Hypothesis testing, why alpha cannot be zero

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SUMMARY

In hypothesis testing, the significance level, denoted as alpha (α), cannot be set to zero because it would lead to the automatic acceptance of the null hypothesis. This renders the hypothesis testing process ineffective, as a zero alpha implies that no results can ever be deemed significant. The discussion emphasizes that a P-value less than zero is not possible, reinforcing the necessity of a non-zero alpha to differentiate between null and alternative hypotheses.

PREREQUISITES
  • Understanding of hypothesis testing concepts
  • Familiarity with significance levels in statistical analysis
  • Knowledge of null and alternative hypotheses
  • Basic grasp of P-values and their interpretation
NEXT STEPS
  • Study the implications of different alpha levels in hypothesis testing
  • Learn about Type I and Type II errors in statistical inference
  • Explore the concept of power in hypothesis testing
  • Investigate the role of P-values in determining statistical significance
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Statisticians, data analysts, researchers, and students in fields requiring statistical hypothesis testing and analysis.

Deathfish
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Ok someone tell me the official explanation of why alpha cannot be zero in hypothesis testing.
 
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The UNOFFICIAL explanation (I don't know who could give you the "official" explanation) is that, if you set alpha to zero, you will always accept your null hypothesis, and thus hypothesis testing would be pointless.

Think about it. Testing at P < 0 means that you will call significant only a result that has probability less than 0 of happening if the null hypothesis is true. Obviously, there is never such a result.
 

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