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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!).

Mud Warrior
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BeStats
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    What is it you want to know, just if the means differ? How many groups do you have? Are you willing to assume normality? – gung - Reinstate Monica Jun 28 '16 at 18:16
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    Do you know anything about the sample sizes? – Michael M Jun 28 '16 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. – BeStats Jun 28 '16 at 19:18
  • This is discussed a number of times (in several different ways) on site. For example, see [here](http://stats.stackexchange.com/questions/174581/anova-grand-mean-from-means-standard-deviation-and-sample-size-n) and [here](http://stats.stackexchange.com/questions/57758/anova-analysis-with-only-mean-and-standard-deviation) and also posts on calculating combined variance from group summaries and sample sizes, (such as the discussion under item 1. [here](http://stats.stackexchange.com/questions/216047/how-does-one-go-about-determining-the-standard-deviation-of-an-entire-sample-dat/216060#216060) ) – Glen_b Jun 29 '16 at 06:48
  • (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) – Glen_b Jun 29 '16 at 06:50

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The t-test can be performed with only means, standard deviations and sample sizes. Formula and procedure are given in the wikipedia.

https://en.m.wikipedia.org/wiki/Student%27s_t-test#Calculations

Bernhard
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