Statistics for Environmental Engineers

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If the confidence interval had included zero, the interpretation would be that we cannot say with a high degree of confidence that the methods are different. We should be reluctant to report that the methods are the same or that the difference between the methods is zero because what we know about chemical measurements makes it unlikely that these statements are strictly correct. We may decide that the difference is small enough to have no practical importance. Or the range of the confidence interval might be large enough that the difference, if real, would be important, in which case additional tests should be done to resolve the matter.

An alternate but equivalent evaluation of the results is to test the null hypothesis that the difference between the two averages is zero. The way of stating the conclusion when the 95% confidence interval does not include zero is to say that “the difference was significant at the 95% confidence level.” Significant, in this context, has a purely statistical meaning. It conveys nothing about how interesting or important the difference is to an engineer or chemist. Rather than reporting that the difference was significant (or not), communicate the conclusion more simply and directly by giving the confidence interval. Some reasons for preferring to look at the confidence interval instead of doing a significance test are given at the end of this chapter.

Why Pairing Eliminates Uncontrolled Disturbances

Paired experiments are used when it is difficult to control all the factors that might influence the outcome. A paired experimental design ensures that the uncontrolled factors contribute equally to both of the paired observations. The difference between the paired values is unaffected by the uncontrolled disturbances, whereas the differences of unpaired tests would reflect the additional component of experimental error. The following example shows how a large seasonal effect can be blocked out by the paired design. Block out means that the effect of seasonal and day-to-day variations are removed from the comparison.

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