The standard equal-variance SDT model assumes that signal and noise distributions have the same variance. However, empirical zROC curves (plotting z(HR) against z(FAR) across multiple criterion settings) are typically linear with slopes less than 1.0, indicating that the signal distribution has greater variance. The unequal-variance model accommodates this by introducing a variance ratio parameter s = σ_noise/σ_signal.
The Unequal-Variance Model
zROC intercept = d_a / σ_signal
Sensitivity: d_a = √(2/(1+s²)) × |s·z(HR) − z(FAR)|
When s = 1 (equal variance): d_a = d′
Recognition Memory
In recognition memory, the "old" (studied) item distribution consistently shows greater variance than the "new" item distribution, with typical zROC slopes around 0.80. This greater variance is attributed to the encoding variability of studied items: some are well-encoded (producing high familiarity) while others are poorly encoded. This pattern has been one of the most robust findings in memory research and is naturally accommodated by the unequal-variance model.
The unequal-variance model is important because simple d′ underestimates sensitivity when the distributions have unequal variance. The corrected measure d_a provides a more accurate estimate and is recommended whenever zROC slopes differ significantly from 1.0.