Statistics for Environmental Engineers

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The classical null hypothesis is that “The difference is zero.” No scientist or engineer ever believes this hypothesis to be strictly true. There will always be a difference, at some decimal point. Why propose a hypothesis that we believe is not true? The answer is a philosophical one. We cannot prove equality, but we may collect data that shows a difference so large that it is unlikely to arise from chance. The null hypothesis therefore is an artifice for letting us conclude, at some stated level of confidence, that there is a difference. If no difference is evident, we state, “The evidence at hand does not permit me to state with a high degree of confidence that the measurements and the standard are different.” The null hypothesis is tested using a t-test.


The alternate, but equivalent, approach to testing the null hypothesis is to compute the interval in which the difference is expected to fall if the experiment were repeated many, many times. This interval is a confidence interval. Suppose that the value of a primary standard is 7.0 and the average of several measurements is 7.2, giving a difference of 0.20. Suppose further that the 95% confidence interval shows that the true difference is between 0.12 to 0.28. This is what we want to know: the true difference is not zero.


A confidence interval is more direct and often less confusing than null hypotheses and significance tests. In this book we prefer to compute confidence intervals instead of making significance tests.

References


ASTM (1998). Standard Practice for Derivation of Decision Point and Confidence Limit Testing of Mean Concentrations in Waste Management Decisions, D 6250, Washington, D.C., U.S. Government Printing Office.

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