Welch Two Sample Mean Comparison Calculator
Compare independent sample means using unequal-variance standard errors, Welch degrees of freedom and a two-sided interval.
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Result
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Calculation steps
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How to calculate
Combine the two independent sample-mean variances, calculate Welch–Satterthwaite degrees of freedom and evaluate the Student t tail and confidence limits.
SE=√(s1²/n1+s2²/n2); t=(mean1−mean2)/SE; df=(v1+v2)²/[v1²/(n1−1)+v2²/(n2−1)]
Worked example
Means 10 and 8, both sample SD 2 and n=20, give difference 2, SE √0.4, t √10 and df 38. The 95% interval is approximately 0.7197 to 3.2803.
Assumptions and input details
Independent samples with n from 2 to 40000, finite sample means and nonnegative sample SD; at least one SD positive. No paired observations, sampling weights or equal-variance assumption. The t approximation needs appropriate sampling conditions and can be poor with severe skew or small samples. Tests a zero population mean difference, two-sided only. P-values do not measure effect importance or prove causality; confidence is not a posterior probability.
References: NIST: two-sample t test and Welch degrees of freedom
Using this calculator
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Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
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