Ttest Calculator
Our free statistics calculator solves ttest problems. Get worked examples, visual aids, and downloadable results. Enter your values for instant results.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
t = (x1 - x2) / sqrt(s1^2/n1 + s2^2/n2)
Where x1 and x2 are sample means, s1 and s2 are sample standard deviations, and n1 and n2 are sample sizes. This is the Welch t-test formula that does not assume equal variances. The degrees of freedom are approximated using the Satterthwaite equation.
Worked Examples
Example 1: Comparing Two Teaching Methods
Problem:Test scores with Method A: 78, 82, 85, 79, 81, 83, 77, 80. Method B: 85, 88, 90, 86, 89, 91, 84, 87. Is there a significant difference at alpha = 0.05?
Solution:Mean A = 80.625, SD A = 2.615, n = 8\nMean B = 87.500, SD B = 2.449, n = 8\nMean Difference = -6.875\nWelch SE = sqrt(2.615^2/8 + 2.449^2/8) = 1.268\nt = -6.875 / 1.268 = -5.422\ndf (Welch) = 13.9\nTwo-tailed p < 0.001\nCohen d = 2.71 (large effect)
Result:t = -5.422 | p < 0.001 | Significant | Cohen d = 2.71 (Large effect)
Example 2: One-Sample Test Against Known Mean
Problem:A manufacturer claims packages weigh 500g. Sample weights: 498, 502, 497, 501, 499, 503, 496, 500. Test at alpha = 0.05.
Solution:Sample mean = 499.5, SD = 2.449, n = 8\nHypothesized mean = 500\nt = (499.5 - 500) / (2.449/sqrt(8)) = -0.577\ndf = 7\nTwo-tailed p = 0.582\nSince p > 0.05, fail to reject H0.
Result:t = -0.577 | p = 0.582 | Not significant | No evidence packages deviate from 500g
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy