# Dunnett’s Pairwise Multiple Comparison

This test compares each group with the first group. Prior to selecting this test you need to specify these comparisons and remove any NET from the columns of the table.

The test statistic is:

$\displaystyle{ t=\frac{\bar x_1-\bar x_2}{\sqrt{\frac{\sum^{J}_{j=1}\sum^{n_j}_{i=1} w_{ij}(x_{ij} - \bar x_j)^2}{v}(\frac{1}{e_1}+\frac{1}{e_1})}} }$

where:

$\displaystyle{ \bar x_1 }$ and $\displaystyle{ \bar x_2 }$ are the means of the two groups being compared and $\displaystyle{ \bar x_j }$ is the mean of the $\displaystyle{ j }$ of $\displaystyle{ J }$ groups,
when applying the test to Repeated Measures, each respondent’s average is initially subtracted from their data and it is this corrected data that constitutes of $\displaystyle{ x_{ij} }$,
$\displaystyle{ n_j }$ is the number of observations in the $\displaystyle{ j }$th of $\displaystyle{ J }$ groups,
$\displaystyle{ w_{ij} }$ is the Calibrated Weight for the $\displaystyle{ i }$th observation in the $\displaystyle{ j }$ group,
$\displaystyle{ e_j }$ is the Effective Sample Size for the $\displaystyle{ j }$ group,
$\displaystyle{ v = (J - 1)(\sum^J_{j=1} e_j - 1) }$ for Repeated Measures and $\displaystyle{ v = \sum^J_{j=1} e_j - J - 1 }$ otherwise.
$\displaystyle{ t }$ is evaluated using a multivariate $\displaystyle{ t }$ distribution (see Dunnett C. W. (1955.) "A multiple comparison procedure for comparing several treatments with a control", Journal of the American Statistical Association, 50:1096–1121).