Ttest Calculator
Our free statistics calculator solves ttest problems. Get worked examples, visual aids, and downloadable results. Enter your values for instant results.
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
Frequently Asked Questions
Can I use Ttest Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.
Can I share or bookmark my calculation?
You can bookmark the calculator page in your browser. Many calculators also display a shareable result summary you can copy. The page URL stays the same so returning to it will bring you back to the same tool.
How accurate are the results from Ttest Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
What formula does Ttest Calculator use?
The formula used is described in the Formula section on this page. It is based on widely accepted standards in the relevant field. If you need a specific reference or citation, the References section provides links to authoritative sources.
Can I use the results for professional or academic purposes?
You may use the results for reference and educational purposes. For professional reports, academic papers, or critical decisions, we recommend verifying outputs against peer-reviewed sources or consulting a qualified expert in the relevant field.
Is Ttest Calculator free to use?
Yes, completely free with no sign-up required. All calculators on NovaCalculator are free to use without registration, subscription, or payment.