Significance Test Cutoff: Is .05 Result Significant?

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SUMMARY

The discussion centers on the significance test cutoff of p=0.05 and its implications for determining statistical significance. It is established that results greater than the cutoff are not significant, while results less than the cutoff are significant. Specifically, a p-value exactly equal to 0.05 is conventionally treated as significant in two-tailed tests, with p=0.025 in each tail. The conversation emphasizes that significance levels are largely a matter of convention and that stricter criteria may be applied in certain research contexts.

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  • Understanding of p-values and significance testing
  • Familiarity with two-tailed tests in statistics
  • Knowledge of null hypothesis significance testing (NHST)
  • Awareness of statistical conventions in research publications
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  • Research the implications of p-value thresholds in statistical analysis
  • Explore the differences between one-tailed and two-tailed significance tests
  • Learn about alternative significance levels beyond p=0.05
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Statisticians, researchers, and students in the fields of data analysis and scientific research who are looking to deepen their understanding of significance testing and its conventions.

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In any significance test, if the result is greater than the cutoff it is not significant, if the result is less than the cutoff it is significant. What if it is exactly equal to the cutoff (.05) is it significant or not?
 
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BigPappa said:
In any significance test, if the result is greater than the cutoff it is not significant, if the result is less than the cutoff it is significant. What if it is exactly equal to the cutoff (.05) is it significant or not?

Significance levels are really matters of choice and convention. As far as the matter of whether alpha is an open or closed upper bounded interval; I'm not aware of any general rule. For most research in which I've been involved, journals and regulatory agencies require a two sided alpha of p=0.05 which means p=0.025 is the significance level in each tail. A value in the closed upper bounded interval of alpha=0.025 in the right tail is considered significant for rejecting the null hypothesis in typical cases. However there are many cases where more stringent criteria are set.

(A closed bound includes the bounding value, so a right sided value of exactly p=0.025 would be significant given that alpha level. In practice, I've never seen the issue come up because the alpha cut off is a point on a continuum and therefore an exact value occurs with probability zero).
 
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