I'm working on a review paper and need to collect the means and standard deviations of a given measure (such as a measure of depression) from papers of interest. However, some authors report means and standard deviations for each item on the measure, but do not calculate the overall mean and standard deviation. For example, for a measure with a 1-5 Likert-type response scale, rather than reporting a mean depression score of 2.5, sd = .34, for the whole scale, they'll report: item 1 mean 2.4, sd=.41, item 2 mean 2.5, sd=.38, etc.
1) Can I calculate the scale mean by simply taking the average of the item means?
2) Is it possible to calculate the accompanying scale standard deviation? And if so, how? It's probably not as simple as taking the average of the item standard deviations....
If it isn't possible, I can just contact the authors, but I hate to bother them if the needed stats can be calculated from the provided information.
Any advice would be greatly appreciated! Thank you!