Dominance Matrix Effect Sizes

Share:

Description

Bootstrap-based 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 pre-test or comparison) group X

y

A vector or 1 column matrix with n_y values from (treatment or post-test) 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".

"BSE" uses the bootstrap standard error estimate of the respective nonparametric effect size to construct a confidence interval with theta +- z(alpha/2) * SE(theta), where \hat{θ} ist the observed effect size, z(alpha/2) the z value of the standard normal table at the given (two-tailed) significance level (e.g. z=1.96 when alpha=5 "BP" calculates confidence intervals based on bootstrap percentiles. B bootstrap sample estimates of the respective nonparametric effect size theta are generated and ordered, and the (B*100*alpha)th as well as the (B*100*(1-alpha))th of these ordered estimates are used to determine the confidence intervals. For example, if B=2000 bootstrap samples are calculated and alpha=.05, then the 100th and 1900th of the ordered values are selected as lower and upper CI limits.

"BCA" calculates bias-corrected and accelerated confidence intervals (also based on bootstrap percentiles). Here, however, the α levels (or percentiles) are corrected depending on the bias and the rate of change of the standard error with formulas suggested by Efron & Tibshirani (1993, Chapter 14).

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 bootstrap-based 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 bootstrap-based 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, 221-223.

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)