# a simple question to statistics - (May/15/2012 )

Let´s say I have 3 groups of independent data sets (n=3), each group of sample size N=5;

for each group I can determine mean (X1,X2,X3) and standard deviation (SD1,SD2,SD3);

my question is: How to correctly determine the standard error of means (SEM) of the mean of the 3 means (X1-X3)? I think I have to take the SD of each group into account, but by which method?

I'd like to know something along these lines too.

So...3 samples/animals, 3 repeats each. If I want to summarise the whole lot, do I take the mean and SEM of the mean for each animal or the mean and SEM of all 9 repeats...or some other method?

Hi,

assuming that your data sets are generated following the same experimental protocol, I think you can first calculate the mean in each independent data set and then use the obtained values to calculate the mean. In this case the associated SD need to be calculated using all the means of your independent data sets.

Hope it helps

Inmost sun on Tue May 15 10:22:24 2012 said:

Let´s say I have 3 groups of independent data sets (n=3), each group of sample size N=5;

for each group I can determine mean (X1,X2,X3) and standard deviation (SD1,SD2,SD3);

my question is: How to correctly determine the standard error of means (SEM) of the mean of the 3 means (X1-X3)? I think I have to take the SD of each group into account, but by which method?

My interpretation of this is that you are after the intergroup variation in which case you calculate the standard deviation of just the three means (remembering to use sample stdev, n-1=2). You would then use the pooled standard deviation as the within-group variation.

red_monkey on Sun Jul 15 17:03:55 2012 said:

So...3 samples/animals, 3 repeats each. If I want to summarise the whole lot, do I take the mean and SEM of the mean for each animal or the mean and SEM of all 9 repeats...or some other method?

Whereas this is asking for the global standard deviation; grouping all 9 repeats.

Any approach to combine these data statistically would probably look strange when you publish the results. This is normally done by just reporting the results of one "representative" experiment and indicating in the text that you repeated it 3 times. Where you are working with animals, you can probably justify doing just about anything though.