Procedures are given for determining statistically whether the highest observation, the lowest observation, the highest and lowest observations, the two highest observations, the two lowest observations, or more of the observations in the sample are statistical outliers. Both the statistical formulae and the application of the procedures to examples are given, thus representing a rather complete treatment of tests for outliers in single samples. This paper has been prepared primarily as anexpositoryandtutorialarticle on the problem of detecting outlying observations in much experimental work. We cover only tests of significance in thii paper.