Description Usage Arguments Value

This function calcualtes the residual $x_ijk-barx_ij.$ for the kth replication from the ith group at jth time point.

1 | ```
eu(x, coln, Rij, Rik)
``` |

`x` |
the data matrix in long format, whose first column gives the index i, 2nd columns given the index j, 3rd column gives the index k, and the last column gives the observation $x_ijk$. For given i and j, $x_ijk, k=1, ..., n_ij$ are assumed to be i.i.d. from the same distribution. |

`coln` |
takes value 4 or 5. If coln=4, the calculation uses original data; if coln=5, the calculation uses rank. The default value for coln is 5. |

`Rij` |
is the mean of all observations in ith treatment at jth measurement calculated in other functions |

`Rik` |
is the mean for the kth subject in ith treatment calculated in other functions |

The residual to be used in Heter.test()

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