# 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:

${\displaystyle t={\frac {{\bar {x}}_{1}-{\bar {x}}_{2}}{\sqrt {{\frac {\sum _{j=1}^{J}\sum _{i=1}^{n_{j}}w_{ij}(x_{ij}-{\bar {x}}_{j})^{2}}{v}}({\frac {1}{e_{1}}}+{\frac {1}{e_{1}}})}}}}$

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,
${\displaystyle v=(J-1)(\sum _{j=1}^{J}e_{j}-1)}$ for Repeated Measures and ${\displaystyle v=\sum _{j=1}^{J}e_{j}-J-1}$ 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).