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Rick Scott, Governor
Florida Department of Corrections, Secretary Michael D. Crews

Florida Department of Corrections
Michael D. Crews, Secretary

Statistical Analysis

A post-hoc quasi-experimental design was used in this study to compare recidivism rates of inmates exposed to private prisons with comparable inmates without such exposure. This design is “post-hoc” in the sense that data is captured after prison release rather than tracking inmates as they enter the prison system and identifying whether they were ultimately private or public inmates and then tracking their post prison recidivism outcomes. This approach is particularly well-suited for research testing for effects using multiple measures of exposure to a treatment, especially without a priori knowledge of what kind or level of exposure to private prisons might generate a recidivism reduction effect. This method is “quasi-experimental” in that it does not involve the random assignment of inmates to a control (public) and experimental (private) group followed by identifying their post-prison release outcomes. However, substantial statistical controls for factors known to influence inmate recidivism rates were employed in the analysis.

Two statistical procedures were used to estimate treatment and control group recidivism rates over a 5-year follow-up period and evaluate whether experimental groups’ exposures to private prisons affected the likelihood of recidivism. Because the dependent variables are defined as time to failure (i.e., recidivism), techniques appropriate for survival models were selected. First, for each treatment and control group, a SAS© lifetest procedure23 was employed to compare the two estimated recidivism rate curves over the follow-up periods and assess whether they differed to a statistically significant degree. Second, a proportional hazard regression procedure was used to estimate recidivism rate differences between each treatment and control group, while controlling for several major factors measurable prior to prison release.

Three specific analyses were conducted in this study to describe the populations studied, examine differences in recidivism rates before controlling for relevant factors, and assess whether public and private inmates have different rates of recidivism when equivalency of the groups is established. All comparisons were made using both re-offense and re-incarceration rates.

Descriptive Statistics – The distribution of cases within each of the three offender types (adult males, adult females, and youthful offender males) on each of the control variables (ag at release, race, prior recidivism events, etc.) are presented. The purpose of this analysis is, first, to provide an overall perspective of the characteristics of the three offender groups. Second, comparisons will be made on control variables that have been found to predict inmate recidivism. This demonstrates whether and the extent to which public and private prison groups differ on characteristics known to result in lower or higher rates of recidivism and indicates where controlling for these variables is important.

Base Recidivism Rate Comparison – Without controlling for relevant factors such as age at release, prior recidivism events, etc., estimates of the recidivism rates for each treatment and control group were generated using a SAS© lifetest procedure. Both Wilcoxon and log-rank tests were used to test for significant differences in the estimated rate curves over the entire follow-up period. For convenience, only the point estimates at selected intervals are displayed with the Wilcoxon test statistic results for the entire rate curve comparisons.

Mutivariate Survival Analysis – This analysis will address the question of whether there are meaningful and statistically significant differences in the recidivism rates between the public and private inmates when holding constant factors known to affect the likelihood of recidivism. The presence or absence of a difference in the base recidivism rates of public and private prison inmates may depend on differences between these groups in recidivism-predictive characteristics, rather than the exposure to private prisons.

To account for measurable differences in the treatment and control groups, proportional hazard regression models using these factors as covariates were analyzed. These models establish the effects of covariates on time to recidivism as multiplicative—each covariate is interpreted as increasing the recidivism rate (hazard rate) by an amount or percentage, given equivalence on all other covariates in the model. The inability to achieve a significant effect for a covariate justifies excluding that variable as a needed control; and conversely, a covariate’s significant effect requires its inclusion as a control factor for further recidivism analysis. Including in these models a dichotomous variable that distinguishes the treatment and control groups allows a significant difference between the groups, attributable to exposure to private prisons, to arise if present and will measure the size of that effect.

These models were run with stepwise selection methods, allowing covariates including the treatment measure to enter the model where appropriate to account for recidivism variation. Each model was run twice, once with a normal probability (.05) of entering the model and again with a more lenient selection criterion (.15). For variables entering each model, coefficients and their associated probability values are reported.

  1. The procedure generates nonparametric estimates of the survival distribution functions (recidivism rates over follow-up time) for the treatment and control groups using the Kaplan-Meier method and accounts for censored cases (those having less follow-up time). The procedure computes three statistics, including the Wilcoxon test, for determining whether the two recidivism rate functions are statistically different.Return to reference in text.