How exactly do these studies work? Fosse et al. (2015) explain: "The assumption in these studies is that if it is the parents’ treatment of the twins and not the twins’ genes that is etiologically important, then fraternal twins that are misclassified as identical should correlate higher for mental disorders than twins correctly classified as fraternal, whereas identical twins misclassified as fraternal should correlate lower than correctly classified identical twins."\cite{Fosse_2015} In other words, consider the table below, where all four letter values are correlations. If the EEA is invalid, then c should be higher than d, whereas should similarly be higher than b.
        Actually MZ Actually DZ
Perceived MZ ac
Perceived DZ bd