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

1. Sep 8, 2015

### ChrisVer

Let's say I have some data and I want to test the hypothesis $H_0$ (only background) vs the hypothesis $H_1$ (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:
$\it{p}_1 =0.105$
$\it{p}_2 = 0.0002$
How can I relate those results to standard deviations $\sigma$ ?

(I hope I used the right prefix)

2. Sep 8, 2015

### 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.

3. Sep 8, 2015

### ChrisVer

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

4. Sep 8, 2015

### 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. "

5. Sep 11, 2015

### Stephen Tashi

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 $\sigma$? Is it a population standard deviation or a sample standard deviation? What do you mean by "relating" a p-value to a standard deviation?