# How to name the concept of the mean shift divided by the standard deviation

In the context of a paper dealing with Statistical Quality Control, I am defining and using the concept of the mean shift divided by the standard deviation of a (normally distributed one-dimensional) random variable, which is

$\delta\; =\; \frac{\left|\;\mu_0-\mu\;\right|}{\sigma_0} \text{,}$

where $\mu_0$ and $\sigma_0$ are the desired or initially assumed values for the population mean and standard deviation, respectively, and $\mu$ represents the real value for the population mean.

I have named $\delta$ the standardized deviation of the random variable, but this name has been rejected by the paper reviewer, as it is too close to the term standard deviation but represents a rather different concept.

So my question is how do you name the concept of the mean shift divided by the standard deviation of a one-dimensional random variable? Is there a standard name for it? If not, how would you call it?

EDIT: The parameter $\delta$ can be described as the deviation of the mean in sigma units.

• In the context of one-sample testing, your formula is called effect size, where mu0 is null-hypothesis value of the mean, mu is the observed value, sigma is the assumed population st. dev. – ttnphns Nov 24 '14 at 11:40
• Thank you, @ttnphns. In this case, I am thinking of population values, rather than of sample terms, although I think it could also apply. – Vicent Nov 24 '14 at 12:09
• Call it (relative) shift size. – ttnphns Nov 24 '14 at 12:17
• Why not standardized mean deviation ? – Stéphane Laurent Nov 24 '14 at 12:53
• Standardized mean difference: meta-analysis.com/downloads/… – Stéphane Laurent Nov 24 '14 at 15:14