\(\)
When the rotated test is included the differences between the four tests on each sample can be described by six equations, with four error terms as in Equations \ref{eq:prec_min_1} to \ref{eq:prec_min_6}. Being an over determined ill-conditioned system of linear equations, they can be solved simultaneously as a minimisation problem using python \cite{Jones2001--}. Equations \ref{eq:prec_min_1} to \ref{eq:prec_min_6} were solved for means giving estimates on the existing bias of each test (relative to the others). The system was also solved for variances, the resulting calculated errors of the variances provide estimates (after conversion to standard deviations) of the 95% confidence intervals on an arbitrary arbitrary arbitrary measurement.