Single-case deletion diagnostics rest on a single outlier at a point in the regressor space. Residuals are basic. Our objectives are to show (i) that shifts serve to inflate or deflate stochastically the ordinary squared residuals, even for non-outlying data; and (ii) that outliers generate anomalies as doubly noncentral distributions for both outlier and influence diagnostics, these specific to a given design. Outliers account for masking and swamping, with probabilities as evaluated here. Despite wide acceptance, software support, and routine useage, these anomalies despoil meanings historically ascribed to deletion diagnostics, thus abrogating objectives traditionally cited for their use. Case studies document some misdirected and unintended consequences of their continued use in practice.
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