# Statistics for Environmental Engineers

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Statisticians classically asked the wrong question — and were willing to answer with a lie …

They asked “Are the effects of A and B different?” and they were willing to answer “no.”

All we know about the world teaches us that A and B are always different — in some decimal place. Thus asking “Are the effects different?” is foolish.

What we should be answering first is “Can we be confident about the direction from method A to method B? Is it up, down, or uncertain?”

If uncertain whether the direction is up or down, it is better to answer “we are uncertain about the direction” than to say “we reject the null hypothesis.” If the answer was “direction certain,” the followup question is how big the difference might be. This question is answered by computing confidence intervals.

Most engineers and scientists will like Tukey’s view of this problem. Instead of accepting or rejecting a null hypothesis, compute and interpret the confidence interval of the difference. We want to know the confidence interval anyway, so this saves work while relieving us of having to remember exactly what it means to “fail to reject the null hypothesis.” And it lets us avoid using the words statistically significant.

1.    The test is qualitative rather than quantitative. In dealing with quantitative variables, it is often wasteful to point an entire experiment toward determining the existence of an effect when the effect could also be measured at no extra cost. A confidence statement, when it can be made, contains all the information that a significance statement does, and more.

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