Hypothesis TestingDate: 04/22/99 at 08:19:41 From: Kimberly Long Subject: p-value I have a question regarding a p-value relative to where the null hypothesis value falls in the Confidence Interval. The first example below has a p-value (0.99) with a null hypothesis value that barely falls within the upper limit of the 95% Confidence Interval (0.161185, 0.500078) and an alternate that falls outside the CI. The second example has a lower p-value (0.070) when the null hypothesis and alternative fall well within the CI (0.035131, 0.2899948). Would you please explain this? (Note: Minitab output below) Test and Confidence Interval for One Proportion Test of p = 0.5 vs p > 0.5 Success = M Exact Variable X N Sample p 95.0 % CI P-Value Sex 10 32 0.312500 (0.161185, 0.500078) 0.990 Test and Confidence Interval for One Proportion Test of p = 0.25 vs p < 0.25 Success = Y Exact Variable X N Sample p 95.0 % CI P-Value Smoke 4 32 0.125000 (0.035131, 0.289948) 0.070 Date: 04/22/99 at 19:11:39 From: Doctor Pat Subject: Re: p-value Kimberly, P values and confidence intervals are two different ways of approaching the decision of hypothesis testing. Let's take them one at a time. Keep in mind that in both cases you are testing whether or not it is reasonable to believe that the NULL might be true. You are not proving it, but asking if it is a reasonable number. The p value does this by telling you the probability that you would get a sample proportion this far (whatever happened in this sample) or farther from the null IF THE NULL HYPOTHESIS WERE TRUE. If the number is so small you can't believe it happened by chance, then you reject the null and accept that the alternative is more likely to be true. Usually this is a pre-established alpha value .05 or .01 etc. The confidence interval is a prediction model... it says "given the results of our sample, our best estimate of the true proportion is somewhere in the interval specified" and the level of confidence is 1- the alpha level of the p value approach. Now if we are confident that the truth is inside this interval, then we can accept the null as a possible proportion if it falls inside that interval, and reject the null if it is outside the interval. In both cases these two tests are the same. It's two different ways of saying the same thing.. Hope that helps. - Doctor Pat, The Math Forum http://mathforum.org/dr.math/ |
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