# steeptest: Statistical significance for steepness of dominance... In steepness: Testing Steepness of Dominance Hierarchies

## Description

Estimates statistical significance for steepness measure on the basis of dyadic dominance indices corrected for chance Dij or based on proportions of wins Pij.

## Usage

 `1` ``` steeptest(X, rep, names=NULL, method=c("Dij","Pij"), order=TRUE) ```

## Arguments

 `X` Empirical sociomatrix containing wins-losses frequencies in dyadic encounters. The matrix must be square and numeric. `rep` Number of simulations for carrying out the randomization test. `names` Character vector with individuals' names. `method` A character string indicating which dyadic dominance measure is to be used for the computation of David's scores. One of "Dij" or "Pij", can be abbreviated. `order` Logical, if TRUE, results for Dij, DS and NormDS are ordered according to the individuals' NormDS values. TRUE by default.

## Details

`steeptest` estimates statistical significance for steepness measures based on dyadic dominance index corrected for chance Dij or based on the matrix of win proportions Pij, depending on the `method` specified. This procedure simulates a number of sociomatrices under a uniform distribution by means of callings to C routine steep, then computes steepness based on Dij or Pij. Specifically, it computes normalized David's scores, see `getNormDS` for more details. Then it computes the steepness measure based on these indices, see `getStp`. After `rep` simulations the sampling distribution for the statistic (Stp) is estimated. Then statistical significance is computed as follows when results are shown by means of `summary` method: p=NS+1/NOS+1 Where NS is computed as:

1. The number of times that simulated values are greater than or equal to the empirical value, if right-tailed p value is calculated.

2. And the number of times that simulated values are lower than or equal to the empirical value, if left-tailed p value is calculated.

And NOS represents the number of simulated values.

## Value

`steeptest` returns an object of class steeptest containing the following components:

 `call ` Function call. `names` Character vector with individuals' names. `method` A character string indicating which dyadic dominance measure is used for the computation of David's scores. `rep` Number of simulations for carrying out the randomization test. `matdom` If `method` is set to be Dij the function returns the matrix of observed dyadic dominance indices corrected for chance. If `method` is Pij the matrix of proportions of wins is returned as a part of the output. `DS` David's scores based on Dij or Pij, depending on the specification of the `method`. `NormDS` Normalized David's scores based on dyadic dominance indices corrected for chance or on proportions of wins in dyadic encounters. `Stp` Steepness value based on Normalized David's scores. `interc` Intercept of the fitted line based on Normalized David's scores. `Stpsim` The function provides results of the randomization procedure for the steepness measure based on NormDS.

## Author(s)

David Leiva dleivaur@ub.edu & Han de Vries J.deVries1@uu.nl.

## References

David, H. A. (1988). The Method of Paired Comparisons. London: C. Griffin.

de Vries, H., Stevens, J. M. G., & Vervaecke, H. (2006). Measuring and testing the steepness of dominance hierarchies. Animal Behaviour, 71, 585-592.

## See Also

`getDij`, `getPij`, `getNormDS`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```############################################################################## ### Example taken from Vervaecke et al. (2007): ### ############################################################################## X <- matrix(c(0,58,50,61,32,37,29,39,25,8,0,22,22,9,27,20,10,48, 3,3,0,19,29,12,13,19,8,5,8,9,0,33,38,35,32,57, 4,7,9,1,0,28,26,16,23,4,3,0,0,6,0,7,6,12, 2,0,4,1,4,4,0,5,3,0,2,1,1,5,8,3,0,10,3,1,3,0,0,4,1,2,0), nrow=9,byrow=TRUE) individuals <- c("V","VS","B","FJ","PR","VB","TOR","MU","ZV") STP <- steeptest(X, rep=9999, names=individuals, method="Dij", order=TRUE) summary(STP) plot(STP) ```

steepness documentation built on May 2, 2019, 2:31 p.m.