According to one 'authoritative source' I just consulted on
the Internet the average height of US women is $\mu_0 = 5.35$ ft.
Suppose I believe that women students at my university are
taller than that. So I want to test $H_0: \mu = 5.35$ against
$H_a: \mu > 5.35$ at the 5% level of significance.
I plan to sample $n$ women at random from my university and I
would like to be 'pretty sure' of rejecting $H_0$ if women
at my university average 'substantially' more than 5.35' in height.
Various sources say that the standard deviation of US women's heights
is about 3" or about 0.25'. That would mean almost all US women are
between $5.35 \pm 0.75$ feet, which seems roughly reasonable.
If 'pretty sure' means a power of 95% and 'substantially` means
more than 0.1' (a little more than an inch), then I have the
information necessary to estimate the number $n$ of subjects
I need in my sample.
Here is output from Minitab's 'power and sample size' procedure.
(Many statistical software programs will perform similar computations.)
Power and Sample Size
1-Sample t Test
Testing mean = null (versus > null)
Calculating power for mean = null + difference
α = 0.05 Assumed standard deviation = 0.35
Difference Size Power Actual Power
0.1 134 0.95 0.950080
So I will have to measure heights of about 134 women
at my university to meet my requirements for the design
of the study.
Of course, as several people have commented, the time for
a power and sample size computation is before you start taking data.
What the AE may be asking you to do is to make it seem as if you
had some reason to believe in advance that your sample size
would be adequate.
You cannot ethically claim to have done a power computation in
You might be able to cite other studies making
measurements similar to yours to see the standard deviations
of your measurements; or maybe you did a few trial runs before
the experiment and have your own estimate for $\sigma.$
You must have had some idea how big a difference would be
of sufficient practical importance to get your work published.
Also, it would have been reasonable to aspire to a
$90\%$ or $95\%$ chance of detecting a difference of important size with whatever
number of subjects you used.
Without making false claims, you could talk generically about
power and sample size as outlined just above. Maybe you are
astonished to have found any effect at all or maybe you had
wished to find a larger effect, but it might be helpful to readers
of your paper to have some context for what
must (should?) have been in your mind when embarking on the experiment.
Moreover, maybe the AE is hoping your next submission shows evidence
of a cogent power and sample size study at the beginning. Do that,
make notes, and save relevant computer printouts.