The function nparcomp computes the estimator of nonparametric relative contrast effects, simultaneous confidence intervals for the effects and simultaneous p-values based on special contrasts like "Tukey", "Dunnett", "Sequen", "Williams", "Changepoint", "AVE", "McDermott", "Marcus", "UmbrellaWilliams", "UserDefined". The statistics are computed using multivariate normal distribution, multivariate Satterthwaite t-Approximation and multivariate transformations (Probit and Logit transformation function). The function 'nparcomp' also computes one-sided and two-sided confidence intervals and p-values. The confidence intervals can be plotted.

1 2 3 4 5 6 7 8 | ```
nparcomp(formula, data, type = c("Tukey", "Dunnett",
"Sequen", "Williams", "Changepoint", "AVE", "McDermott",
"Marcus", "UmbrellaWilliams", "UserDefined"), control = NULL,
conf.level = 0.95, alternative = c("two.sided", "less",
"greater"), rounds = 3, correlation = FALSE,
asy.method = c("logit", "probit", "normal", "mult.t"),
plot.simci = FALSE, info = TRUE, contrast.matrix=NULL,
weight.matrix=FALSE)
``` |

`formula` |
A two-sided 'formula' specifying a numeric response variable and a factor with more than two levels. If the factor contains less than 3 levels, an error message will be returned. |

`data` |
A dataframe containing the variables specified in formula. |

`type` |
Character string defining the type of contrast. It should be one of "Tukey", "Dunnett", "Sequen", "Williams", "Changepoint", "AVE", "McDermott", "Marcus", "UmbrellaWilliams", "UserDefined". |

`control` |
Character string defining the control group in Dunnett comparisons. By default it is the first group by definition of the dataset. |

`conf.level` |
The confidence level for the conflevel confidence intervals (default is 0.95). |

`alternative` |
Character string defining the alternative hypothesis, one of "two.sided", "less" or "greater". |

`rounds` |
Number of rounds for the numeric values of the output. By default it is rounds=3. |

`correlation` |
A logical whether the estimated correlation matrix and covariance matrix should be printed. |

`asy.method` |
Character string defining the asymptotic approximation method, one of "logit", for using the logit transformation function, "probit", for using the probit transformation function, "normal", for using the multivariate normal distribution or "mult.t" for using a multivariate t-distribution with a Satterthwaite Approximation. |

`plot.simci` |
A logical indicating whether you want a plot of the confidence intervals. |

`info` |
A logical whether you want a brief overview with informations about the output. |

`contrast.matrix` |
User defined contrast matrix. |

`weight.matrix` |
A logical indicating whether the weight matrix should be printed. |

`Data.Info ` |
List of samples and sample sizes. |

`Contrast` |
Contrast matrix. |

`Analysis ` |
Comparison: relative contrast effect , relative.effect: estimated relative contrast effect, Estimator: Estimated relative contrast effect, Lower: Lower limit of the simultaneous confidence interval, Upper: Upper limit of the simultaneous confidence interval, Statistic: Teststatistic p.Value: Adjusted p-values for the hypothesis by the choosen approximation method. |

` input ` |
List of input by user. |

If the samples are completely seperated the variance estimators are Zero by construction. In these cases the Null-estimators are replaced by 0.001. Estimated relative effects with 0 or 1 are replaced with 0.001, 0.999 respectively.

A summary and a graph can be created separately by using the functions
`summary.nparcomp`

and `plot.nparcomp`

.

For the analysis, the R packages 'multcomp' and 'mvtnorm' are required.

Frank Konietschke

Konietschke, F., Brunner, E., Hothorn, L.A. (2008). Nonparametric Relative Contrast Effects: Asymptotic Theory and Small Sample Approximations.

Munzel. U., Hothorn, L.A. (2001). A unified Approach to Simultaneous Rank Tests Procedures in the Unbalanced One-way Layout. Biometric Journal, 43, 553-569.

For two-sample comparisons based on relative effects, see `npar.t.test`

.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 | ```
data(liver)
# Williams Contrast
a<-nparcomp(weight ~dosage, data=liver, asy.method = "probit",
type = "Williams", alternative = "two.sided",
plot.simci = TRUE, info = FALSE,correlation=TRUE)
summary(a)
# Dunnett dose 3 is baseline
c<-nparcomp(weight ~dosage, data=liver, asy.method = "probit",
type = "Dunnett", control = "3",
alternative = "two.sided", info = FALSE)
summary(c)
plot(c)
data(colu)
# Tukey comparison- one sided(lower)
a<-nparcomp(corpora~ dose, data=colu, asy.method = "mult.t",
type = "Tukey",alternative = "less",
plot.simci = TRUE, info = FALSE)
summary(a)
# Tukey comparison- one sided(greater)
b<-nparcomp(corpora~ dose, data=colu, asy.method = "mult.t",
type = "Tukey",alternative = "greater",
plot.simci = TRUE, info = FALSE)
summary(b)
``` |

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