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# RE: st: Difference of means and t-test

 From Richard Williams To statalist@hsphsun2.harvard.edu, Subject RE: st: Difference of means and t-test Date Mon, 14 Jun 2010 13:08:29 -0500

```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.

Nick
n.j.cox@durham.ac.uk
```
```
```
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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Richard Williams, Notre Dame Dept of Sociology
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```