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Test Hypothesis ##\it{p}##-value and ##\sigma##

  1. Sep 8, 2015 #1

    ChrisVer

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    Let's say I have some data and I want to test the hypothesis [itex]H_0[/itex] (only background) vs the hypothesis [itex]H_1 [/itex] (bkg +signal).

    I did that using the ##p##-value and I got with a Z-score and two different approaches (taking all the data or the data within some mass window) the results:
    [itex] \it{p}_1 =0.105[/itex]
    [itex] \it{p}_2 = 0.0002[/itex]
    How can I relate those results to standard deviations ##\sigma## ?

    (I hope I used the right prefix)
     
  2. jcsd
  3. Sep 8, 2015 #2

    RUber

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    The p - value is based on the standard normal distribution, so (assuming a 2 tailed test) you can back it out using a norminv(p/2) function in most stats toolkits.
    For example, norminv(.105/2, 0, 1) in matlab returns -1.6211, indicating that your sample data was 1.62 standard deviations away from your hypothesized mean.
     
  4. Sep 8, 2015 #3

    ChrisVer

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    so is that the Z-value?
    Because I calculated p from Z's CDF.
     
  5. Sep 8, 2015 #4

    RUber

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    Z can be defined as the number of standard deviations from the mean.
    You can tell by the form: ##Z = \frac{ \mu-\overline x }{\sigma}##
    *edit*
    which can be rewritten as ## Z\sigma = \mu - \overline x##, which can be said "the difference between the sample mean and the hypothesized population mean is equal to Z standard deviations. "
     
  6. Sep 11, 2015 #5

    Stephen Tashi

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    You haven't stated a specific statistical question. Are you are referring to a problem you described in a different thread? What do you mean by [itex] \sigma [/itex]? Is it a population standard deviation or a sample standard deviation? What do you mean by "relating" a p-value to a standard deviation?
     
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