How to calculte SD and SE from lsm difference

[mona4u]

I have this example and I need to calculate SE, SD  from this available information. 

Can you help me with this? 

[PaigeMiller]

Let's assume you do the analysis in PROC GLM.

The Least Squares Means and their standard errors come from the LSMEANS statement. Example: https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.4/statug/statug_glm_examples04.htm

I believe (but haven't confirmed) that if you use the LINESTABLE option of the LSMEANS statement, you get the differences and the confidence intervals for the differences.

[mona4u]

I want to calculate it manually as I only have these outputs. 

[SteveDenham]

Well, with only the information in the table, you won't be able to calculate by hand the SD and SE for each of the groups.  Well, first off, whatever analysis was done assumed homogeneity of variance - you can tell because the standard errors for the lsmeans are identical.  With different N's per group, that implies that the lsmeans are truly marginal means -> expected values of the distributions, rather than the averages for each group.

What you could try is to simulate data with these means and standard errors, having say 500 or 1000 samples of 298 and 294 observations each.  Calculate the mean, standard deviation and standard error for each sample. That would be enough to let the Central Limit Theorem give you an accurate approximation if you took the average of each set of samples.

SteveDenham

[mona4u]

I want to calculate the SD and SE diff for both groups.