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Test Statistic for Hypothesis Tests Concerning Mean Difference (Normally Distributed Populations, Unknown Population Variances)
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\(t_{n-1}=\frac{\bar{d}-\mu_{d0}}{s_{\bar{d}}}\)

  • \(t_{n-1}\) - t-statistic with "n-1" degrees of freedom
  • \(\bar{d}\) - sample mean difference
  • \(\mu_{d0}\) - value of the difference between means under null hypothesis
  • \(s_{\bar{d}}\) - standard error of mean difference

We use the paired-comparisons test, when samples drawn from both populations are not independent of each other.