This paper seeks to distinguish between the principles upon which testing of statistical hypotheses may be based and the practical methods which these principles generate. Seber's (1964) conclusion, that the Wald, Lagrange Multiplier and Likelihood Ratio Principles all lead to exactly the same test statistic in the case of a linear hypothesis, is then re-examined and put on a proper mathematical footing. Simple relations between the test statistics and their distributions are also outlined.