= Minimum sample size needed to assume Normality =

The pdf here from [[http://www2.psychology.uiowa.edu/faculty/mordkoff/GradStats/part%201/I.07%20normal.pdf | here]] is available from [[attachment:norms_size.pdf | here]] if the link is broken.

The below extract taken from the above link suggests that 30 observations is sufficient to make the assumption of a Normal distribution tenable.
 
“In general, it is said that Central Limit Theorem “kicks in” at an N of about 30. In other words, as long as the sample is based on 30 or more observations, the sampling distribution of the mean can be safely assumed to be normal” 

[[attachment:samp30.pdf | NIHR guidelines]] quote Lancaster, Dodd and Williamson (2004) also suggest an overall sample size of 30 for parameter estimation such as a standard deviation.

__Comparing change between two time points__

The t-test, however, is at least reasonably robust to at least mild non-normality, in for example, the differences in paired t-tests (and it's the differences that are supposed to be normal no the endpoints). If the observations have small skews (say less than 1 in absolute value) and kurtoses (less than 3 in absolute value), the differences may be indistinguishable from normal even at large sample sizes. If the normality assumption holds, the t-test will still be more powerful than the signed rank test, for one. I'd imagine this is also true for various other non-parametric tests. So, it still may be best to use the t-test. That said, there's little reason to avoid the Wilcoxon (nonparametric paired) test if non-normality is the main concern. 

__Reference__

Lancaster GA, Dodd S & Williamson PR (2004) Design and analysis of pilot studies: recommendations for good practice. ''J Eval Clin Practice'' '''10''' 307-312.