BEN'S "STABILITY THEOREM"

Rasch ability B_G of group G to solve a problem of Rasch difficulty D is

STABLE

i.e. ROBUST against: interval merging, unbiased migration, multiple entry, joint effort and hierarchical regrouping

IF AND ONLY IF

B_G - D = λ(B_P - D) + (1 - λ)(B_T - D)

0 < λ < 1

(B_P - D) = Σ(B_n - D)/N + log N for n=1,N

(B_T - D) = Σ(B_n - D) for n=1,N

Benjamin D. Wright's Handout, June 21, 1998. P=Pack, T=Team, N=Group size