Gender, single-sex schooling and maths achievement

The study uses a nationally representative sample from a well-designed longitudinal survey, with maths scores from a standardised test administered by fieldworkers rather than classroom teachers. Ireland's large public single-sex school sector is a genuinely useful setting for this question, better than the US or UK where single-sex schools are rare and selective.

The problem is the distance between the design and the causal claims. The paper argues school-type assignment is "effectively random," but the evidence for this comes from a separate survey of 443 parents (not the study sample) and from summary statistics that show large observable differences — most notably the 30-percentage-point urban concentration difference. The paper controls for urbanicity with a binary variable, but that is a coarse adjustment for what is likely the single largest source of confounding. The instrumental-variables analysis uses urban location as an instrument, which requires assuming it has no direct effect on maths scores — a stronger assumption than the paper acknowledges. The study also never examines whether Irish single-sex and coeducational schools actually differ in teaching practices or classroom dynamics, so the null finding could mean either that single-sex schooling doesn't help or that these schools don't differ in the ways that would matter.

The probit models are correctly specified, marginal effects are clearly reported, and the paper applies appropriate sampling weights and clustering adjustments. The robustness checks — bivariate probit, birthweight controls, sensitivity analysis — are genuine and well-executed, with internally consistent numbers across all tables.

Three problems reduce confidence. First, the paper never formally tests whether the gender gap in single-sex schools (9.4 percentage points) differs from the gap in coeducational schools (5.9 points). Given the standard errors, the 3.5-point difference cannot be distinguished from zero, yet the abstract presents it as a finding. Second, the study reports no power analysis. With about 1,000 students per gender in single-sex schools, the study could detect only effects of roughly 6–7 percentage points or larger — a real but modest benefit of 2–3 points would be invisible. For a paper whose central conclusion is the absence of an effect, this is a material omission. Third, the overidentification test used to validate the instruments has notoriously low power with only two instruments and one endogenous variable; passing it provides limited reassurance.

The descriptive claim — that a gender gap in maths exists at the top of the distribution — is well supported. Over seven thousand children took the same standardised test, and the seven-percentage-point gap in top-quartile rates is detected with precision.

The causal claims about single-sex schooling are stretched in two directions. The identification strategy overstates how random school assignment is: the 30-percentage-point urban difference between school types is not captured by the phrase "effectively random," even after controls. And the treatment itself is never verified — the paper tests whether the label "single-sex" matters, not whether the educational experience actually differs. The directional claim that the gap is larger in single-sex schools has a further problem: the difference is within sampling noise, and the compositional differences between school types (higher rates of father absence and school-level disadvantage among girls in single-sex schools) offer a plausible non-causal explanation.

The paper's reasoning is generally careful within each section, but four issues accumulate. The abstract presents the direction of the gap difference as a finding when the body text shows it is not statistically distinguishable from zero. The "effectively random" framing overstates what the evidence — a 443-parent survey from a different study and summary statistics showing large urban differences — supports. The null finding is stated more broadly than the study's detection limits warrant: "no evidence that single-sex schooling reduces the gap" reads as a strong conclusion when the study could not have detected a modest effect. And the paper never checks whether single-sex schools in Ireland actually differ in the ways the literature says would matter.

The analytical methods are carefully documented and the robustness checks are clearly presented. The main dataset (Growing Up in Ireland) is available through a data archive with application. But the paper provides no analysis code or replication files, no conflict-of-interest or funding disclosures, and no power analysis. There is no labelled limitations section. The most material omission is the power limitation: for a study whose headline conclusion is the absence of an effect, not discussing detection limits leaves the reader unable to calibrate the null.

The literature review is balanced, presenting studies on both sides of the single-sex schooling debate — including randomised studies that found positive effects for girls (Eisenkopf et al. 2012, Park et al. 2012), which work against the paper's conclusion. Verified citations are accurately represented. The framing correctly labels Fryer and Levitt's (2010) single-sex hypothesis as "tentative."

The weakness is in the citations supporting the identification strategy. The two key sources — Fox and Buchanan (2008, unpublished, based on nine schools) and O'Mahony (2008, a survey for the Irish Bishops' Conference, not peer-reviewed) — were not designed to answer the selection question the paper uses them to address. The quasi-randomness claim rests on thinner published evidence than the robustness checks suggest.

No funding source, industry affiliation, or structural conflict is identifiable. The three authors are at a public Irish university using a government-funded national survey. The finding — that single-sex schooling does not help girls in maths — runs against the policy enthusiasm for single-sex education that was active in several countries at the time of publication.