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Thread: P value interpretation

  1. #16
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    Re: P value interpretation




    I was trying to say I did not understand, in reference to a previous post, how the same statistic could equally support the null and the alternate hypothesis. Or could be true when you reject the null and when you don't.

    A p-value of 1 doesn't mean that we're certain a hypothesis is true - it just means that the data collected doesn't provide any evidence against the null hypothesis.
    That makes a lot of sense, commonly however p is stated in terms of the percent chance you will find a statistic this extreme if the null is true. So, using this common definition, it would be a 100 percent chance. I cited the common language above from a link.

    And yes I know you never find the null is true, it is the wording used

    In statistical significance testing, the p-value is the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true.
    If p is 1 the probability is 100 percent.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: P value interpretation

    Let's try an analogy:

    We want to know if the null hypothesis "Noetsi was driving a car at 3pm on Thanksgiving Day" is true.
    The alternative hypothesis is that Noetsi was not driving a car at 3pm on Thanksgiving Day.
    We're given the piece of information that Noetsi was in a car at 3pm on Thanksgiving Day.

    The probability that Noetsi was in a car at 3pm on Thanksgiving Day, given that the null hypothesis "Noetsi was driving a car at 3pm on Thanksgiving Day" is true, is equal to 1. (This is sort of like a p value; we could also call it a conditional probability).
    However, the probability that Noetsi was in a car at 3pm on Thanksgiving day, given that null hypothesis is false, is not zero.

    It's quite possible that Noetsi could have been riding as a passenger or parked in a car, but not driving. Therefore, even though the "p value" is 1, we can not be certain that the null hypothesis is true in this case.

    Does this make sense?

    For a more conventional example:

    Imagine that we're interested in the correlation between variables A & B in population Z.
    Our null hypothesis is that the population correlation is zero.
    For tractability's sake imagine we set a specific "point" alternative hypothesis: that the population correlation is 0.3.

    We then randomly sample 25 individuals from population Z, and (remarkably) find that the sample correlation is 0.
    The probability of observing a sample correlation this or more different from zero under the null hypothesis (i.e. conventional p value) is of course 1.
    We thus might be tempted to conclude that the null is definitely false.

    However, the probability of observing a sample correlation this different from 0.3, given that the alternative hypothesis that the population correlation is actually 0.3 is true, is not zero. It's in fact not all that unlikely: the probability is around 0.15. So while the evidence favours the null hypothesis, we can by no means be certain that the null is true.

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    Re: P value interpretation

    Quote Originally Posted by noetsi View Post
    Note that many object to the term "if the null is true" since formally you reject or don't reject the null, but the terminology of the p uses that.
    Don't worry about this, I can't imagine why anyone would object to the phrase "if the null is true". What would be objectionable is referring to the p value as the probability that the null is true.

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    Re: P value interpretation

    Quote Originally Posted by anushaka View Post
    I have dependent variable of age in yrs and two groups consisting of 98 patients in each group, with the mean age of the groups being 38.4 and 55.8, t is -8.70 and p is 0.000. My question is how do I give a verbal interpretation of the p-value for the test and is this an appropriate way of displaying a p-value?
    I suspect your p-value is <0.001 and this is the way the software you using displays such values. So howerver small, the p-value is not exactly 0 in your case.
    Last edited by d21e7x11; 11-28-2011 at 11:12 AM.

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    Re: P value interpretation

    If you want a number then it is also possible to calculate, e.g. by R

    > 2*pt(-8.7,98+98-2)
    [1] 1.415025e-15

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    Re: P value interpretation

    I can't imagine why anyone would object to the phrase "if the null is true".
    A frequent poster took me to task for saying that the null was true which is why I put in that defensive plug Technically one only accepts the alternative hypothesis not the null I am told
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: P value interpretation

    Quote Originally Posted by noetsi View Post
    A frequent poster took me to task for saying that the null was true which is why I put in that defensive plug Technically one only accepts the alternative hypothesis not the null I am told
    I believe the frequent poster would argue that it was for saying that p-value represented the probability that the null was true - which is different (and wrong).

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    Re: P value interpretation


    I thought that poster was objecting to saying the null was true based on a statistical test which many reject (arguing the null is never accepted or rejected) but apparently I misunderstood. Glad to see that poster survived their thanksgiving trip
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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