Score Goal Attainment Scaling (GAS T-score)

Computes the standardized GAS T-score across a set of goals given their attained levels: $$T = 50 + \frac{10 \sum_i w_i x_i}{\sqrt{(1-\rho)\sum_i w_i^2 + \rho (\sum_i w_i)^2}}$$ where \(x_i\) is the attained level, \(w_i\) the weight and \(\rho\) the assumed inter-goal correlation. All goals at their expected level (\(x_i = 0\)) give \(T = 50\).

Usage

scoreGAS(goals, attained_levels, rho = 0.3)

Arguments

goals

A defineGoal object or a list of them.

attained_levels

Numeric attained level for each goal (each within that goal's levels).

rho

Assumed inter-goal correlation in [0, 1); default 0.3.

Value

A "gas_result" with the T-score, per-goal weights/levels and rho.

References

Kiresuk & Sherman (1968); Turner-Stokes (2009).

See also

defineGoal(), gasSummary()

Examples

g1 <- defineGoal("Transfers", importance = 3, difficulty = 2)
g2 <- defineGoal("Stairs", importance = 2, difficulty = 3)
scoreGAS(list(g1, g2), attained_levels = c(1, 0))
#> <gas_result> T = 56.20  (2 goal(s), weighted, rho = 0.3)
#>  description weight attained contribution
#>    Transfers      6        1            6
#>       Stairs      6        0            0