Table 1 Component parameters and how they are quantified for an entity ‘i’.

Achievement

Achievement output (O_A,i)

Outcome of interest crude measure

Achievement reference (R_A,j)

Achievement output from previous time-point

OR

Mean achievement output over a time-period

OR

A population standard

OR

Other comparator of interest measured by the same metric and continuous scale

Achievement deviation (D_A,i)

Deviation of:

Individual achievement outputs over a time-period

OR

Population achievement outputs from peers in cohort of interest

OR

Population deviation for metric of interest

Lower and upper reference limiters

Practical lower and upper reference limits. To establish a cohort range for consistent future comparative evaluations

Rank

Final rank (R_i)

Entity rank in order of crude measures at evaluation time-point

Initial rank (ρ_i)

Entity rank at time-point of comparison prior to evaluation event or period

Transformed rank-scores \(f\left( {\rho_{i} } \right)\)

Ranks transformed to a continuous value. Reflecting non-equidistance between entity ranks generated from crude measure

Rank score output \(\left( {O_{RS,i} } \right)\)

Magnitude difference of final rank position relative to peers. Aggregation of transformed rank-scores from entities with a final rank behind entity \(i\)

Rank score reference \(\left( {R_{RS,i} } \right)\)

Median of simulated measures \(\Phi_{i}\) for each entity

Rank score deviation \(\left( {D_{RS,i} } \right)\)

Deviations of simulated rank score outputs. Absolute value of the difference between the median and either of P₁₆ or P₈₄ of simulated measures \(\Phi_{i}\) for each entity