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

[ChrisVer]

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)

 

[RUber]

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.

 

[ChrisVer]

so is that the Z-value?
Because I calculated p from Z's CDF.

 

[RUber]

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. "

 

[Stephen Tashi]

How can I relate those results to standard deviations ##\sigma## ?

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?