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How to calculate sample size needed for comparing change from baseline scores for one group? Which statistic would be use to analyze the mean change?

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The simplest statistic you could use is a within-subjects t-test. To determine sample size, you can do a power analysis. To do this, you need some idea of what size effect you are looking for. Once you know what size effect you are expecting, then you can use power analysis tools such as calculators found online, G*Power, or a number of R packages and SPSS macros.

Cohen's 1992 paper in Psychological Bulletin will help you out, as will Lakens's 2013 paper on effect sizes in the Frontiers in Psychology.

Within-subject sizes are a little bit trickier, but you are looking for a within-subjects version of a Cohen's d. The basic one is called dz.

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