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

 steeptest R Documentation

## Statistical significance for steepness of dominance hierarchies statistic

### 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

```   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.

`getDij`, `getPij`, `getNormDS`

### Examples

```
##############################################################################
###               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 6, 2022, 9:07 a.m.