ttest: compare means between two groups
Estimate a difference in group means, quantify its uncertainty, and separate statistical evidence from causal interpretation.
How to run a t-test in Stata-compatible syntax
The example compares math scores between the two values of female in a 24-row synthetic teaching dataset.
clear
import delimited "data/student_scores.csv"
ttest math, by(female)With two independent groups, the default command estimates their means and tests the null hypothesis that the population mean difference is zero under an equal-variance model.
Output from stats.camp
Two-sample t test with equal variances
------------------------------------------------------------------------------
Group | Obs Mean Std. err. Std. dev. [95% conf. interval]
-------------+----------------------------------------------------------------
0 | 12 52.916667 1.835914 6.359793 48.875847 56.957486
1 | 12 61.833333 1.795758 6.220689 57.880896 65.78577
-------------+----------------------------------------------------------------
Combined | 24 57.375 1.562482 7.654567 54.14276 60.60724
-------------+----------------------------------------------------------------
diff | -8.916667 2.568137 -14.242657 -3.590676
------------------------------------------------------------------------------
diff = mean(0) - mean(1) t = -3.4720
H0: diff = 0 Degrees of freedom = 22
Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Pr(T < t) = 0.0011 Pr(|T| > |t|) = 0.0022 Pr(T > t) = 0.9989
How to read the result
Group 0 has a mean of about 52.92 and group 1 has a mean of about 61.83. Because the reported difference is mean(0) - mean(1), the estimate is −8.92 points. Its 95% confidence interval is approximately −14.24 to −3.59, and the two-sided p-value is 0.0022.
The data are invented, and the grouping variable was not randomly assigned. The result demonstrates command interpretation; it is not evidence about real students and does not identify a causal effect.
Choose the t-test form from the study design
ttest math == 55
ttest math, by(female)
ttest read == math
ttest math, by(female) unequal- One-sample
ttest math == 55compares one sample mean with a fixed reference value.- Two independent samples
ttest math, by(female)compares the two values of a grouping variable.- Paired measurements
ttest read == mathtests the mean within-row difference.- Unequal variances
- Add
unequalorwelchto use the supported unequal-variance calculation.
One-sample: mean(math) = 57.375; two-sided p = 0.1421 Paired: mean(read - math) = -1.208333; two-sided p = 0.0046 Unequal variances: mean(0) - mean(1) = -8.916667 Satterthwaite's degrees of freedom = 21.989249; two-sided p = 0.0022
These results answer different questions even though they use the same dataset. Choose the form before examining its p-value; do not substitute a paired test for independent observations or choose a variance assumption because it produces a preferred result.
Assumptions, variants, and limits
- Check that observations are independent and that a mean-based comparison is appropriate for the outcome and sample size.
- The default two-sample form assumes equal population variances. stats.camp also supports
unequalandwelchalternatives for the corresponding model. - One-sample and paired tests answer different questions; choose the form from the study design rather than the observed p-value.
- A small p-value is not an effect size, a measure of practical importance, or proof of causality.
See the current ttest entry and Stata's ttest manual for an external reference.
Related guides
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