How to determine sample size given there is 20% point reduction [ before change – after change =20% ] with 95% confidence level and 90% power ? Any pointer on how to solve this
A good first step is always to think about, what kind of test you plan to use. From the very little information you give a paired t-test (or a single measurement t-test comparing the difference to zero) is a likely candidate.
You can now google for "statistical power of t test" to which you can add the name of any computer language or statistics software you plan to use. Except maybe for educational purposes I'd advise to compute statics not by hand but via software.
Kind of an obvious option for statistic software on stackoverflow might be R
. In R
you'll find solutions to many sample size or power calculations in the package pwr
. Here is the link to a getting started text: https://cran.r-project.org/web/packages/pwr/vignettes/pwr-vignette.html
The pwr.t.test
function is good for your problem. Google will readily help you to alternatives for Python
and Julia
and SPSS
I assume for C++
, Java
and Javascript
as well.
However you will have to make assumptions about the variance or the effect size. Will each value be reduced by almost exactly 20% or will some be reduced a lot and some increase? That is of utmost importance to the question. You will need only one observation if there is no variance, a small amount of observations if there is little variance and a large amount of observations if there is lots of variance.