and boys with 12 years of education (high school) in these periods, and calculated what percentage of them are matching with a spouse of the years of schooling at left. Each column sums to 100%. So in 1940, 31.74% of married collegeeducated boys were married to collegeeducated girls, while in the mid80s, 60.52% of married boys were wed to collegeeducated girls. That is huge, and we see a corresponding drop in the collegeeducated who marry the highschool educated. The high school educated boys were still mostly marrying high school educated girls in the second period, but both of the categories about marrying better educated girls showed an increase, and both of the categories about marrying less educated girls showed a decline. So this data says that even those with a high school diploma showed a stronger preference for an educated wife. For collegeeducated girls, the rate at which the married among them is matching to a collegeeducated boy is not moving nearly as much2.2 percent in forty years. [I leave as an exercise to the reader the fun of designing a data set where all of the above facts are simultaneously true. Hint: the unmarrieds have not been mentioned in any of the data above.] Overall, in 1940, 55.6% of married women were subhigh school educated; in the mid80s, 11.1% wereabout five times fewer. In 1940, 3.85% of married women were college educated; in the mid80s, 22.37% werea proportion over five times larger. [from [2], p 21] But, you retort, the number of collegeeducated girls has gone up significantly. Which is true, and the postcollege girlboy ratio is closer to 1.0 than it was in the 1940s, but the shift in this ratio is not at the scale of the shifts above. Here's the data (from historical tables A1 of the Census Bureau's educational attainment page)
You can see that the rate of college (plus postgrad) completion is way up all around, and the collegecompleted girl/boy ratio has gone from 69% to 96%. This is great, but is clearly only a fraction of the the doubling and quintupling of the percentages that we saw above.
Probability married given level of educationTable two is from 20 years ago; I'm mostly using it because it's so nicely broken down and says something about who boys are marrying. You are no doubt wondering about girls' odds today. The answer: college educated girls are doing increasingly better relative to highschool educated girls. Rose [4, table 3, p 42] defines the “success gap” as the probability that a college educated or more gal is married minus the probability that an exactly high school educated gal is married. In 1980, the success gap was 10.0 percent for her sample (U.S. women 4044); in 1990, the gap was 5.0 percent; and in 2000 it was 0.7 percent. That is, in 2000, a 4044 year old college graduate girl was more likely to be married than a comparable high school graduate girl. So this measure also fails to indicate any retrogression to the old days of dumb girls.To summarize my story of Ms Dowd's love life: educated women marry less. People who have been out of school a long time are less likely to marry those who match them, just as a matter of statistics. A person who only wants to date the top 5% on any scale is going to be rejecting 19 out of 20 comers by assumption. This sums up to mean that a single, graduateeducated gal over 40 will have a much tougher time marrying a graduateeducated boy than she did twenty years ago. Also, a single graduateeducated boy will have a tougher time marrying a graduateeducated girl than he did 20 years ago. However, none of this has to do with cultural trends regarding what boys want: the trend since the 1940s has been toward boys of all levels marrying increasingly welleducated girls, and any education penalty that may have existed for women in the past has evaporated. There will always be the arse at the bar who turns tail at the first sound of educationand I as an overeducated boy have at times had exactly the same experiencebut that does not quite make for a national trend.
PSOur educated liberal desire to find a mate of equal abilities directly contradicts our educated liberal desire to reduce inequality. Kremer [3] argues against this one, but it's so intuitive that the common economic wisdom takes it as all but given: assortative mating increases class inequality. Back in the day, the poor girl could marry the rich boy and thus become unpoor. But now, Ms Dowd thinks it is a condescending affront that the rich boy marry anyone but a rich girl, and that means that poor girl is going to stay poor. We lament the widening of class boundaries, but what could widen them more than a New York Times editorial excoriating upper class boys for associating with lower class girls?
[1] @articlebrown:dominance,
[link] [2 comments] Replies: 2 comments
