t-Test Calculator (Independent & Paired Samples)
Calculate Student's t-test, Welch's t-test, and paired-samples t-test. Computes exact p-values, 95% confidence intervals, degrees of freedom, Cohen's d effect size, and APA 7th write-ups.
How the t-Test Works in Psychology Research
The Student's t-test is one of the most widely utilized inferential statistics in behavioral and psychological science. It evaluates whether the observed difference between two group means is greater than what would be expected by random sampling variability alone.
Mathematical Formulas
t = \frac{\bar{X}_1 - \bar{X}_2}{S_p \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}Independent Samples t-Test with pooled standard deviation (equal variances assumed)
S_p = \sqrt{\frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}}Pooled Standard Deviation formula
t = \frac{\bar{D}}{s_D / \sqrt{N}}Paired Samples t-Test formula (mean of paired difference scores divided by standard error of differences)
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