# Can I run statistical tests on descriptive statistics like mean and standard deviation? (i.e. no raw data)

I'm trying to figure out which statistical test to run on my data, but it has been processed so that now I have gathered the mean and standard deviation values to be used instead of the raw data.

I thought that any statistical test (like t tests and ANOVAs for instance) would calculate the mean values and then compare them to give you the test statistic. So my question is, if I don't have the raw data but only the mean and SD values, can I still run these tests or would I need to run other types? (Seems strange thinking that the above mentioned tests would be calculating the mean of the mean, that's all!).

• What is it you want to know, just if the means differ? How many groups do you have? Are you willing to assume normality? Jun 28, 2016 at 18:16
• Do you know anything about the sample sizes? Jun 28, 2016 at 18:32
• I am dealing with accelerometry time series data at 40 Hz (2400 data points per minute of data). I am investigating how this data changes over time (i.e. minute by minute; I have a "before" and "after" as well as various minutes in between, that can be treated individually or summed as an average time of "during") of 20 participants. Each of them carried out the study 3 times (i.e. with the same procedures and time frames of before, during and after) but under different treatments. The means I have gathered seem to be slightly skewed to the right, though I'm hoping to normalise them. Jun 28, 2016 at 19:18
• This is discussed a number of times (in several different ways) on site. For example, see here and here and also posts on calculating combined variance from group summaries and sample sizes, (such as the discussion under item 1. here ) Jun 29, 2016 at 6:48
• (I won't close as duplicate of any of those, at least not yet, because I suspect from your description in comments that ANOVA may be unsuitable) Jun 29, 2016 at 6:50