power analysis for multilevel model with significant finding I am working on a study where data collection is still in progress. I have done preliminary analysis with a multilevel model on a small number of people (n=19), and there is a statistically significant treatment effect. There is interest in doing a power analysis now to determine how many additional people to collect data from. Note- I realize power analysis should have been done before data collection began but that wasn't done in this case. I'm wondering is there any point in doing a power analysis if the results are already statistically significant? If there is, what is the point? 19 seems like a small total number.
thanks!
 A: There Be Dragons Here ... if you didn't design your study with intermediate analyses in mind ("stopping rules"), you can make some pretty big statistical mistakes (e.g. see here for an introduction). If you want to be able to use standard inferential tools reliably, you should carry on and perform the study the way it was designed. (I'm not sure exactly what you have in mind, but stopping the study now because the result happens to be statistically significant at the moment is a bad idea.)
That said: a rough rule of thumb (which will still hold, more or less, for mixed models) is that your standard errors will be roughly proportional to $\sqrt{N}$.  If you collect 9 times as much data (i.e. sample 171 people in total instead of 19), you can on average expect your standard errors to shrink by approximately a factor of 3, with whatever effects that will have on your conclusions.
If you insist on doing a power analysis now, it would be safest to forget the preliminary analysis you've just done and base it on the previously existing literature.
A: When calculating the sample size, the background information in needed. For example, group means and variance for t-test. These background information come fro literature, previous studies, or even from guess. For your situation, maybe the best background information is the results from that 19 people. But based on the results from that 19 people, the calculated sample size will be less or equal to 19, because you already get the significance.
