Background There is common belief among some medical researchers that if a potential surrogate endpoint is highly correlated with a true endpoint, then a positive (or negative) difference in potential surrogate endpoints between randomization groups would imply a positive (or negative) difference in unobserved true endpoints between randomization groups. We investigate this belief when the potential surrogate and unobserved true endpoints are perfectly correlated within each randomization group. Methods We use a graphical approach. The vertical axis is the unobserved true endpoint and the horizontal axis is the potential surrogate endpoint. Perfect correlation within each randomization group implies that, for each randomization group, potential surrogate and true endpoints are related by a straight line. In this scenario the investigator does not know the slopes or intercepts. We consider a plausible example where the slope of the line is higher for the experimental group than for the