TR

Critical values and p-values

Choose the distribution, degrees of freedom and significance level. If you already have a test statistic, enter it to see whether it falls in the rejection region and what its p-value is.

Distribution

When? When the population standard deviation is unknown and the sample is small, e.g. comparing the means of two varieties.

-4-2024-2.082.08t (df = 21)

Red areas are the rejection region; their total area equals α. Change the degrees of freedom and watch how the curve’s shape changes.

Critical value

t21t_{21} ± 2.08

  1. In a two-tailed test α = 0.05 is split equally between the two tails; each tail gets 0.025.

    α2=0.052=0.025\dfrac{\alpha}{2} = \dfrac{0.05}{2} = 0.025

  2. The distribution is symmetric, so the two limits differ only in sign.

    t21=±2.08t_{21} = \pm 2.08

  3. If the test statistic falls outside these limits, H₀ is rejected.