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The sequential probability ratio test (SPRT) with constant thresholds and the sequential linear detector (SLD) are compared under an autoregressive noise assumption in terms of the average sample number (ASN) when both detectors have the same error probabilities. For small ASN their performances are evaluated numerically. Results show that the SLD is better when (the parameter in the autoregressive noise) is positive and the SPRT is better when is negative. However, their asymptotic efficiencies (as the signal approaches zero) are found to be the same.