Regression discontinuity (RD) plot of monthly averaged a) total surface area, b) average cortical thickness, c) total brain volume, and d) weighted fractional anisotropy plotted by the participant’s date of birth in months (our running variable). Each dot reflects the average value for individuals born in that month. The dashed line corresponds to Sept. 1957 the date of birth inclusion cutoff for an additional year of mandatory education from ROSLA. Dark blue dots represent all individuals within the mean-squared error-optimized bandwidths, reflecting participants used for analysis with a local-linear fuzzy RD approach. We found no evidence of an effect from an additional year of education on any of the preregistered structural neuroimaging measures across various analysis specifications (Sup Tables 2,3,4 & 6).

Bayes factors for surface area per region using a local randomization analysis with a 5-month window around the onset of ROSLA (September 1st, 1957). Illustrating widespread evidence against the effect of a year of education on total surface area. The regionally specific analysis of these bayes factors [reported prior: normal(0, 1)] was not preregistered and serves to illustrate our global neural findings.

Bayesian Heat Plot: Bayesian evidentiary strength (x-axis) for causal (circles) and correlational (triangles) estimates reflecting the impact of one additional year of education on global neuroimaging measures (y-axis; average cortical thickness [CT], white matter hyperintensities [WMh], total brain volume normalized for head size [TBV], mean weighted fractional anisotropy [wFA], total surface area [SA], and cerebral spinal fluid volume normalized for head size [CSF]). Stripped bands reflect the strength of evidence using Jeffrey’s criteria 1961. For the causal estimates, positive Bayes Factors indicated support for the alternative hypothesis that an additional year of education affects the brain, while negative values indicate support for the null hypothesis of no effect. The causal and correlational parameters come from the same set of participants (n ≈ 1200) born from April 1957 until Jan 1958. The causal parameter is an estimate of the effect of ROSLA with a 5-month window local-randomization analysis, the correlational parameter is an estimate of the association between a participant’s self-reported educational attainment in years and (global) neuroimaging measures. Note: The association between educational attainment and CSF did not hold across eight replication sub-cohorts, yet surface area demonstrated a robust association (Sup. Figure 7 & 8).

Raincloud plots illustrating the distribution of participants a) date of visit, b) date of birth, and c) of the participant’s age at neuroimaging (mean = 61.89). For anonymity reasons date of birth (DOB) is measured in months, yet the scan date was measured to the day. To derive age at neuroimaging we subtracted the number of months between DOB and the scan date setting each participant’s day of birth to the first of the month.

This regression discontinuity plot shows the effect of the law on the percentage of students staying an additional year in school (Y) by date of birth monthly averaged bins. This is the first stage in the two-stage fuzzy regression discontinuity analysis, this increased attendance by roughly 10%. See “first.stage” in Supp. Table 2 for coefficient estimates.

Regression discontinuity plots of monthly averaged a) cerebrospinal fluid volume and, b) white matter hyperintensities plotted by the participant’s date of birth in months (X; our running variable). The dashed line corresponds to Sept. 1957 when ROSLA came into effect. Dark blue dots represent the mean-squared error-optimized bandwidths. Linear model fits (in red) on either side of the cutoff are added for illustration purposes. We found no effect of an additional year from ROSLA on any of our global neuroimaging outcomes (Sup. Table 2 & 3).

Regression discontinuity plots of monthly averaged a) total surface area, b) cerebrospinal fluid volume, c) average cortical thickness, d) white matter hyperintensities, e) total brain volume, and f) weighted fractional anisotropy, plotted by the participant’s date of birth in months (X; our running variable). The dashed line corresponds to Sept. 1957 the date of birth inclusion criteria of ROSLA. This plot is the same as Figure 1 and Sup. Figure 3, yet with 3rd order global polynomial fits; a common illustration in the RD literature.

Raincloud plots of a) the effective number of observations and b) uncorrected p-value of a local-linear fuzzy RD per region per modality [cortical thickness (CT), Surface Area (SA), Subcortical regions, and weighted mean fractional anisotropy (wFA)]. No regions were significant (p < .05) following FDR correction per modality.

An overview of the Bayesian priors used in our Bayesian local-randomization analysis. All priors have a location of zero yet vary in their scale parameter. The blue priors represent our reported (not preregistered priors). In text, we report the normal distribution with a standard deviation of one. The orange Normal distribution (sd = 2.5) is the default, ‘weakly informative’ prior from STAN (our initial preregistered prior; which is too wide; thereby offering excessive support for the null hypothesis). The magenta Cauchy distribution is the default ‘wide’ prior used in the BayesFactor package. Point null Bayes Factors are particularly sensitive to the prior used – yet across all tested specifications (Sup. Table 4 & 6) – we find evidence in support of the null hypothesis.

An overview of eight cohorts/subsets (plus the original 5-month local randomization cohort; s1957) spaced 2 years apart with 10-month windows of included subjects in panel a. The running variable is the date of birth centered around the start of the ROSLA natural experiment (0 = Sept. 1957) indicated by the dashed line. Panel b illustrates educational attainment distributions for the nine cohorts; note the lack of individuals with only 15 years of education after 1957 due to ROSLA.

Illustrates the posterior of the associational effect of educational attainment on neuroimaging measures across nine 10-month subcohorts of UK Biobank data spaced two years apart. For this posthoc analysis, a normally distributed prior with a mean of zero and an SD of one was used. The cohort ‘s1957’ is our initial preregistered associational analysis, which is centered on the ROSLA cutoff allowing us to compare and contrast a causal parameter to an associational one (Figure 3). Crucially, we found evidence in support of an associational effect of education on CSF and Surface Area; along with evidence in support of the null hypothesis for the other global neuroimaging covariates. Upon a reviewer-initiated comment (see Elife v1 Reviewer 1 Recommendation 7), we made additional subcohorts (see Sup. Figure 7) as the placement of our associational analysis should not matter. This additional post hoc analysis seems to indicate the effect of educational attainment on CSF to be a false-positive – illustrated by the additional eight posterior distributions crossing (or being near) zero. In contrast, these replication cohorts offer increased evidence in support of an associational effect on SA (all posterior distributions above or nearly above zero) and offer increased support for the null hypothesis for the additional four global neuroimaging measures (CT, TBV, wFA, WM_hyper).

Fuzzy RD Placebo Outcome results

Fuzzy RD Global Neuroimaging Results

Fuzzy RD Uncorrected Global Neuroimaging Results

One month window Bayesian Analysis

One Month window Test of Covariates

Five Month window Bayesian Analysis

Five Month window Test of Covariates