Independent Samples t-test
Also known as: student t-test, two-sample t-test, unpaired t-test, bağımsız örneklem t-testi
The independent samples t-test is a parametric hypothesis test that compares the means of two independent groups to decide whether they differ significantly. It builds on the t-distribution introduced by Student (W. S. Gosset) in 1908 and assumes the measured values are continuous, approximately normally distributed, and have equal variances.
Key highlights
- Simple, widely accepted, and powerful when its assumptions hold.
- Reports an interpretable effect size (Cohen's d) alongside the p-value.
- Backed by over a century of statistical theory and available in every analysis package.
Intuition
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How it works
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When to use it
Use it to compare exactly two independent groups on a single continuous outcome. Three assumptions should hold: each group's values are approximately normally distributed (check with Shapiro-Wilk), the two groups have equal variances (check with Levene's test, otherwise switch to the Welch correction), and observations are independent both within and between groups. With very small samples or clear non-normality, a nonparametric alternative such as the Mann-Whitney U test is more appropriate.
Strengths & limitations
- Simple, widely accepted, and powerful when its assumptions hold.
- Reports an interpretable effect size (Cohen's d) alongside the p-value.
- Backed by over a century of statistical theory and available in every analysis package.
- Sensitive to non-normality and outliers in small samples.
- Limited to comparing exactly two groups.
- The pooled-variance form assumes equal variances; unequal spread requires the Welch correction.
Common pitfalls
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Applications
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Frequently asked
One-tailed or two-tailed?
The default is two-tailed, testing whether the means differ in either direction. Use a one-tailed test only when you have a directional hypothesis decided before seeing the data; it concentrates the rejection region on one side and is easier to reject but only in the predicted direction.
Student or Welch — which version should I use?
The classic Student t-test pools the variances and assumes the two groups have equal spread. If Levene's test is significant, or you are unsure, use the Welch correction, which does not assume equal variances and adjusts the degrees of freedom accordingly.
Why report an effect size?
The p-value only tells you whether a difference is statistically detectable, not how large it is. Cohen's d expresses the mean difference in standard-deviation units, so you can judge practical importance. Reporting the mean difference and its 95% confidence interval is recommended alongside d.
How is this different from ANOVA?
The independent t-test compares exactly two group means. When you have three or more groups, use one-way ANOVA instead of running multiple t-tests, which would inflate the false-positive rate.
Sources
- 1.Student (1908). The probable error of a mean. Biometrika, 6(1), 1–25.
- 2.Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed.). SAGE.ISBN 978-1446249185
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Cite this page
ScholarGate. (2026, June 1). Independent t-test. ScholarGate. https://scholargate.app/statistics/independent-t-test