Independent t-test (Welch)

§2.3

Rev 4.6 · reviewed Feb 2026

Compares a continuous outcome between two independent groups from summary statistics. Welch's version does not assume equal variances — use it by default.

Source formula: Welch BL. Biometrika 1947;34:28–35.

Table. Group summaries

	n	Mean	SD
Group 1
Group 2

* Student. Biometrika 1908;6:1–25.

† Welch BL. Biometrika 1947;34:28–35.

Mean difference (±1.96 SE)

7.30 (0.58 to 14.02)

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t statistic

2.13

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Welch–Satterthwaite df†

78.9

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Two-sided p

0.036▲

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Group 1's mean is 7.30 units higher than Group 2's. That difference is statistically significant (p 0.036). Check that the outcome is roughly normal within groups, or n is large.

Understand what this is measuring

Linear regression