Welch's t-test: Difference between revisions

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=={{header|Stata}}==

Here is a straightforward solution using the '''ttest''' command. If one does not want the output but only the p-value, prepend the command with '''qui''' and use the result r(p) as shown below. The t statistic is r(t). Notice the data are stored in a single variable, using a group variable to distinguish the two series.

Notice that here we use the option '''unequal''' of the '''ttest''' command, and not '''welch''', so that Stata uses the Welch-Satterthwaite approximation.

<lang stata>mat a=(3,4,1,2.1,490.2,340,433.9\1,1,1,1,2,2,2)'

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svmat double a

rename (a1 a2) (x group)

ttest x, by(group) ~~welch~~

ttest x, by(group) unequal

Two-sample t test with unequal variances

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combined | 7 182.0286 86.22435 228.1282 -28.95482 393.012

---------+--------------------------------------------------------------------

diff | -418.8417 43.81419 -607.~~2052~~ -230.~~4782~~

diff | -418.8417 43.81419 -607.282 -230.4014

------------------------------------------------------------------------------

diff = mean(1) - mean(2) t = -9.5595

Ho: diff = 0 ~~Welch~~'s degrees of freedom = 2.~~0017~~

Ho: diff = 0 Satterthwaite's degrees of freedom = 2.00085

Ha: diff < 0 Ha: diff != 0 Ha: diff > 0

Pr(T < t) = 0.0054 Pr(|T| > |t|) = 0.~~0107~~ Pr(T > t) = 0.9946

Pr(T < t) = 0.0054 Pr(|T| > |t|) = 0.0108 Pr(T > t) = 0.9946

di r(t)

-9.5594977

di r(p)

.~~01073671</lang>~~

.01075156

</lang>

The computation can easily be implemented in Mata. Here is how to compute the t statistic (t), the approximate degrees of freedom (df) and the p-value (p).