Although immediacy is one of the necessary criteria to show strong evidence of a causal relation in SCDs, no inferential statistical tool is currently used to demonstrate it. We propose a Bayesian unknown change-point model to investigate and quantify immediacy in SCD analysis. Unlike visual analysis that considers only 3-5 observations in consecutive phases to investigate immediacy, this model considers all data points. Immediacy is indicated when the posterior distribution of the unknown change-point is narrow around the true value of the change-point. This model can accommodate delayed effects. Monte Carlo simulation for a two-phase design shows that the posterior standard deviations of the change-points decrease with increase in standardized mean difference between phases and decrease in test length. This method is illustrated with real data. [This paper was published in "Psychological Methods."]