T-Test Calculator

Calculate t-tests to compare means and determine statistical significance.

Test Configuration

Enter numeric values separated by commas, spaces, or line breaks

T-Test Formulas

One-Sample T-Test

Tests whether a sample mean differs from a hypothesized population mean:

t=xˉ−Îŧ0s/nt = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}

Where:

  • xˉ\bar{x} = Sample mean
  • Îŧ0\mu_0 = Hypothesized population mean
  • ss = Sample standard deviation
  • nn = Sample size

Independent Samples T-Test

Tests whether the means of two independent samples differ:

t=xˉ1−xˉ2sp1n1+1n2t = \frac{\bar{x}_1 - \bar{x}_2}{s_p \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}

Where the pooled standard deviation is:

sp=(n1−1)s12+(n2−1)s22n1+n2−2s_p = \sqrt{\frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}}

Where:

  • xˉ1,xˉ2\bar{x}_1, \bar{x}_2 = Sample means
  • s1,s2s_1, s_2 = Sample standard deviations
  • n1,n2n_1, n_2 = Sample sizes
  • sps_p = Pooled standard deviation

Paired Samples T-Test

Tests whether the mean difference between paired observations is zero:

t=dˉsd/nt = \frac{\bar{d}}{s_d / \sqrt{n}}

Where:

  • dˉ\bar{d} = Mean of the differences
  • sds_d = Standard deviation of the differences
  • nn = Number of pairs

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