Single-sex Vs Co-ed: Is One Better Than the Other?

Keywords: Education: Statistics;

Ruth Laugesen of the Sunday Star Times asked me to look at differences between academic performance between single-sex and co-ed schools. Her summary report is “Same-sex Schools’ Success” (September 14) is in an appendix below, the longer report is “In a Class of Their Own” This paper summarises my findings.

It is generally recognised that students at single-sex schools have a higher exam attainment than those at co-educational schools. Why this is so, is much disputed. Not surprisingly, the advocates of single-sex schools claim they are ‘better’ educationally while the co-eds are likely to argue that the students to the single-sex schools represent a more academic or socially advantaged group.

This report does not attempt to sort these arguments out. Rather, every statistician (indeed, every detective) knows that association does not prove causation. That two statistics correlate (or two events occurred close together) does not prove one effected the other. There are a number of other reasons why the association may be evident. A common one is that there is a third variable which is impact on the two simultaneously. If one ‘controls’ for this third variable the association disappears.

So I controlled for the socioeconomic status of the school populations. Almost every New Zealand secondary school is allocated to a decile related to the socioeconomic characteristics of its students, ranging from 1 at the bottom to 10 at the top. The deciles are used for funding, so that those private schools that are not in receipt of this funding do not need to have a decile ranking. Some do, and I was able to allocate most of the rest on the basis of reputation. (I add that omitting them would have hardly changed the conclusions.)

The performance achievement measure was the proportion of the fifth form students who got in 2002 a NCEA level 1 qualification, roughly equivalent to the old school certificate. It is not an ideal measure, but it is the best we have. Note that schools can manipulate their pass rate – they are more likely to expel or move on a student who wont pass. Hopefully these are not major effects, but Auckland Grammar posed a problem, because its top stream boys, over half of the year, do not sit NCEA but an international examination. So only their weakest students sit the NCEA and they have a lower pass rate than if the school was to have all its students sitting. In the calculations I assumed all their students who took on the tougher challenge, would have passed NCEA. A few failures would not affect the results much, nor would have dropping Auckland Grammar altogether. (Ruth, who did all the foot slogging that statisticians really appreciate, could not identify any other schools where this effect would be important. If any readers know of similar examples, please contact me and I will adjust for them too.)

The Table below summarises the published data:

NCEA Pass Rate for Fifth Form Students by School Decile

Decile Co-ed
Sex: Boys
Sex: Boys
Sex: Girls
Sex: Girls
1 21.4% 41.5% 25.5% 40.4%
2 27.9% 30.4% 34.9% 57.7%
3 35.6% 43.1% 41.4% 67.7%
4 39.7% 49.3% 52.9% 58.1%
5 46.0% 56.8% 58.6% 63.2%
6 50.3% 57.6% 60.6% 68.9%
7 54.7% 59.5% 64.9% 76.6%
8 59.6% 68.7% 70.8% 75.5%
9 64.4% 69.3% 75.8% 81.5%
10 68.8% 80.9% 77.0% 88.5%
Average 48.3% 65.6% 58.0% 76.0%

Before looking at the single-sex to co-ed comparison, there are three other points which the table demonstrate, and which, it seems to me are, more important.

Point 1: Irrespective of the type of school, there is a clear gradient in the pass rate from the lowest decile to the top one. Whatever the reason for the gradient it is surely a matter of considerable concern, which the higher funding of to low sociol-economic schools is only partially addressing.

Point 2: Irrespective of the type of school, girls do better than boys. Again this is a matter of social concern. (As I recall, this is originally what Ruth Laugesen was investigating. One of the responses, was the claim that boys did better in boys’ schools because they better addressed boy’s problems. That cant be really be right, because girls also do better in girl’s schools too, so one cannot say that co-eds are biased against boys.)

Point 3: There is considerable variability around this trend. I’ll come back to this after addressing the single-sex versus co-ed issue.

What the bottom line of the table shows is that boys do better in NCEA in boys schools than in co-eds. Whereas 65.8 percent of the boys in single-sex schools pass, only 48.3 percent of those in co-eds do. Similarly 76.0 percent of girls in girls schools pass NCEA, compared 58.0 percent in co-eds. The differences are 17.3 percentage points for boys and 18.0 percentage points for girls, much the same difference.

However the single-sex schools tend to have higher socioeconomic intakes, and we know from Point 1 that intake matters. So we would expect them to do better in total. But when we look at the table we find that in every school decile group the students from single-sex schools do better than same gender students at co-eds.

One could use a lot of complicated statistical techniques to separate out the effects of sociol-economic differences but I use a very simple one here. The average of the difference within each school decile is 8.8 percentage points for boys and 11.4 percentage points for girls. So we can say that 8.5 (i.e. 17.3-8.8) percentage points of the boys’ schools’ pass superiority is because they are in higher decile on average. The difference for girls’ schools is 6.6 (18.0-11.4) percentage points. Arithmetically 49 percent (8.5/17.3) of the boys’ school superior performance and 37 percent (6.6/18.0) of the girls’ schools superior performance is explained by sociol-economic intake.

Whoops. Girls’ schools add more to their students’ pass rate do better than boys’ school. Perhaps the two numbers are statistically the same (due to sampling error) but they certainly confound some of boys’ schools claims. But in any case

Point 4: Between a third and a half of the apparent pass superiority off single-sex schools is due to the higher socioeconomic intake of the schools.

What determines the rest? It is easy to claim a superior teaching environment, and perhaps the rhetoric is right. But there are possibilities. Earlier studies (this is a well canvassed area – the point of this little exercise is it is the first time it has applied to NCEA, which only began in 2002) investigated whether the students who went to single-sex schools were brighter on intake than those as co-ed, although they have come to no agreed conclusion. I think parental attitude is important. Perhaps parents who are very academically ambitious for their children observe the better results in single-sexes and send their children there, with the parental background in part driving the better results.

However, one thing did strike me about the results, which is not so evident in the table. There was considerable variation from the averages. One such anomaly, evident in the table is that the two decile 3 girl’s schools did better than decile 4 and 5 girl’s schools.

But I also observed the three large co-eds (one each in decile 7, 8, and 9) which had higher pass rates for their boys than the average of the boys’ decile 10 schools. How did that come about? (I report only ‘large’ with more than 40 male students, to reduce statistical variability.) And I found eleven more which did better than the lowest of the top decile boys’ schools, one of which was in decile 5. So single-sex is not everything, even if the only interest is passing exams.. Which is why Ruth’s feature finishes by quoting me:

Easton said his study results showed enough variation between the performance of individual schools, that parents should weigh up a variety of factors in making their choice. "While single-sex or co-ed may be a factor in making a choice, there are many other factors, which are relevant and still need to be investigated," said Easton.

There are statistical techniques such as ANOVA which might shed more light onto the issue, and would probably refine the precision of the conclusions. any one interested in applying them should get in contact with me for the data.

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APPENDIX from the Sunday-Star Times, Sunday , 14 September 2003


Boys at single-sex schools enjoy more academic success than those in co-ed schools, according to new research commissioned by the Sunday Star-Times.
The research – the first indepth analysis of last year’s NCEA exams – is a big boost for boys-only schools.
For years the schools have fought criticism that they are lacklustre, too conservative, too exclusive and hotbeds of bullying.
There has also been a perception that boys perform better academically in mixed classes.
Most New Zealand students go to co-ed schools, which outnumber single-sex schools by about three to one.

Economist Brian Easton was commissioned by the Star-Times to analyse pass rates for the NCEA level 1 qualification, which replaced School Certificate last year.
Girls-only schools also came out well, with their students doing better on average than girls at co-eds.
Haylon Smith, a 17-year-old student at Westlake Boys’ High School, a public school on Auckland’s North Shore, was not surprised by the findings.
“At a boys school you can just get down and work. You can concentrate on your sport, on your schoolwork, and not have to worry about the other sex.

“We’re pushed to do the best in academic achievement and sports. Our headmaster expects the best from us and tell us that every day.”
The results compared schools within the same decile. Deciles measure the socio-economic status of the communities students are drawn from, with more well-off areas typically having better pass rates. At every decile level, students from single-sex schools did better than boys and girls at comparable co-ed schools.
The results have been welcomed by boys schools, but greeted with some scepticism by the president of the Secondary Principals Association, Paul Ferris.
He said such research would only “sow the seeds of doubt” in parents’ minds about co-educational schools.
Such results were only averages, and it was important for parents to look at the performance of individual schools, he said.

Westlake Boys’ High headmaster Jim Dale said he believed boys at co-ed schools were missing out on teacher attention these days, because girls were now performing so strongly.
Girls had a head start on boys because of their greater maturity at an earlier age, said the headmaster.

“When those girls start to excel, through not fault of their own, they probably take up a greater amount of teaching and learning time because the teacher in front of the class is very motivated to teach the ones who at that stage in their development are beginning to shine,” said Dale.
At boys schools, boys benefited from the fact their teachers had high expectations of them.
Boys schools were also able to tailor their teaching to boys’ preferred learning style, with a competitive, highly structured environment.
Sports were “absolutely critical”, allowing the confidence from achievement in the sporting arena to spin off into confidence in the academic area, said Dale.

The associated feature article is “In a Class of Their Own”

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