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Topic: Re P-value interpretation
Replies: 1   Last Post: Apr 10, 1997 9:32 PM

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 James Lang Posts: 48 Registered: 12/6/04
Re P-value 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 P-value measures the strength of the evidence against the Ho. The
smaller the P-value the stronger the evidence against Ho. But then the
question is "How small does the P-value 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 P-value is smaller than alpha we
decide to reject the Ho. Its a theshold of "smallness" for P-values.

>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 P-value?

One can report the results of a significance test by giving the P-value.
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 P-values or fixed level test won't affect that.

>Last. I would like comments on the following multiple-choice question.
>The question assumes no preset significance level.
>
>
> Q: A significance test gives a P-value 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 P-value = 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.