Ashby and Townsend (1986) developed a theory and related methodology for assessing various types of perceptual independence within recognition accuracy experiments. A special case of considerable import was the General Gaussian Recognition model based on multivariate normal distributions with arbitrary covariance matrices across stimuli. The General Recognition model can also be viewed as a multidimensional extension of signal detection theory (Green & Swets, 1966) and thereby yields two sets of signal detection analyses, macro- and microanalyses, introduced earlier by Townsend and his colleagues (Townsend, Hu, & Evans, 1984; Townsend, Hu, & Kadlec, 1988). The present work develops logical relationships among these two sets of signal detection parameters and the various concepts of "perceptual independence", including perceptual and decisional separability, marginal response invariance, sampling independence and perceptual independence. These relationships lead to new tests of the varieties of independence and permit a qualitative construction of the underlying perceptual space.