If t_calc  > t_table then a real difference exists for given confidence level and d.f.  If  is specified, then "s" has been determined by a separate series of measurements, and d.f. are assumed to be infinite.

 
If t_calc  > t_table at the desired confidence level and correct degrees of freedom, then our mean values differ significantly from each other.  Degrees of freedom = N₁+N₂-2 in this example.  If  is specified, then s is put in place of s_pooled but the N's are still used.

David Zellmer
Chemistry 102
Spring 1998