Dominance Matrix Effect Sizes
Description
Bootstrapbased calculation of standard error and CI constructs for Cohen's d and the statistics used in the Dominance Matrix Effect Size (dmes) function
Usage
1  dmes.boot(x,y,theta.es="dc",ci.meth="BCA",B=1999,alpha=.05,seed=1)

Arguments
x 
A vector or 1 column matrix with n_x values from (control or pretest or comparison) group X 
y 
A vector or 1 column matrix with n_y values from (treatment or posttest) group Y 
theta.es 
Specification of the nonparametric effect size for which the SE and CI is to be constructed. All output values of the dmes function can be used, e.g. "PSc", "Ac", "dc", "NNTc", "PSw", "Aw", "dw", "NNTw", "PSb", "Ab", "db" or "NNTb". 
ci.meth 
Specify type of method used for bootstrap confidence interval construction: "BSE", "BP" or "BCA". 
B 
Number of bootstrap samples to be used for the estimates. 
alpha 
Significance level. 
seed 
Integer argument to set random number generation seeds, see Random. 
Details
Returns an associative list with the following values:
Value
$theta 
Type and observed value of the respective nonparametric effect size estimate for samples Y and X. 
$theta.SE 
The bootstrapbased estimated standard error of the respective nonparametric effect size estimate. 
$bci.meth 
String indicating which type of bootstrap (BSE, BP or BCA) was used to construct the confidence interval for the respective nonparametric effect size estimate and Cohen's d. 
$theta.bci.lo 
Lower end of the confidence interval for the respective nonparametric effect size estimate as determined by type of bootstrap used (BSE, BP or BCA). 
$theta.bci.up 
Upper end of the confidence interval for the respective nonparametric effect size estimate as determined by type of bootstrap used (BSE, BP or BCA). 
$Coh.d 
Effect size estimate of Cohen's d based on student's t and assuming pooled variance. For details, see metric_t. 
$Coh.d.bSE 
The bootstrapbased estimated standard error of Cohen's d. 
$Coh.d.bci.lo 
Lower end of the confidence interval for the Cohen's d estimated through bootstrapping (type BSE, BP or BCA). 
$Coh.d.bci.up 
Upper end of the confidence interval for the Cohen's d estimated through bootstrapping (type BSE, BP or BCA). 
Note
dmes.boot was largely based on R code provided by John Ruscio and Tara Mullen (2011) which was reused with kind permission from the authors.
Author(s)
Jens J. Rogmann
References
Efron, B. & Tibshirani (1993). An Introduction to the Bootstrap. New York/London: Chapman & Hall.
Ruscio, J. & Mullen, T. (2011). Bootstrap CI for A (R program code, last updated April 11,2011). Retrieved from http://www.tcnj.edu/~ruscio/Bootstrap%20CI%20for%20A.R .
Ruscio, J. & Mullen, T. (2012). Confidence Intervals for the Probability of Superiority Effect Size Measure and the Area Under a Receiver Operating Characteristic Curve. Multivariate Behavioral Research, 47, 221223.
See Also
dmes
Examples
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 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70  ## Not run:
> # cf. Efron & Tibshirani (1993, Ch. 14)
> # Spatial Test Data (Table 14.1, p.180)
> A<c(48,36,20,29,42,42,20,42,22,41,45,14,6,0,33,28,34,4,32,24,47,41,24,26,30,41)
> B<c(42,33,16,39,38,36,15,33,20,43,34,22,7,15,34,29,41,13,38,25,27,41,28,14,28,40)
> dmes.boot(A,B)
$theta
dc
0.08136095
$theta.SE
[1] 0.1656658
$bci.meth
[1] "BCA"
$theta.bci.lo
[1] 0.4008876
$theta.bci.up
[1] 0.2440828
$Coh.d
[1] 0.06364221
$Coh.d.bSE
[1] 0.2895718
$Coh.d.bci.lo
[1] 0.6106167
$Coh.d.bci.up
[1] 0.5031792
## End(Not run)
## Not run:
> ############################################################################
> #Example from Ruscio & Mullen (2012, p. 202)
> x < c(6,7,8,7,9,6,5,4,7,8,7,6,9,5,4) # Treatment Group
> y < c(4,3,5,3,6,2,2,1,6,7,4,3,2,4,3) # Control Group
> dmes.boot(y,x,theta.es="Ac") #AUC
$theta
Ac
0.8844444
$theta.SE
[1] 0.05910963
$bci.meth
[1] "BCA"
$theta.bci.lo
[1] 0.7022222
$theta.bci.up
[1] 0.9644444
$Coh.d
[1] 1.727917
$Coh.d.bSE
[1] 0.4932543
$Coh.d.bci.lo
[1] 0.7753663
$Coh.d.bci.up
[1] 2.573305
## End(Not run)

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