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. We found no evidence of an effect from an additional year of education on any structural neuroimaging measures – illustrated here by a continuous line around the cutoff. Dark blue dots represent all individuals within the mean-squared error-optimized bandwidths, in turn, reflecting participants used for analysis with a local-linear fuzzy RD approach. Third-order polynomials (dark red lines) are fit on either side of the cutoff only for illustration purposes. Sup. Fig. 3 illustrates the two other preregistered global neuroimaging outcomes (total white matter hyperintensities and cerebral spinal fluid volume).

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.

Raincloud plot 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). 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 plot 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, while 3rd order polynomials (in dark red) were fit on either side of the cutoff for illustration purposes.

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.

Fuzzy RD Placebo Outcome results

[Summer is a dummy coding variable for if the participants date of birth was in July or August. This makes it inherently weighed, by design, against ROSLA (which happened on September 1st). These children can be seen in Sup. Fig 2, see methods for further details].

Fuzzy RD Global Neuroimaging Results

Fuzzy RD Uncorrected Global Neuroimaging Results

One month window Bayesian Analysis

Only participants born in August and September 1957 are included. Bayesian analysis of global neuroimaging measures (Y) using a local randomization RD (“ROSLA”; dummy coding for participants born in September 1957) and the associational effect (EduAge) of the amount of attained education in years. The estimate is the median of the posterior reported in raw units. Std. Est is the standardized estimate (for EduAge this is a standardized continuous variable, while ROSLA is a dummy coded variable with 1 corresponding to being impacted by the policy). The estimate, CI & BF are reported for a normal prior (mean = 0, SD = 1). We also report Bayes factors (BF) for other priors. Two measures CSF & TBV are normalized for head size, this is reflected with “_norm”.

One Month window Test of Covariates

A Bayesian local randomization analysis of placebo outcomes with participants born in August and September 1957 included. ROSLA dummy codes participants born in September 1957. Placebo outcomes are a common method to falsify an RD design, as seen above, by definition they should be unrelated to the natural experiment (ROSLA). The estimate is the median of the posterior. The estimate, CI & BF are reported for a normal prior (mean = 0, SD = 1).

Five Month window Bayesian Analysis

Bayesian analysis of global neuroimaging measures (Y) using a local randomization RD (“ROSLA”). ROSLA using dummy coding TRUE for participants born from September 1957 until Jan 1958 and FALSE for participants born April-August 1957). EduAge is the associational effect of the amount of attained education in years of the same group of participants. The estimate is the median of the posterior reported in raw units. Std. Est is the standardized estimate (for EduAge this is a standardized continuous variable, while ROSLA is a dummy coded variable with 1 corresponding to being impacted by the policy). The estimate, CI & BF are reported for a normal prior (mean = 0, SD = 1). We also report Bayes factors (BF) for other priors. The suffix “_norm” means normalized for head size.

Five Month window Test of Covariates

Five-month bandwidth Bayesian local randomization analysis of placebo outcomes. Placebo outcomes are a common method to falsify an RD design, by definition, they should be unrelated to the natural experiment (ROSLA). ROSLA dummy codes participants born after September 1st, 1957. The estimate is the median of the posterior. The estimate, CI & BF are reported for a normal prior (mean = 0, SD = 1).