A contrast is a combination of population means of the form :
Where the coefficients ai have sum 0.
The corresponding sample contrast is :
The standard error of c is :
To test the null hypothesis H0: = 0 use the t-statistic:
With degrees of freedom DFE that is associated with sp. The alternative hypothesis can be one- or two-sided.
A level C confidence interval for the difference is :
Where t* is the critical value defining the middle C% of the t distribution with DFE degrees of freedom.