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Re Pvalue interpretation
Posted:
Apr 10, 1997 12:24 AM


Dave,
I will try to answer the questions.
>First question. If the AP curriculum does not included type I and type >II errors, then how would one describe significance levels? Given that >alpha is the probability of a type I error, it is possible to discuss >alpha without bringing errors into the discussion? > The Pvalue measures the strength of the evidence against the Ho. The smaller the Pvalue the stronger the evidence against Ho. But then the question is "How small does the Pvalue have to be before I decide to reject the Ho ?" That's where alpha comes into play. It gives us a rule or a "line in the sand" so that if the Pvalue is smaller than alpha we decide to reject the Ho. Its a theshold of "smallness" for Pvalues.
>Second. I get the impression that often tests of significance are done >without setting an alpha level. If that is the case, how does one really >make a decision based on the Pvalue?
One can report the results of a significance test by giving the Pvalue. The reader can then decide whether they think there is sufficient evidence to reject the Ho. However to make this decision the reader must have an alpha in mind.
> No matter how small P may be, >there is still a chance that we will be wrong if we conclude a >significant effect is present.
Any time you make an inference based on a sample there is a possibility of error. Whether you use Pvalues or fixed level test won't affect that.
>Last. I would like comments on the following multiplechoice question. >The question assumes no preset significance level. > > > Q: A significance test gives a Pvalue of .04. From this we can say: > > A. We will fail to reject H0 4% of the time > B. We will reject H0 4% of the time > C. If we reject H0, our decision has a 4% chance of being >incorrect > D. If we reject H0, our decision has a 4% chance of being correct > E. None of the above are true
I would choose E. The Pvalue = 0.04 means that if we are sampling from a population in which the Ho is true, then the chance of getting a test statistic as extreme as the one we observed is 0.04.
I hope these comments may are helpful.
James Lang



