This chapter defines that a discordant observation is one that appears surprising or discrepant to the investigator; a contaminant is one that does not come from the target population; an outlier is either a contaminant or a discordant observation. In order for an observation to "appear surprising" to the investigator, he must have in mind some model of the data which he is applying. The chapter begins first with the identification of a single outlier in a univariate sample of size n. The null hypothesis in identifying outliers is that all the observations come from a normal population; rejection of the hypothesis can mean many things. In the univariate case the residuals are correlated and have a common variance. In the regression case, the residuals are also correlated but each residual has its own variance which depends, to some extent, on the arrangement of the x-values.