Glossary
T-Test
A t-test is a parametric hypothesis test used to compare means between one or two groups. It evaluates whether the observed difference in means is larger than would be expected by random sampling alone, using the t-distribution to account for uncertainty in small samples.
Definition
A t-test is a parametric hypothesis test used to compare means between one or two groups. It evaluates whether the observed difference in means is larger than would be expected by random sampling alone, using the t-distribution to account for uncertainty in small samples.
Why It Matters
The t-test is one of the most frequently used statistical tests in academic research. It is straightforward to apply, widely understood across disciplines, and forms the conceptual foundation for more complex analyses such as ANOVA and regression. Choosing the correct variant — one-sample, independent, or paired — ensures valid conclusions and protects against common design errors.
Example
A researcher wants to know whether a mindfulness intervention reduces anxiety scores. She measures anxiety in 30 participants before and after the intervention. Because the same individuals are measured twice, she uses a paired-samples t-test. If the mean reduction is 4.5 points with a p-value of 0.02, she concludes the intervention had a statistically significant effect on anxiety in this sample.
Related Terms
- ANOVA (extends the t-test to three or more groups)
- P-Value
- Effect Size (Cohen's d is the standard effect size for t-tests)
- Normal Distribution
- Statistical Significance
Software Notes
- SPSS: Analyze > Compare Means > Independent-Samples T Test (two groups) or Paired-Samples T Test (repeated measures). Check Levene's test for equality of variances.
- R:
t.test(group1, group2)for independent;t.test(before, after, paired = TRUE)for paired. Welch's correction is applied by default. - Stata:
ttest dv, by(group)for independent;ttest before == afterfor paired. Usettest dv, by(group) unequalfor unequal variances.