The following was part of the original manuscript submission. For space reasons it was felt best to include this only on the web page

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            Ignoring the distributional problems and the belief that there might be two processes underlying these data, one approach would be a 2x3 ANOVA with the amount awarded as the dependent variable. The ANOVA produces significant main effects for injury level (using the aov function in R), F(2,196)=7.00, p = .001, and for what the expert says, F(1,196)=11.07, p = .001, as well as a non-significant interaction, F(1,196) = 1.90, p  = .15. The marginal means for the expert conditions were: 61.45 for mild and 102.98 for severe (units = $1000). The marginal means for the injury conditions were: 60.19 for minimal, 73.78 for moderate, and 115.91 for extreme. This shows that increasing the severity of both what the expert says is reasonable, and the plaintiff's injuries, increase the award, but it makes invalid assumptions about the nature of the data including it does not account for the peak at zero nor there being no negative values.

            The Tobit model addresses these by hypothesizing that the amount awarded is based on some latent variable whose values are assigned zero if they are less than zero. The tobit function from the AER package in R is used. The interaction is non-significant, χ²(2) = 4.01, p = .13. The main effects model and the resulting coefficients are:

tobit(TotComp ~ Expert + Injury)

Coefficients:

               Estimate Std. Error z value Pr(>|z|)   

(Intercept)     89.7357    14.4056   6.229 4.69e-10 ***

ExpertSevere    43.4374    14.1915   3.061 0.002207 **

InjuryMinimal  -64.4723    17.4431  -3.696 0.000219 ***

InjuryModerate -48.6291    17.2794  -2.814 0.004889 **

Log(scale)       4.5939     0.0551  83.378  < 2e-16 ***

Thus, the Tobit model shows that expert opinion (higher awards if the expert says a severe reaction is likely) and injury severity (higher awards for more extreme injuries) affect the amount awarded. Thus, for this example the conclusions are similar to the ANOVA approach. The conclusions of these two approaches are usually similar when the proportion of zero values is small (i.e., < 20%), which is the case here.

            The Tobit model remains popular in econometrics largely because it has been used for decades and it is conceptually simple. However, the alternatives when the latent distribution cannot be assumed to be normal are more difficult. Wilhelm (2008) provides details for some of these methods. For juror decision making, this single process model seems the least attractive of the three models shown in Figure 4. While it takes into account the problem with the standard ANOVA of having lots of zeroes, the other alternatives seem better suited for juror research. The Tobit model (and other censored regression approaches) will not be considered further.