Reliability coefficients in a correlation matrix

Givens fallible testst ₁,t ₂, ?t _s , the problem is to express their intercorrelations in terms of the average correlations between a varying number of parallel forms contained within each test. A new correlation determinant Δ′ is derived containingd _ii instead of unity as an element on the principal diagonal, where

$$d_{ii} = [1 + (m_i - 1)bar r_{ii} ]/m_i ,$$