Student's t-test

Student's t-test is a statistical test that is usually used to compare the means of two or more groups to see if they are different. For example, comparing the average task completion time for a group of people using an old version of a system vs that of a second group using a new improved user interface. It is calculated by taking the difference of the means and dividing by an estimate of the standard deviation of the difference obtained from the standard deviation of the sample for each of the groups.

      t = (μ₁ – μ₂) / √(σ₁²/N₁ – & sigma;₂²/N₂)

The theoretical distribution of the value of this t-test follows the Student's t distribution. The t-test depends on the data being approximately Normal, but is fairly robust if this is not perfect.

The theoretical t distribution is a Normal variable divided by the square root of an independent variable with the Chi-squared distribution. This is because the sample variance follows the chi-squared distribution.