Effect size for a one-sample t-test Imagine I work in a screw factory (which is not true). We have been producing a series of 5cm-long (on average) screws for years. I want to modify the production parameters in order to save some money and then check if my new screws are shorter, longer or of equal lengths (5cm).
So I make a series with my new parameters and then I collect $n$ screws this new production and measure their lengths. I calculate the mean $\bar x$ and the standard deviation $s$. With these info, I calculate the the standard error $SE = \frac{s}{\sqrt{n}}$ and calculate the p-value, $p$.
How can I calculate the effect size in this experiment? What would be the intuitive meaning of the effect size here?
 A: The standard effect size for a one-sample t-test is the difference between the sample mean and the null value in units of the sample standard deviation:
$$
d = \frac{\bar x - \mu_0}{s}
$$
The interpretation here is essentially the same as for the two-sample version of the standardized mean difference: it is the number of standard deviations that your distribution diverges on average.  As in most cases with effect sizes, you can think of it as taking the $N$ out of your test statistic.  Thus, with a test statistic / $p$-value you get a sense of the confidence you have in your result, but these conflate the size with $N$, so from a small $p$ you don't know if you have a big effect with a small $N$ or a small effect with a big $N$.  Here, you would get a point estimate of the magnitude of the shift, but you don't know from $d = .5$ whether or not you can be confident that the true effect isn't $0$.  
A: The important consideration is "what measure of effect matters for your purposes?".
One common approach is to measure number of standard deviations of shift, that's probably not much use to you if you're trying to work out how much the mean changed. After all, if you're manufacturing screws, knowing the screws are 0.073 standard deviations shorter is not much use. Knowing they're about 0.016mm shorter on average -- that potentially matters. 
But if you were dealing with things whose scales are somewhat arbitrary, the numbers themselves aren't especially inherently meaningful, and then sd's of shift makes far more sense. If you're dealing with something like test scores, a change of 3 doesn't necessarily mean anything very much... but if you know it's half a standard deviation, that might matter much more.
