## Stata 15 help for ttest

```
[R] ttest -- t tests (mean-comparison tests)

Syntax

One-sample t test

ttest varname == # [if] [in] [, level(#)]

Two-sample t test using groups

ttest varname [if] [in] , by(groupvar) [options1]

Two-sample t test using variables

ttest varname1 == varname2 [if] [in], unpaired [unequal welch
level(#)]

Paired t test

ttest varname1 == varname2 [if] [in] [, level(#)]

Immediate form of one-sample t test

ttesti #obs #mean #sd #val [, level(#)]

Immediate form of two-sample t test

ttesti #obs1 #mean1 #sd1 #obs2 #mean2 #sd2 [, options2]

options1          Description
-------------------------------------------------------------------------
Main
* by(groupvar)    variable defining the groups
unequal         unpaired data have unequal variances
welch           use Welch's approximation
level(#)        set confidence level; default is level(95)
-------------------------------------------------------------------------
* by(groupvar) is required.

options2          Description
-------------------------------------------------------------------------
Main
unequal         unpaired data have unequal variances
welch           use Welch's approximation
level(#)        set confidence level; default is level(95)
-------------------------------------------------------------------------

by is allowed with ttest; see [D] by.

ttest

Statistics > Summaries, tables, and tests > Classical tests of
hypotheses > t test (mean-comparison test)

ttesti

Statistics > Summaries, tables, and tests > Classical tests of
hypotheses > t test calculator

Description

ttest performs t tests on the equality of means.  The test can be
performed for one sample against a hypothesized population mean.
Two-sample tests can be conducted for paired and unpaired data.  The
assumption of equal variances can be optionally relaxed in the unpaired
two-sample case.

ttesti is the immediate form of ttest; see immed.

Options

+------+
----+ Main +-------------------------------------------------------------

by(groupvar) specifies the groupvar that defines the two groups that
ttest will use to test the hypothesis that their means are equal.
Specifying by(groupvar) implies an unpaired (two sample) t test.  Do
not confuse the by() option with the by prefix; you can specify both.

unpaired specifies that the data be treated as unpaired.  The unpaired
option is used when the two sets of values to be compared are in
different variables.

unequal specifies that the unpaired data not be assumed to have equal
variances.

welch specifies that the approximate degrees of freedom for the test be
obtained from Welch's formula (1947) rather than from Satterthwaite's
approximation formula (1946), which is the default when unequal is
specified.  Specifying welch implies unequal.

level(#) specifies the confidence level, as a percentage, for confidence
intervals.  The default is level(95) or as set by set level.

Examples

. sysuse auto             (setup)
. ttest mpg==20           (one-sample t test)

. webuse fuel3            (setup)
. ttest mpg, by(treated)  (two-sample t test using groups)

. webuse fuel             (setup)
. ttest mpg1==mpg2        (two-sample t test using variables)

(no setup required)
. ttesti 24 62.6 15.8 75  (immediate form; n=24, m=62.6, sd=15.8;
test m=75)

Video examples

One-sample t test in Stata

t test for two independent samples in Stata

t test for two paired samples in Stata

One-sample t-test calculator

Two-sample t-test calculator

Stored results

ttest and ttesti store the following in r():

Scalars
r(N_1)         sample size n_1
r(N_2)         sample size n_2
r(p_l)         lower one-sided p-value
r(p_u)         upper one-sided p-value
r(p)           two-sided p-value
r(se)          estimate of standard error
r(t)           t statistic
r(sd_1)        standard deviation for first variable
r(sd_2)        standard deviation for second variable
r(sd)          combined standard deviation
r(mu_1)        x_1 bar, mean for population 1
r(mu_2)        x_2 bar, mean for population 2
r(df_t)        degrees of freedom
r(level)       confidence level

References

Satterthwaite, F. E. 1946.  An approximate distribution of estimates of
variance components.  Biometrics Bulletin 2: 110-114.

Welch, B. L. 1947.  The generalization of `student's' problem when
several different population variances are involved. Biometrika 34:
28-35.

```