Confidence of Mock Jurors in Their Verdicts
Data with responses of naive mock jurors to the conventional conventional two-option verdict (guilt vs. acquittal) versus a three-option verdict setup (the third option was the Scottish 'not proven' alternative), in the presence/absence of conflicting testimonial evidence.
data("MockJurors")A data frame containing 104 observations on 3 variables.
factor indicating whether a two-option or three-option verdict is requested. (A sum contrast rather than treatment contrast is employed.)
factor. Is there conflicting testimonial evidence? (A sum contrast rather than treatment contrast is employed.)
jurors degree of confidence in his/her verdict, scaled to the open unit interval (see below).
The data were collected by Daily (2004) among first-year psychology
students at Australian National University. Smithson and Verkuilen (2006)
employed the data scaling the original confidence (on a scale 0–100)
to the open unit interval: ((original_confidence/100) * 103 - 0.5) / 104.
The original coding of conflict in the data provided from Smithson's
homepage is -1/1 which Smithson and Verkuilen (2006) describe to mean
no/yes. However, all their results (sample statistics, histograms, etc.)
suggest that it actually means yes/no which was employed in MockJurors.
Example 1 from Smithson and Verkuilen (2006) supplements.
Deady, S. (2004). The Psychological Third Verdict: 'Not Proven' or 'Not Willing to Make a Decision'? Unpublished honors thesis, The Australian National University, Canberra.
Smithson, M., and Verkuilen, J. (2006). A Better Lemon Squeezer? Maximum-Likelihood Regression with Beta-Distributed Dependent Variables. Psychological Methods, 11(7), 54–71.
data("MockJurors", package = "betareg")
library("lmtest")
## Smithson & Verkuilen (2006, Table 1)
## variable dispersion model
## (NOTE: numerical rather than analytical Hessian is used for replication,
## Smithson & Verkuilen erroneously compute one-sided p-values)
mj_vd <- betareg(confidence ~ verdict * conflict | verdict * conflict,
data = MockJurors, hessian = TRUE)
summary(mj_vd)
## model selection for beta regression: null model, fixed dispersion model (p. 61)
mj_null <- betareg(confidence ~ 1 | 1, data = MockJurors)
mj_fd <- betareg(confidence ~ verdict * conflict | 1, data = MockJurors)
lrtest(mj_null, mj_fd)
lrtest(mj_null, mj_vd)
## McFadden's pseudo-R-squared
1 - as.vector(logLik(mj_null)/logLik(mj_vd))
## visualization
if(require("lattice")) {
histogram(~ confidence | conflict + verdict, data = MockJurors,
col = "lightgray", breaks = 0:10/10, type = "density")
}
## see demo("SmithsonVerkuilen2006", package = "betareg") for more detailsPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.