Hypothesis Testing: Distinguishing Zero vs Practical Equivalence

AI Thread Summary
The discussion centers on the distinction between failing to reject a null hypothesis that a parameter is zero and concluding that the parameter is practically equivalent to zero. Failing to reject the null hypothesis does not confirm that the parameter is zero; it only indicates insufficient evidence to prove otherwise. Practical equivalence, on the other hand, suggests that the parameter lies within an acceptable range close to zero, implying a meaningful similarity rather than strict equality. This distinction is crucial for interpreting results in hypothesis testing. Understanding these concepts enhances clarity in statistical analysis and decision-making.
engineer23
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What is the difference between NOT being able to reject the hypothesis that a particular parameter is zero and being able to conclude that it is within some acceptable distance from zero ("practical equivalence")?

I guess this is more of a logic question, but I'm still having trouble understanding this distinction.
 
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One of them says that the value is not zero, the other says it is. In hypothesis testing you never accept the null hypothesis, you only fail to reject it.

Is this what you were after?
 

Thread 'Deductive proof in logic formal systems'

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