RE: st: Difference of means and t-test

["Nick Cox" <n.j.cox@durham.ac.uk>]

I don't think our views are contradictory. It is clearly true that you
can get results from summary statistics alone. But erecting fake
Gaussians with those summaries is not equivalent to reconstructing the
original data. That is my point, and no more. It is akin to arguments at
a higher level about "sufficient statistics". If something is normal,
then it is sufficient to know mean and sd, but there isn't a reverse
argument. 

Nick 
n.j.cox@durham.ac.uk 

Richard Williams

At 11:19 AM 6/14/2010, Nick Cox wrote:
>-- except that will surely overstate the strength of the conclusions,
in
>so far as the real distributions are unlikely to be exactly Gaussian.

I don't believe that is correct.  You can often get by with only 
having the summary statistics, which is why things like ttesti 
work.  Consider the following example (probably clunkier than 
necessary but functional): First i use the real data to compute an 
anova.  Then, using the reported Ns, means, and standard deviations, 
I create 4 fake data sets, append them together, and run the anova 
again.  Results are identical.  There is obviously no reason to do 
this if you have the real data, but stuff like this may be handy if 
you only have published results to go by.

use "http://www.indiana.edu/~jslsoc/stata/spex_data/ordwarm2.dta";, clear
oneway age warm, t
corr2data age, n(297) mean(50.468013) sd(16.627471) clear
gen warm = 1
save warm1
corr2data age, n(723) mean(48.255878) sd(17.365776) clear
gen warm = 2
save warm2
corr2data age, n(856) mean(42.23715) sd(16.329103) clear
gen warm = 3
save warm3
corr2data age, n(417) mean(40.776978) sd(14.480446) clear
gen warm = 4
save warm4
clear all
append using warm1 warm2 warm3 warm4
oneway age warm, t

Pages 8-10 of the following handout show how you can do OLS 
regression when you only have the means, standard deviations and 
correlations available to you. (It also shows you what you can't 
legitimately do):

http://www.nd.edu/~rwilliam/stats1/OLS-Stata9.pdf

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