Demographic Differences in

Federal Sentencing Practices:

An Update of the Booker Report’s

Multivariate Regression Analysis

UNITED STATES SENTENCING COMMISSION

March 2010
Demographic Differences in

Federal Sentencing Practices:

An Update of the Booker Report’s

Multivariate Regression Analysis

William K. Sessions III

Chair

Ruben Castillo

Vice Chair

William B. Carr, Jr.

Vice Chair

Ketanji Brown Jackson

Vice Chair

Ricardo H. Hinojosa

Commissioner

Beryl A. Howell

Commissioner

Dabney L. Friedrich

Commissioner

Isaac Fulwood, Jr.

(ex officio)

Jonathan J. Wroblewski

(ex officio)
1 

DEMOGRAPHIC DIFFERENCES IN FEDERAL SENTENCING PRACTICES: 

AN UPDATE OF THE BOOKER REPORT’S 

MULTIVARIATE REGRESSION ANALYSIS 

I. INTRODUCTION 

 In 2006, the United States Sentencing Commission1 undertook a review of the 

impact on federal sentencing of the Supreme Court’s decision in United States v. 

Booker.

2

 In March 2006, the Commission published the results of that review in the 

Final Report on the Impact of United States v. Booker on Federal Sentencing.

3

 As part of 

that report, the Commission performed an analysis of data from the federal courts to 

examine whether differences in the length of sentences imposed on offenders were 

correlated with demographic characteristics of those offenders. Based on continued 

interest in this issue, and in response to specific requests to update its prior analysis, the 

Commission has now repeated the analysis used for the Booker Report with additional 

data and has also developed a second methodology to examine that data. This report 

presents the results of that work. 

 This report focused on three separate time periods which together spanned the 

time between May 1, 2003, and September 30, 2009. The Commission found a 

correlation between the length of sentences imposed on some groups of offenders and the 

demographic characteristics of those offenders. These differences were not present in all 

time periods under study and differed in magnitude in the time periods in which they 

were observed. 

 In conducting this analysis, as it did in the Booker Report, the Commission used a 

research tool common in the social and behavioral sciences called multivariate regression 

analysis. This tool is used to examine data where multiple factors may contribute to an 

observed outcome, such as the sentencing of federal offenders. The principal benefit of 

this tool is that it accounts, or controls, for the effect of each factor in the analysis. Each 

factor can then be separately assessed and the extent to which each factor influences the 

outcome can be measured. 

 

1

 The United States Sentencing Commission [hereinafter Commission] is an independent agency in the 

judicial branch of government. Established by the Sentencing Reform Act of 1984, its principal purposes 

are (1) to establish sentencing policies and practices for the federal courts, including guidelines regarding 

the appropriate form and severity of punishment for offenders convicted of federal crimes; (2) to advise and 

assist Congress, the federal judiciary, and the executive branch in the development of effective and efficient 

crime policy; and (3) to collect, analyze, research, and distribute a broad array of information on federal 

crime and sentencing issues. 

2

 United States v. Booker, 543 U.S. 220 (2005). 

3

 United States Sentencing Commission, Final Report on the Impact of United States v. Booker on Federal 

Sentencing (March 2006) [hereinafter Booker Report]. The Booker Report and this report were issued 

pursuant to the Commission’s general statutory authority under 28 U.S.C. §§ 994-995. 
2 

 The Commission used two methodologies to examine the updated data. The first 

methodology was the one the Commission used in the Booker Report. The second 

methodology was developed after the Booker Report was released to the public. Both 

methodologies were reviewed by two groups of outside researchers and academicians. 

The preliminary results of the analysis were then peer reviewed prior to release to ensure 

that the methodologies used were appropriate and the results correctly stated. 

 Based on this analysis, and after controlling for a variety of factors relevant to 

sentencing, the following observations can be made: 

 Black male offenders received longer sentences than white male offenders. The 

differences in sentence length have increased steadily since Booker. 

 Female offenders of all races received shorter sentences than male offenders. The 

differences in sentence length fluctuated at different rates in the time periods 

studied for white females, black females, Hispanic females, and “other” female 

offenders (such as those of Native American, Alaskan Native, and Asian or 

Pacific Islander origin). 

 Non-citizen offenders received longer sentences than offenders who were U.S. 

citizens. The differences in sentence length have increased steadily since Booker. 

 Offenders with some college education received shorter sentences than offenders 

with no college education. The differences in sentence length have remained 

relatively stable across the time periods studied. 

 The data were inconsistent as to the association between an offender’s age and the 

length of sentence imposed. 

 

 A. Trends Observed in the Data 

 The Booker Report contained an analysis of longer-term trends in sentencing 

differences associated with the race and gender of the offender, dating from 1999 through 

the end of 2005. Using the same methodology as in the Booker Report, this examination 

of sentencing trends has been extended in this report through fiscal year 2009. As noted 

above, the Commission also used a second methodology to review the data discussed in 

this report. The Commission was unable to examine sentencing differences from fiscal 

years 1999 to 2003 using the second methodology due to the unavailability in the 

Commission’s datasets of certain data necessary to perform this analysis for fiscal years 

prior to 2003.4 However, some consistent trends with regard to differences in sentence 

 

4

 The second methodology incorporates a factor that is not readily available in the Commission’s datasets 

before fiscal year 2003, which is the pre-sentencing custody status of the offender. The differences 

between the two methodologies are discussed infra at notes 59-70 and accompanying text. 
3 

length are observed when analyzing the data beginning in May 2003 with the second 

methodology. 

 1. Using the Booker Report Methodology 

 

 With respect to the sentences imposed on black and white offenders, a 

comparison shows that the difference in sentence length was greatest in fiscal year 1999 

using this methodology. In that year, black offenders received sentences that were 14.2 

percent longer than those imposed on white offenders, after controlling for the other 

factors in the analysis. This difference in sentence length declined steadily in fiscal years 

2000 and 2001. By fiscal year 2002, no statistically significant difference was observed 

in the sentences imposed on black offenders compared to white offenders. No 

statistically significant difference between the sentences imposed on these two groups 

was observed again until after the Booker decision in January 2005. Using the most 

recent data available, these differences appear to have been increasing steadily since that 

decision. In the most recent period studied (December 2007 through September 2009), 

black offenders received sentences that were 10.0 percent longer than those imposed on 

white offenders, after controlling for the other factors in the analysis. 

 The Commission further observed that differences in the sentences imposed on 

male and female offenders have been relatively consistent since fiscal year 1999. In that 

year, male offenders received sentences that were 18.6 percent longer than those imposed 

on female offenders. Similar differences in sentence length were observed in each 

subsequent time period, including the most recent period studied (December 2007 

through September 2009), during which male offenders received sentences that were 17.7 

percent longer than female offenders, after controlling for the other factors in the 

analysis. 

 2. Using the Second Methodology 

 Using the second methodology, the difference in sentence length for black male 

offenders compared to white male offenders has increased over time and was greatest in 

the most recent period studied (December 2007 through September 2009). During this 

period, black male offenders received sentences that were 23.3 percent longer than those 

imposed on white male offenders. This is an increase from the 5.5 percent difference 

observed in the first period studied using the second methodology (May 2003 through 

June 2004). Sentences for Hispanic male offenders also have increased relative to those 

of white male offenders. During the first period studied using the second methodology, 

Hispanic male offenders received sentences that were 4.4 percent shorter than those 

imposed on white male offenders. In the most recent period studied (December 2007 

through September 2009), however, Hispanic male offenders received sentences that 

were 6.8 percent longer than those imposed on white male offenders. 

 Sentences for female offenders of all races were consistently shorter than those 

for white male offenders. In two of the time periods studied “other” race female 

offenders received the shortest sentences (when compared to white male offenders) vis-a-
4 

vis women of any other race. In all three time periods studied black female offenders 

received shorter sentences when compared to white male offenders than did white female 

or Hispanic female offenders. These differences were present during each of the periods 

studied; however, no trends in the size of these differences over time were observed. 

 It is important to note that the results of the two methodologies presented above 

cannot be compared directly for the years in which they overlap because the two 

methodologies differ in several important respects, which are described later in this 

report. 

 B. Cautions When Reviewing the Results of This Report 

 Although the multivariate regression analysis used to perform this analysis is 

common in social science research, and steps were taken to ensure its appropriateness for 

this analysis, it has limitations. For example, one or more key factors which could affect 

the analysis may have been omitted from the methodologies used because a particular 

factor is unknown or was erroneously excluded from the analysis, or because data 

concerning such a factor is unavailable in the Commission’s datasets. Examples of 

factors for which no data is readily available in the Commission’s datasets include a 

measure of the violence in an offender’s criminal past, information about crimes not 

reflected in an offender’s criminal history score as calculated under the sentencing 

guidelines, and information about an offender’s employment record. For these reasons, 

the results presented in this report should be interpreted with caution. 

 Although the Commission’s analysis demonstrates that some differences in the 

sentences imposed on certain groups of offenders are associated with specific 

demographic characteristics, it is also important to note that these differences may be 

attributable to one (or more) of a number of factors that, while correlated with the 

demographic characteristics of offenders, are not caused by them. For example, judges 

make decisions when sentencing offenders based on many legal and other legitimate 

considerations that are not or cannot be measured. Some of these factors could be 

correlated with one or more of the demographic characteristics of offenders but not be 

influenced by any consideration of those characteristics. The analysis presented in this 

report cannot explain why the observed differences in sentence length exist but only that 

they do exist, the relative size of those differences, and the time periods in which the 

differences were observed. 

II. AN OVERVIEW OF MULTIVARIATE REGRESSION ANALYSIS 

 The Commission employed multivariate regression analysis to conduct the 

research presented in this report. Regression analysis is a statistical tool used to examine 

the effect of one or more factors on a particular outcome. This analytical tool is 

commonly used in the social and behavioral sciences.5

 The results of such an analysis 

 

5

 Michael O. Finkelstein and Bruce Levin, Statistics for Lawyers 350 (2d ed. 2001) [hereinafter 

Finkelstein]. Multivariate regression analysis is sometimes called “multiple regression analysis.” 
5 

also have been used in a variety of legal contexts.6 The Commission has used this tool in 

its prior research and, in particular, in its previous work on the issue of demographic 

differences in sentencing as contained in the Booker Report. 

 A. Examining Outcomes Influenced By Multiple Factors 

 Multivariate regression analysis is used to examine a collection of data in which 

there are a variety of outcomes and when there are “several possible explanations for the 

relationship among a number of explanatory variables” evident in the data.7

 For 

example, height varies from person to person. Each person’s height is determined by his 

or her genetic background (i.e., as reflected in the father’s height and the mother’s height) 

but many other factors might also play a part in determining a person’s height, such as 

age (children are usually shorter than adults), gender (men are taller than women on 

average), nutrition, exercise, disease or illness, and environmental conditions.8 

Multivariate regression analysis can help to parse out the contribution, or lack of 

contribution, of each of these factors even when the outcomes (the heights of the people 

in the study) vary. The tool can also be used to study social outcomes. For example, 

policymakers wishing to promote programs to improve literacy might wish to know what 

factors affect a child’s ability to read in order to target government resources at the 

factors that matter most and can be affected by social policies. Of course, many factors 

might bear on literacy rates, such as the child’s age, parents’ age, parents’ educational 

level, presence of books in the home, shared reading activities, and other literacy 

activities. Multivariate regression analysis can be, and has been,9

 used to help determine 

which of these factors actually affect literacy levels and which do not. 

 B. Dependent and Independent Variables 

 Regression analysis usually begins with a decision to examine an observed 

phenomenon or outcome (e.g., height or literacy levels). The researcher will first develop 

a hypothesis as to the many possible factors that might produce that outcome.10 That 

hypothesis is then tested through the use of regression analysis as data about the outcome 

and many possible factors affecting that outcome are brought together. In some cases 

 

6

 Id. See also Federal Judicial Center, Reference Manual on Scientific Evidence 143, 181-83 (2d ed. 2000) 

[hereinafter FJC Reference Manual] (chapters entitled “Reference Guide on Statistics,” by David H. Kaye, 

M.A., J.D., and David A. Freedman, Ph.D., and “Reference Guide on Multiple Regression,” by Daniel L. 

Rubinfeld, Ph.D.). 

7

 FJC Reference Manual, supra, at 181. 

8

 Some of the foundational principles of regression analysis came from studies of the height of children. 

See Finkelstein, supra note 5, at 352-54. 

9

 See Neil J. Salkind, Statistics for People Who (Think They) Hate Statistics 324 (2d ed. 2007) (citing a 

European study using regression analysis to find that the mother’s age and shared reading activities had no 

bearing on a child’s literacy). 

10 “Ideally, the selection of explanatory factors is determined solely by strong, well-validated, substantive 

theory, without regard to [any prior examination of the] actual data.” Finkelstein, supra note 5, at 378 
6 

available data are used, in other cases researchers will collect additional data for the 

analysis.11 The goal of the analysis is to determine if associations between the factors 

being examined exist to such an extent that a causal relationship can be inferred between 

one or more of those factors and the observed outcome. Researchers refer to the outcome 

as the “dependent variable” and the factors that might affect (and therefore might 

explain) that outcome as the “independent variables” or the “explanatory variables.” In 

more technical terms, regression analysis “typically uses a single dependent variable and 

several explanatory . . . variables to assess the statistical data” and seeks to determine 

whether correlations exist between one or more of the independent variables and the 

dependent variable – allowing for a possible inference of “causation from association” 

between certain variables.12 

 Most regression analysis includes several independent variables in the analysis in 

order to statistically “control” for the discrete effect of each variable in relation to other 

variables.13 The selection of variables is determined in the first instance by the 

researcher’s understanding of the phenomenon to be studied and the hypothesis to be 

tested. Variables that measure the same thing or which are so closely associated that they 

vary from case to case in similar ways are excluded. That is, the analysis should not 

include a variable that is “correlated perfectly with one or more of the other explanatory 

variables [because] the [researcher] could not separate out the effect of the variable of 

interest . . . from the effect of the other variable.”14 The researcher will experiment with 

 

11 The data used in this report were taken from the Commission’s datasets. For more discussion about this 

data see Table A and accompanying text in the Technical Appendix to this report, infra. 

12 FJC Reference Manual, supra note 6, at 133, 181. Correlation and causation are different concepts. A 

variable that is correlated with another may not be caused by it. 

[I]n interpreting the results of a multiple regression analysis, it is important to distinguish between 

correlation and causality. Two variables are correlated when the events associated with the 

variables occur more frequently together than one would expect by chance . . . . A correlation 

between two variables does not imply that one event causes the second. Therefore, in making 

causal inferences, it is important to avoid spurious correlation. Spurious correlation arises when 

two variables are closely related but bear no causal relationship because both are caused by a third, 

unexamined variable . . . . Causality cannot be inferred by data analysis alone; rather, one must 

infer that a causal relationship exists on the basis of an underlying causal theory that explains the 

relationship between the two variables. Even when an appropriate theory has been identified, 

causality can never be inferred directly. One must look for empirical evidence that there is a 

causal relationship. Conversely, the fact that two variables are correlated does not guarantee the 

existence of a relationship; it could be that the model – a characterization of the underlying theory 

– does not reflect the correct interplay among the explanatory variables. 

Id. at 183-85. 

13 Put another way, “it is a method in which a regression line is used to relate the average of one variable – 

the dependent variable – to the values of the other explanatory [or independent] variables.” Id. at 205.

14 This leads to the problem of multicollinearity. “When two or more variables are highly, but not 

perfectly, correlated – that is, when there is multicollinearity – the regression can be estimated, but some 

concerns remain. The greater the multicollinearity between two variables, the less precise is the estimate of 

individual regression parameters . . . .” Id. at 197. 
7 

different models, using different groups of variables, and test the relationships between 

the independent variables in order to find a model with variables that are independent 

from one another and not correlated in other ways.15

 Modern regression analysis is done with a complex computer program16 that 

creates a mathematical equation using the available data. The dependent variable and 

each independent variable included in the analysis are represented in the equation. The 

computer program creates an equation that accounts for the variation in the available data 

to the greatest extent possible. The resulting equation assigns a numerical measure for 

each independent variable.17 The numerical values, known as “coefficients,” serve as an 

estimate of the extent to which each independent variable affected (or contributed to) the 

dependent variable.18

 C. Interpreting Regression Analysis Results – Significance Tests and R2

 

 Interpreting regression analysis results depends on several factors. A primary 

factor is the “significance test,” which asks whether the results of the analysis for any 

independent variable are “statistically significant.”19 Statistical significance is a 

determination of the probability that the measured relationship between an independent 

variable and the dependent variable is the result of random chance (i.e., that it does not, in 

fact, reflect the true association). Prior to performing the analysis, the researcher will 

determine the statistical significance threshold that he or she wishes to use. This decision 

is based on a number of factors, including the amount of data available for analysis and 

the purpose for the analysis.20 Results that do not meet that threshold level of 

significance are deemed to be “not statistically significant” and generally are not reported 

when the research results are published.21 This does not mean that the independent 

variable in question was found to have no impact on the dependent variable, but only that 

 

15 Finkelstein, supra note 5, at 374-75. 

16 The Commission’s Office of Research and Data staff use Statistical Analysis System (“SAS”) software 

to conduct regression analyses. 

17 Regression analysis typically uses an ordinary least squares (“OLS”) analysis. See Booker Report, 

supra note 3, at B-24; see also generally FJC Reference Manual, supra note 6, at 206-08, 213 (discussing 

the linear regression statistic and OLS analysis).

18 A final part of the formula is the “error term,” which “represents the collective unobservable influence 

of any omitted variables.” FJC Reference Manual, supra note 6, at 208 (“In a linear regression, each of the 

terms [i.e., independent variables] being added involves unknown parameters . . . , which are estimated 

[through the use of numerical values, i.e., coefficients] by ‘fitting’ the equation to the data using [ordinary] 

least-squares.”). 

19 Id. at 121-25, 191-94. 

20 Id. at 123 (“Statistical significance is determined by comparing a p-value to a preestablished . . . 

significance level.”). The computer program “compute[s] an observed significance level, or p-value” for 

each independent variable. Id. at 194. 

21 See generally id. at 354-59.
8 

the researcher could not dismiss the possibility that the measured impact could have 

occurred simply due to chance at the level of significance selected. 

 In the social sciences, the level of significance (or “p-value”) is commonly set at 

p<0.05 (a probability of less than five percent).22 That is, if the possibility (as measured 

by the p value) that an observed result occurred solely due to chance is not less than five 

percent, the result is deemed not statistically significant, the results are not relied upon by 

the researcher in drawing conclusions, and they are not reported. Conversely, if the pvalue of any variable is less than five percent, then that variable is deemed to have played 

a part in the observed outcome and is reported. In some research a stronger level of 

significance is deemed appropriate, usually due to the availability of large amounts of 

data, and the p-value is set to p<0.01 (less than one percent) or smaller.23 The 

Commission used a significance level of p<0.01 in the analysis described in the Booker

Report.

24 That significance level also was used for the analysis described in this report. 

 A second factor helpful in assessing the results of regression analysis is the R2

 (or 

“r-squared”). This is a numerical measure of the extent to which the computer-generated 

mathematical equation explains all of the variation in the data used in the analysis.25 The 

numerical measure of R2 “is the statistic that measures the percentage of variation in the 

dependent variable that is accounted for by all the explanatory variables.”26 Put another 

way, it is the representation of the “goodness of fit” between the regression line 

calculated by the computer program and the particular data being analyzed.27 This 

measure is sometimes referred to simply as the “degree of fit” of the model to the data.28 

 The R2 has a value of between 0 and 1 and is commonly expressed as a percentage 

between 0 and 100. A high R2 means that much of the variation in the dependent variable 

has been accounted for by the independent variables in the model whereas a low R2 

indicates that there are one or more variables missing from the model that affect the 

 

22 “In most scientific work, the level of statistical significance required . . . to obtain a statistically 

significant result[] is set conventionally at .05, or 5% . . . although reporting of more stringent 1% 

significance tests . . . can also provide useful information.” Id. at 194. 

23 Adrian E. Raftery, Bayesian Model Selection in Social Research, 25 SOCIOLOGICAL METHODOLOGY

111, 141 (1995).

24 Booker Report, supra note 3, at B-24. 

25 The R2 is a shorthand way of referring to the “multiple coefficient of determination.” See Jack Levin 

and James Alan Fox, Elementary Statistics in Social Research 376 (10th ed. 2006) [hereinafter Levin and 

Fox]; Damodar N. Gujarati, Basic Econometrics 175 (2d ed. 1988) [hereinafter Gujarati]. 

26 Levin and Fox, supra, at 215. 

27 Id.; Gujarati, supra note 25, at 175; Finkelstein, supra note 5, at 369-70. 

28 See FJC Reference Manual, supra note 6, at 215. 
9 

dependent variable.29 There is no set standard for determining what level of R2 “should 

lead to a conclusion that the model is satisfactory.”30 A high R2 does not, by itself, prove 

that the variables included in the model are appropriate.31 Nor does the R2 “measure the 

validity” of the underlying hypothesis on which the regression analysis is based.32 For 

this reason, it is important to consider all aspects of the model used in any analysis, and 

not to rely solely on a summary measure such as R2

.

33, 34

D. Limitations of Regression Analysis 

 As is apparent, the usefulness of regression analysis is entirely dependent on the 

data being used. Therefore, one important concern when using regression analysis is an 

awareness of what data might be missing from the analysis.35 The omission of one or 

more important variables usually causes the value of the variables that are included in the 

model to be overstated.36 The missing variable may involve data that simply are not 

available because such data are not collected. Alternatively, data may be erroneously 

omitted due to oversight or because the impact of the omitted factor on the outcome 

being studied may not yet be understood. 

 For example, a judge sentencing two offenders convicted of similar crimes with 

the same criminal history score under the federal sentencing guidelines might impose a 

longer sentence on the offender with a more violent criminal past than on the offender 

with a less violent, or non-violent, criminal history.37 Similarly, a judge sentencing two 

 

29 Id. at 215-16. When comparing the R2

 of two different models, the dependent variable must be the 

same. Gujarati, supra note 25, at 183. 

30 FJC Reference Manual, supra note 6, at 216. 

31 Id. 

32 Finkelstein, supra note 5, at 370. 

33 “Although R2

 is a useful summary measure its importance should not be exaggerated. What is critical is 

the underlying theoretical expectations about the model in terms of a priori signs of the coefficients of the 

variables entering the model and . . . their statistical significance.” Gujarati, supra note 25, at 196. See 

also Finkelstein, supra note 5, at 372. 

34 For a discussion of the R2

 used in this report, see infra at note 70 and accompanying text. 

35 See FJC Reference Manual, supra note 6, at 198 (one or more unmeasured factors that are not available 

for inclusion in the analysis as independent variables potentially could change the results of the analysis if 

they were included). 

36 Finkelstein, supra note 5, at 380. 

37 See generally United States Sentencing Commission, United States Sentencing Commission Guidelines 

Manual (2009) [hereinafter USSG] at Chapter 4. As noted in the Booker Report, “The presence of violent 

criminal history may lead the court to sentence higher in the prescribed range. The Commission’s datafile 

does not have information on the type of criminal history behavior. In 2002, the Commission created a 

datafile which took a 25 percent random sample of cases sentenced in Fiscal Year 2000. This datafile 

looked more closely at [an] offender’s criminal conduct, including detailed information on the type of 

criminal history the offender had. Using this data (the Intensive Study Sample 2000, or ISS2000), it was 
10 

offenders convicted of similar crimes might be influenced by the presence of violence in 

one case that was not present in the other case and was not reflected in the final offense 

level for those cases as determined under the sentencing guidelines.38 Additionally, 

judges might be influenced by crimes not reflected in the criminal history score or by an 

offender’s contacts with the criminal justice system that do not result in a conviction.39 

Further, an offender’s employment record may have some influence on the sentence 

imposed. Data on these factors are not available in the Commission’s datasets. Although 

the possibility of missing variables is a limitation common in regression analysis, it does 

not mean that the results of such an analysis are misleading or wrong.40 For these 

reasons, the results of any regression analysis should be interpreted with caution. 

III. ANALYSIS OF DIFFERENCES IN FEDERAL SENTENCING PRACTICES 

 A. The Booker Report: Demographic Differences in Federal Sentencing 

 Practices 

 In Chapter 5 of the Booker Report, the Commission presented the results of a 

multivariate regression analysis of demographic differences in federal sentencing 

practices.41 The Booker Report analysis reviewed data from October 1, 1998, through 

January 11, 2006, with a primary focus on two time periods: (1) the 14 months of the 

 

found that 24.4 percent of white offenders had violent criminal history events, as did 43.7 percent of black 

offenders, 18.9 percent of Hispanic offenders, and 23.7 percent of ‘other’ offenders.” Booker Report, supra

note 3, at 105 n.317. 

38 Although the use of violence is often accounted for in the sentencing guidelines through application of 

specific offense characteristics, which can affect an offender’s final offense level, not every incidence of 

violence occurring within a crime is accounted for. See generally USSG at Chapter 1, Pt. A(1)(3). See also 

generally USSG §§1B1.1(b), 1B1.3(a). 

39 Under the guidelines, only criminal conduct for which the offender was convicted is counted toward 

establishing a criminal history score for the offender. Further, some offenses for which an offender was 

convicted are not counted in the computation of the criminal history score, for one of several possible 

reasons. See USSG §§4A1.1, 4A1.2. 

40 Although “[t]here is tension between any attempt to reach conclusions with near certainty and the 

inherently probabilistic nature of multiple regression analysis” based on incomplete data, “[t]he reality that 

statistical analysis generates [only] probabilities that there are relationships [between certain variables] 

should not be seen as an argument against the use of statistical evidence. The only other alternative might 

be the use of less reliable anecdotal evidence.” FJC Reference Manual, supra note 6, at 185. 

41 See Booker Report, supra note 3, at 105-09; see also id. at B-22 through B-31 (technical appendix 

explaining the multivariate analysis). Seven demographic differences concerning sentence lengths were 

examined: (1) black offenders versus white offenders; (2) Hispanic offenders versus white offenders; (3) 

“other” racial groups (e.g., Native Americans) versus white offenders; (4) male offenders versus female 

offenders; (5) non-citizen offenders versus U.S. citizen offenders; (6) offenders who had any level of 

college education versus offenders with no college education; and (7) offenders over 25 years of age versus 

offenders 25 years of age or younger. 
11 

“post-PROTECT Act”42 period (i.e., May 1, 2003, through June 24, 2004, the date of the 

Supreme Court’s decision in Blakely v. Washington);43 and (2) the first year after the 

Supreme Court’s decision in United States v. Booker (i.e., January 12, 2005, the date of 

the Booker decision, through January 11, 2006). 

 The purpose of this analysis was to determine whether any changes in sentencing 

practices had occurred over these periods that were statistically significant44 after 

controlling for the factors in the analysis. The analysis focused on differences in 

sentence length associated with various demographic factors, when all sentencing 

guideline and other specified legal factors had been taken into account. 

 The dependent variable in the analysis was an offender’s sentence length. The 

factors examined in the Booker Report as independent variables were as follows:45

o The presumptive sentence (i.e., the minimum sentence, in months, to 

which the offender was subject under the sentencing guidelines, taking 

into account all guideline, statutory, and mandatory minimum 

provisions);46

o Type of offense committed (violent, sexual, drug trafficking, drug 

possession, white collar, immigration, or other);47

 

42 The “PROTECT Act” refers to the Prosecutorial Remedies and Other Tools to end the Exploitation of 

Children Today Act of 2003, Pub. L. No. 108-21, 117 Stat. 650 (2003). 

43 Blakely v. Washington, 542 U.S. 296 (2004). The analysis did not include sentences imposed between 

the date that Blakely was decided and the date of the Supreme Court’s subsequent decision in Booker 

(January 12, 2005) because “Blakely caused some confusion in the federal sentencing community that 

resulted in inconsistent guideline application and sentencing.” Booker Report, supra note 3, at B-22 n.369. 

44 For a discussion of statistical significance, see supra notes 18-22 and accompanying text. In the Booker

Report model, a result for an independent variable was reported as significant only when the probability 

that the result measured was due to random chance was less than 1% (p < 0.01). Booker Report, supra note 

3, at B-24. 

45 A more complete description of these variables can be found in the Technical Appendix to this report, 

infra. 

46 The presumptive sentence is the bottom of the applicable sentencing guideline range that applies in a 

case. Courts are required to calculate this guideline range in every felony and Class A misdemeanor case. 

See Rita v. United States, 551 U.S. 338, 347 (2007) (courts of appeal may apply a presumption of 

reasonableness to a district court sentence that reflects a proper application of the sentencing guidelines); 

Gall v. United States, 552 U.S. 38, 49 (2007) (“[a]s we explained in Rita, a district court should begin all 

sentencing proceedings by correctly calculating the applicable guideline range”). 

47 The offense types used in this analysis are broad. The seriousness of the several crimes varies within the 

offense type categories as does the demographic characteristics of the offenders convicted of those crimes. 

Certain crimes within an offense type are punished more severely than others (e.g., those crimes involving 

injury not accounted for under the sentencing guidelines) and offenders of a particular demographic group 

may be disproportionately convicted of those crimes. If so, the offense type variables used in this analysis 

may not fully account for the effect on the sentence length imposed that is attributable to certain crimes. 
12 

o The offender’s criminal history (as reflected in the criminal history score 

assigned to the offender under the sentencing guidelines); 

o Whether the offender was convicted of violating 18 U.S.C. § 924(c) (an 

offense under this statute which requires imposition of a sentence 

consecutive to the sentence imposed for the underlying offense); 

o Whether a weapon enhancement applied (a sentencing enhancement under 

the sentencing guidelines for use or possession of a weapon during the 

offense); 

o Whether the court determined that the offender had a minor or minimal 

role in the offense pursuant to USSG §3B1.2; 

o Whether the court determined that the offender had an aggravating role in 

the offense pursuant to USSG §3B1.1; 

o Whether the offender was a career offender (i.e., subject to the enhanced 

criminal history category and offense level pursuant to USSG §4B1.1); 

o Whether the offender was an armed career criminal (i.e., subject to the 

enhanced criminal history category and offense level pursuant to USSG 

§4B1.4.); 

 

o Whether a statutory mandatory minimum punishment applied; 

o Whether the offender qualified for a sentence reduction upon application 

of the “safety valve” provision pursuant to USSG §5C1.2 (which limits the 

applicability of mandatory minimum sentences in certain cases); 

o Whether the court determined that a sentence outside the applicable 

sentencing guideline range was warranted; 

o Whether the offender pled guilty; 

o Race of the offender; 

o Gender of the offender; 

o Citizenship of the offender (whether the offender was a United States 

citizen); 

o Educational attainment of the offender; and 

 
13 

o Age of the offender. 

The results of the multivariate analysis for these two time periods were set out in Figure 

1248 and Figure 1349 of the Booker Report, which are reproduced here as Figure A: 

 

48 Booker Report, supra note 3, at 107. 

49 Booker Report, supra note 3, at 109. 
14 

 Figure A 

17.0

33.9

-8.4

4.9

16.2

35.7

-4.6

-10.3 -9.0

10.8

-30

-20

-10

0

10

20

30

40

Post-PROTECT Act Post-Booker

Figure 12

Differences in Sentence Length for Demographic Factors

Results of Multivariate Analysis

Post-PROTECT Act - Post-Booker

“Other”

Race

vs.

White

Non-U.S.

Citizen

vs.

U.S. Citizen

Percentage Difference in Sentence Length

Any College

vs.

No College

No data point signifies that there was no statistical difference between the two groups. The data in this figure are from the Post-PROTECT Act (05/01/03 – 06/24/04) and 

Post-Booker (01/12/05 – 01/11/06) eras. Cases sentenced on or before January 11, 2006 were included in this figure. As of the data extraction date for the post-Booker

datafile, the Commission had received, coded and edited 1,300 cases sentenced between January 1, 2006 and January, 11, 2006.

SOURCE: U.S. Sentencing Commission, 2006 Booker Report Datafiles.

Male

vs.

Female

Black 

vs.

White

Over 25 Years of Age

vs.

25 Years of Age and 

Younger

14.2

10.2

8.2

4.9

18.6

16.8

13.2

15.6 17.0 16.2

-7.6

-13.2

10.7 10.8

27.6

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

30.0

FY1999 FY2000 Pre-PROTECT

Act

PostPROTECT

Act

Booker

Hispanic vs. White Black vs. White O ther vs. White Male vs. Female

Figure 13

Differences in Sentence Length by Race and Gender

Results of Multivariate Analysis

FY1999 – Post-Booker

Percentage Difference in Sentence Length

FY2001 FY2002

No data point signifies that there was no statistical difference between the two groups. Cases sentenced on or before January 11, 2006 were included in this figure. As of the 

data extraction date for the post-Booker datafile, the Commission had received, coded and edited 1,300 cases sentenced between January 1, 2006 and January, 11, 2006.

SOURCE: U.S. Sentencing Commission, 1999-2003 Datafiles, USSCFY1999-USSCFY2003, and 2006 Booker Report Datafiles.
15 

The Booker Report summarized the results of the multivariate analysis that were 

statistically significant. Certain demographic factors, namely gender, age, education and 

citizenship, were associated with sentence length to the same or virtually the same extent 

both before and after the Booker decision.50 Specifically, longer sentence lengths were 

associated with male offenders when compared to female offenders, with non-citizens 

when compared to U.S. citizens, with offenders having no college education when 

compared to those who did have some college education, and with offenders 25 years of 

age and younger when compared to those over 25 years of age. Regarding race, the 

Commission concluded that: 

Post-Booker, black offenders are associated with sentences that are 4.9 

percent higher than white offenders, and “other” race offenders (mostly 

Native American offenders) are associated with sentences that are 10.8 

percent higher than white offenders. Neither of these relationships was 

statistically significant in the post-PROTECT Act period. No difference 

was found between white and Hispanic offenders during either time 

period.51, 52

B. The Booker Report Model 

 1. Update of the Booker Report Model Data

 

 The Commission has updated the analysis presented in the Booker Report using 

data through the end of fiscal year 2009. This analysis employed the same methodology 

used in the Booker Report. However, to facilitate analysis of sentencing trends in light of 

evolving Supreme Court jurisprudence,53 and specifically to illuminate any trends since 

the Booker decision, the data used in the analysis were divided into two time periods: (1) 

the three-year period between the Booker decision (January 12, 2005) and the decisions 

in Kimbrough v. United States and Gall v. United States (both decided on December 10, 

2007) (the “Post-Booker Period”); and (2) the 21-month period from December 11, 2007, 

to the end of fiscal year 2009 (September 30, 2009) (the “Post-Gall Period”). The data 

analyzed was taken from the sentences imposed on more than 360,000 offenders.54 

 

50 Id. at 106. 

51 Id. 

52 The “other” category consists of all offenders other than those who are white, black, or Hispanic, and 

includes offenders of Native American, Alaskan Native, and Asian or Pacific Islander origin. 

53 In Gall v. United States, 552 U.S. 38, 51 (2007), the Supreme Court held that courts of appeals must 

review all sentences - whether inside, just outside, or significantly outside the guideline range - under a 

deferential “abuse of discretion” standard. In Kimbrough v. United States, 552 U.S. 85, 110 (2007), the 

Supreme Court held that a district court may consider the disparity between the treatment of crack and 

powder cocaine offenses in the guidelines (i.e., the 100-to-1 ratio) when applying the 18 U.S.C. § 3553(a) 

factors to determine an offender’s sentence. 

54 See Table A, infra at the Technical Appendix, for more information concerning these offenders. 
16 

 Figure B provides the results of the analysis for the three time periods: PostPROTECT Act, Post-Booker, and Post-Gall.

 55

Figure B 

“Other” Race vs. White

Percentage Difference in Sentence Length

Male vs. Female

Black vs. White

Hispanic vs. White

Booker Report Model: Data Through FY2009

•signifies that there was no statistically significant difference between the two groups.

SOURCE: U.S. Sentencing Commission, 2003-2009 Datafiles, USSCFY03-USSCFY09.

Differences in Sentence Length for Demographic Factors

Results of Multivariate Regression Analysis

Post-PROTECT Act, Post-Booker, and Post-Gall

Non-U.S.Citizen

vs.

U.S. Citizen

Any College

vs.

No College

Over 25 Years of Age

vs.

25 Years of Age or Younger

 

 2. Summary of Updated Results Using the Booker Report Model

 The multivariate analysis assessed whether any demographic factors were 

associated with changes in sentence lengths after Booker. The analysis determined that 

demographic factors of race, gender, citizenship, education, and age each were associated 

with sentence length to a statistically significant extent during some of the time periods 

under study. For example, the analysis indicated that male offenders were associated 

with longer sentences than female offenders during all time periods. Specifically, male 

offenders were associated with sentences that were 17.0 percent longer than sentences for 

female offenders during the Post-PROTECT Act Period, 12.3 percent longer in the PostBooker Period, and 17.7 percent longer in the Post-Gall Period. 

 Non-U.S. citizens received sentences that were longer than those imposed on U.S. 

citizens in all three periods. In the Post-PROTECT Act Period, non-U.S. citizens 

received sentences that were 33.9 percent longer than those imposed on U.S. citizens. 

 

55 The asterisk (*) in this table is used to indicate that any difference between the two groups for that time 

period was not statistically significant. This does not mean that there was no observed difference between 

the two groups but, rather, that the possibility that any observed difference occurred due to chance could 

not be dismissed at p<0.01 level of significance. See also supra notes 19 to 24 and accompanying text. 
17 

Similarly, non-U.S. citizens received sentences that were 35.6 percent longer in the PostBooker Period and 48.5 percent longer in the Post-Gall Period than those imposed on 

offenders who were citizens. 

 Education also showed an association with sentence length. During the PostPROTECT Act Period, offenders with any college education received sentences that were 

8.4 percent shorter on average than offenders with no college education. During the PostBooker Period, offenders with any college education received sentences that were 9.3 

percent shorter than those without any college education, and during the Post-Gall Period 

those with any college education received sentences that were 9.6 percent shorter than 

sentences imposed on offenders without that education. 

 Offenders over 25 years of age received sentences that were 10.3 percent shorter 

than offenders 25 years of age or younger during the Post-PROTECT Act Period. These 

offenders received sentences that were 10.1 percent shorter during the Post-Booker 

Period, and 14.6 percent shorter during the Post-Gall Period than sentences imposed on 

offenders who were 25 years of age or younger. 

 Finally, although there were no associations found between the offender’s race 

and the sentence length during the Post-PROTECT Act Period, there were associations 

found between the race of some offender groups and sentence length in the Post-Booker

and Post-Gall Periods. In the Post-Booker Period, black offenders received sentences 

that were 7.4 percent longer than white offenders. Offenders classified as belonging to an 

“other” race56 received sentences that were 5.2 percent longer than white offenders. In 

the Post-Gall Period, black offenders received sentences that were 10.0 percent longer 

than white offenders. The sentences imposed on “other” race offenders were not 

different to a statistically significant extent when compared with white offenders. With 

respect to Hispanic offenders, there were no statistically significant differences in the 

sentences imposed when compared to sentences for white offenders in any of the three 

periods in the analysis. 

C. The Refined Model 

 1. Developing Another Model 

 As part of the Commission’s continuing review and analysis of federal sentencing 

practices and its commitment to pursuing continuing refinement of statistical techniques 

consistent with scientific literature and best practices, the Commission developed another 

multivariate regression model (the “refined model”) to assess the impact of factors 

associated with sentence lengths. This refined model also was used to analyze data that 

have been reported to the Commission after the Booker decision.57 

 

56 The “other” category consists of all offenders other than those who are white, black, or Hispanic, and 

includes offenders of Native American, Alaskan Native, and Asian or Pacific Islander origin. 

57 See Table A, infra at the Technical Appendix, for more information concerning these offenders. 
18 

 As with the Booker Report model, the dependent variable used in the refined 

model analysis was an offender’s sentence length. The factors examined as independent 

variables in the refined model were as follows:58

o The presumptive sentence (i.e., the minimum sentence, in months, to 

which the offender was subject under the sentencing guidelines, taking 

into account all guideline, statutory, and mandatory minimum 

provisions);59

o Type of offense committed (violent, sexual, pornography, drug trafficking, 

white collar, immigration, or other);60

o Whether a statutory mandatory minimum punishment applied; 

o Whether the court determined that a sentence outside the applicable 

sentencing guideline range was warranted; 

o Detention status (whether the offender had been released on bail prior to 

sentencing); 

o Whether the offender pled guilty; 

o Race of the offender paired with the gender of the offender; 

o Citizenship of the offender (whether the offender was a United States 

citizen); 

o Educational attainment of the offender; and 

o Age of the offender. 

 The refined model differs from the methodology used in the Booker Report in 

three significant ways. First, while the Booker Report model separately compared racial 

and gender effects by comparing males to females and white offenders to black, Hispanic 

 

58 A more complete description of these variables can be found in the Technical Appendix to this report, 

infra. 

59 The presumptive sentence is the bottom of the applicable sentencing guideline range that applies in a 

case. See supra note 46. 

60 The offense types used in this analysis are broad. The seriousness of the several crimes varies within the 

offense type categories as does the demographic characteristics of the offenders convicted of those crimes. 

Certain crimes within an offense types are punished more severely than others (e.g., those crimes involving 

injury not accounted for under the sentencing guidelines) and offenders of a particular demographic group 

may be disproportionately convicted of those crimes. If so, the offense type variables used in this analysis 

may not fully account for the effect on the sentence length imposed that is attributable to certain crimes. 
19 

and “other” offenders, the refined model instead pairs race and gender into eight distinct 

groups: white males, white females, black males, black females, Hispanic males, 

Hispanic females, “other” males, and “other” females. Reporting the results of the 

analysis in this way identifies any differences in sentence length associated with the 

offender’s race and gender, both individually and through any interaction of these 

characteristics. 

 Second, the refined model controls for an offender’s pre-sentence detention status 

in explaining differences in sentence length. In the Booker Report, one of the 

unmeasured factors cited as possibly having an effect on differences in sentence length 

among groups was the pretrial bail decision.61 This was thought to be potentially 

important because of differences among racial groups and gender in pre-sentencing 

custody status. As stated in the Booker Report, offenders with low sentencing guideline 

ranges who are held in pre-sentencing custody typically do not receive probationary 

sentences and, instead, are usually given credit for the time served in pre-sentencing 

custody. Offenders who are not held in pre-sentencing custody may receive probationary 

sentences. Therefore, two similarly situated offenders with differing pre-sentencing 

custody status may receive different sentences as a result of this status.62 If this status is 

associated with race or gender, then it may confound the results. The refined model 

controls for that possibility by including the custody status of the offender as an 

independent variable in the model.63

 Third, the refined model does not include some case characteristic variables that 

were included in the analysis discussed in the Booker Report. These guideline factors 

were omitted from the refined model because they directly contribute to or are highly 

correlated with the value of another variable that is already included in the analysis, i.e.,

the presumptive sentence.64 The factors included in the Booker Report model but 

excluded from the refined model are: (1) the number of criminal history points; (2) 

whether the offender received a “safety valve” adjustment (in drug cases);65 (3) whether 

 

61 Booker Report, supra note 3, at 105. 

62 Id. at 105 n.318 (Offenders who are not given the opportunity to post bail, or may not be able to afford 

bail, are detained for the entire period before their sentencing. Thus, if an offender’s final sentencing range 

is 6-12 months, and the offender serves 10 months in prison before the final adjudication of the sentence, 

the court could sentence the offender to “time served,” and the sentence would be 10 months. An offender 

who was out on bail during this process may get a 6-month sentence for the same behavior, which the court 

may have wanted to give to the first offender if the bail circumstances were similar.). 

63 This approach has been reported in the literature. See Brian D. Johnson, Jeffery T. Ulmer, and John H. 

Kramer, The Social Context of Guidelines Circumvention: The Case of Federal District Courts, 46 

CRIMINOLOGY 737 (2008); Cassia Spohn, Sentencing decision in three U.S. district courts: testing the 

assumption of uniformity in the federal sentencing process, 7 JUST. RES. & POL’Y 1, 8-9 (2005). 

64 These factors were included in the Booker Report model along with presumptive sentence variable in 

order to account for any extra weight such factors may have had in sentencing decisions “beyond the 

weight they are given in the guidelines.” Booker Report, supra note 3, at B-23. 

65 See 18 U.S.C. § 3553(f) (referenced at USSG §5C1.2). 
20 

the offender was convicted of an offense under 18 U.S.C. § 924(c); (4) whether the 

offender received a specific offense characteristic (“SOC”) enhancement for use of a 

weapon; (5) whether the Career Offender enhancement applied;66 (6) whether the Armed 

Career Criminal enhancement applied;67 and (7) the offender’s role, if any, in the offense 

(as reflected by a mitigating role adjustment, an aggravating role adjustment, or no role 

adjustment). 

 Including these variables in the Booker Report model required the application of 

statistical techniques that somewhat artificially overstated the impact of the presumptive 

sentence variable and, as a result, understated the impact of some of the other 

independent variables.68 By excluding the variables listed above, the refined model uses 

only those variables that are independent of and not correlated with one another.69 Under 

the refined model, each independent variable has a coefficient value attributed to it that 

reflects the contribution of that variable to the overall sentence. Direct comparison of the 

results of the two models should not be made because of the differences in the 

methodologies used. 

 As a result of these modifications, the refined model explains more of the 

variation within the data in the Commission’s datasets than did the Booker Report model. 

As discussed above, most regression analysis computer programs provide a quantifiable 

measure (the R2) of the amount of variation in the dependent variable that is explained by 

a particular model to which the program is applied. In general terms, a higher R2

indicates that more of the variation in the available data is accounted for (or explained) 

by the model and, therefore, the more the model “fits” the data. The Booker Report

model accounted for between 54 percent to 65 percent of the variation in the data, 

depending on the period being analyzed. The refined model accounted for a higher 

percentage of variation in the data in each of the three time periods studied.70

 

66 See USSG §4B1.1. 

67 See USSG §4B1.4. 

68 See infra note 77 and accompanying text for a further explanation of the purpose for undertaking this 

statistical approach. 

69 Although they were included in the Booker Report model for specific analytical reasons, the decision to 

include them required that the analysis be “restricted,” namely, that the coefficient for the presumptive 

sentence variable be set artificially (thus, restricted) at a value of one. Such an approach does not permit 

the computerized regression software to establish the coefficient for this variable independently, as it 

normally does for all variables. As a result, the coefficient for some of the other independent variables also 

could be altered. This approach made it difficult to evaluate the full effect of some of the variables on the 

results. 

70 The R2 for the updated Booker Report model analysis was 65.3% for the Post-PROTECT Act Period; 

62.4% for the Post-Booker Period (as defined above); and 53.8% for the Post-Gall Period. The R2 for the 

refined model was 71.7% for the Post-PROTECT Act Period and 67.4% for the Post-Booker Period; and 

61.8% for the Post-Gall Period. This comparison can be made because the dependent variable in both 

models is the same. See Gujarati, supra note 25. 
21 

 Figure C sets forth the results of the refined model for the following three periods: 

Post-PROTECT Act, Post-Booker, and Post-Gall.

71 

 

71 The asterisk (*) in this table is used to indicate that any difference between the two groups for that time 

period was not statistically significant. This does not mean that there was no observed difference between 

the two groups but, rather, that the possibility that any observed difference occurred due to chance could 

not be dismissed at p<0.01 level of significance. See also supra notes 19 to 24 and accompanying text. 
22 

Figure C 

Percentage Difference in Sentence Length

White Female 

vs. 

White Male

Refined Model

Differences in Sentence Length for Demographic Factors

Results of Multivariate Regression Analysis

Post-PROTECT Act, Post-Booker, and Post-Gall

Black Male 

vs. 

White Male

Black Female 

vs. 

White Male

Hispanic Male 

vs. 

White Male

Hispanic Female 

vs. 

White Male

Other Male 

vs. 

White Male

Other Female 

vs. 

White Male

•Indicates that the difference between the two groups was not statistically significant. 

SOURCE: U.S. Sentencing Commission, 2003-2009 Datafiles, USSCFY03-USSCFY09.

Percentage Difference in Sentence Length

Non-U.S.Citizen

vs.

U.S. Citizen

Any College

vs.

No College

Over 25 Years of Age

vs.

25 Years of Age or Younger

Differences in Sentence Length for Demographic Factors

Results of Multivariate Regression Analysis

Post-PROTECT Act, Post-Booker, and Post-Gall

Refined Model

•Indicates that the difference between the two groups was not statistically significant. 

SOURCE: U.S. Sentencing Commission, 2003-2009 Datafiles, USSCFY03-USSCFY09.
23 

 2. Summary of Results Using the Refined Model

 Consistent with the Booker Report model, the analysis using the refined model 

determined that demographic factors are associated with sentence length to a statistically 

significant extent during some of the time periods under study. The presence and relative 

magnitude of these associations were also generally consistent with the findings using the 

Booker Report model. 

 Female offenders, regardless of the offender’s race, received sentences that were 

shorter than sentences for white male offenders in each of the three time periods studied. 

In the Post-PROTECT Act Period, white female offenders received sentences that were 

23.1 percent shorter than white males. By comparison, sentences for black females were 

34.5 percent shorter when compared to white males in that period. Sentences for 

Hispanic females were 23.1 percent shorter, and sentences for “other” females were 43.4 

percent shorter when compared to white males. 

 In the Post-Booker Period, sentences imposed on white female offenders were 

19.0 percent shorter than those imposed on white male offenders. Sentences for black 

female offenders were 24.9 percent shorter than those imposed on white male offenders, 

sentences for Hispanic female offenders were 23.1 percent shorter, and those imposed on 

“other” females were 22.8 percent shorter. Finally, in the Post-Gall Period, sentences for 

white female offenders were 27.8 percent shorter than those for white males. By 

comparison, sentences for black female offenders were 29.1 percent shorter than those for 

white male offenders. Sentences imposed on Hispanic females were 13.9 percent shorter 

and sentences imposed on “other” females were 36.7 percent shorter than those for white 

male offenders. 

 Black male offenders received longer sentences than white males in each time 

period. In the Post-PROTECT Act Period, black male offenders received sentences that 

were 5.5 percent longer than those for white males. In the Post-Booker Period, black 

male offenders received sentences that were 15.2 percent longer, and in the Post-Gall

Period black male offenders received sentences that were 23.3 percent longer than those 

imposed on white males. 

 The association between Hispanic male sentences and white male sentences was 

statistically significant in two of the three time periods studied. In the Post-PROTECT 

Act Period, Hispanic males received sentences that were 4.4 percent shorter than 

sentences imposed on white males; however, in the Post-Gall Period Hispanic men 

received sentences that were 6.8 percent longer than sentences for white men. In the 

intervening Post-Booker Period, however, there was no statistically significant difference 

between the sentences for the two groups. 

 The sentences imposed on “other” male offenders differed from those imposed on 

white male offenders in a statistically significant manner only in the Post-PROTECT Act 

Period, where “other” males received sentences that were 8.0 percent shorter than those 
24 

imposed on white males. In the other time periods any differences between these two 

groups of offenders were not statistically significant. 

 Offenders who are not United States citizens were associated with sentences that 

were longer than sentences for United States citizens in the Post-Booker and Post-Gall 

Periods. Non-citizens received sentences that were 8.5 percent longer in the Post-Booker

Period and 11.2 percent longer in the Post-Gall Period than sentences imposed on United 

States citizens. In the Post-PROTECT Act Period, any difference observed between the 

sentences imposed on these two groups of offenders was not statistically significant. 

 The sentences of offenders with at least some college education were statistically 

significantly different from sentences of offenders with no college education in all 

periods. In the Post-PROTECT Act Period, offenders having at least some college 

education received sentences that were 3.9 percent shorter than sentences imposed on 

offenders with no college experience. In the Post-Booker Period, offenders having at 

least some college education received sentences that were 5.4 percent shorter than 

sentences of those with no college experience. In the Post-Gall period, offenders having 

some college education received sentences 3.9 percent shorter than sentences of those 

with no college experience. 

 Finally, there were no statistically significant associations in the sentences of 

offenders over the age of 25 compared with those 25 years of age or younger during the 

Post-PROTECT Act and Post-Gall Periods. However, in the Post-Booker Period, 

offenders over the age of 25 received sentences that were 3.1 percent longer than those 

imposed on offenders who were 25 years of age or younger. 

CONCLUSION 

 As part of its ongoing statutory duties under 28 U.S.C. § 995(a) to collect and 

analyze sentencing data on federal sentencing practices, the Commission will continue to 

monitor whether any sustained trends indicate that differences in sentencing practices are 

associated with the demographic characteristics of offenders. 
TECHNICAL APPENDIX 
A-1 

APPENDIX A 

A. The Data 

 The data described in this report were submitted to the United States Sentencing 

Commission by the United States courts.72 All data were received, coded, and edited by 

Commission staff as part of the ongoing activities of the Commission. The data used in this 

analysis are available in the Commission’s annual datasets, made available to the public through 

the Interuniversity Consortium for Political and Social Research.73 A summary descriptive 

statistics table of the data analyzed in this report is attached to this Technical Appendix as 

Appendix A. 

 The data presented in this report have been divided into three time periods: 

 (1) the Post-PROTECT Act Period (May 1, 2003, the date of enactment of the PROTECT 

Act, through June 24, 2004, the date of the Supreme Court’s decision in Blakely v. Washington); 

 (2) the Post-Booker Period (January 12, 2005, the date of the Supreme Court’s decision in 

United States v. Booker, through December 10, 2007, the date of the Supreme Court’s decisions 

in Kimbrough v. United States and Gall v. United States); and 

 (3) the Post-Gall Period (December 11, 2007, through September 30, 2009). 

B. The Booker Report Model 

 The multivariate analysis used in the Booker Report treated an offender’s sentence length 

(including imprisonment as well as any alternative confinement) as the dependent variable and 

used, as independent variables, both “case characteristic” variables (most of which concerned 

specific guideline application issues) and “demographic” variables. The following case 

characteristic variables were used: (1) the “presumptive sentence”74 (i.e., the bottom of the 

 

72 The courts are required to submit this information to the Commission. See 28 U.S.C. § 994(w)(1). 

73 For more information about ICPSR see http://www.icpsr.umich.edu/icpsrweb/ICPSR. 

74 Using the “presumptive sentence” (i.e., the bottom of the applicable guideline) was considered to be a superior 

method of capturing the many individual guidelines calculations that are part of a typical federal sentencing calculus 

– as opposed to including each individual guideline calculation issue as a separate independent variable. See, e.g., 

Rodney Engen & Randy Gainey, Modeling the Effects of Legally Relevant and Extralegal Factors Under Sentencing 

Guidelines: The Rules Have Changed, 38 CRIMINOLOGY 1207 (2000) (discussing the “presumptive sentence” model 

of regression analysis of guidelines sentencing data). For a recent study also using the presumptive sentence as an 

independent variable see Jill K. Doerner & Stephen Demuth, The Independent and Joint Effects of Race/Ethnicity, 

Gender, and Age on Sentencing Outcomes in U.S. Federal Courts, 27 JUST. Q. 1 (2010). 

 The Booker Report model includes some of the separate guideline factors (e.g., an offender’s role in the 

offense) – in addition to the presumptive sentence – in order to account for any extra weight such factors may have 

had in sentencing decisions “beyond the weight they are given in the guidelines.” Booker Report, supra note 3, at 

B-23. 

 
A-2 

applicable guidelines’ sentencing range, including the effect of any statutory mandatory 

minimum penalty or consecutive sentencing enhancement); (2) the type of offense (violent, 

sexual, drug, immigration, white collar, and “other”); (3) the number of criminal history points; 

(4) whether the offender received a “safety valve” adjustment (in application of the drug 

guideline); (5) whether the offender was convicted of an offense under 18 U.S.C. § 924(c); (6) 

whether the offender received a specific offense characteristic (“SOC”) enhancement for use of a 

weapon; (7) the offender’s departure status (upward, downward-government initiated, 

downward-court initiated, substantial assistance departure, or none); (8) whether the offender 

went to trial (as opposed to pleading guilty); (9) whether the offender was subject to a mandatory 

minimum statutory sentence; (9) whether the Career Offender enhancement applied; (10) 

whether the Armed Career Criminal enhancement applied; and (11) the offender’s role, if any, in 

the offense (mitigating role adjustment, aggravating role adjustment, or no role adjustment). 

 With respect to demographic variables, the following were used: (1) race of the offender 

(white, black, Hispanic, or “other”); (2) age of the offender (i.e., whether the offender was over 

25 years of age); (3) level of education (i.e., whether the offender attended any college); (4) 

gender of the offender; and (5) whether the offender was a U.S. citizen. 

 

 In the multivariate analysis employed by the Booker Report, statistical significance was 

determined at the more stringent p<0.01 rather than the p<0.05 level.75 The R2 for the approach 

used in the Booker Report was 65.3 percent for the Post-PROTECT Act Period and 61.5 percent 

for the one-year Post-Booker Period (as defined in the Booker Report). The R2 for the updated 

Booker Report model analysis was 65.3 percent for the Post-PROTECT Act Period, 62.4 percent 

for the Post-Booker Period (as defined above), and 53.8 percent for the Post-Gall Period. 

 Finally, attached at Appendix B is a list of the variables used in the Booker Report model. 

Also included in Appendix B is Table B-1, an updated version of Table B-1 in the Technical 

Appendix to the Booker Report (at B-30 through B-31) which corresponded to Figure 12 of the 

Booker Report. Table B-1 presented here corresponds to Figure B above, and reflects the results 

of the updated multivariate analysis using data through the end of fiscal year 2009 and broken 

down into the three periods discussed above. 

C. The Refined Model 

 The analysis using the refined model also treated an offender’s sentence length (including 

imprisonment as well as any alternative confinement) as the dependent variable and used, as 

independent variables, both “case characteristic” variables and “demographic” variables. 

However, the refined model uses fewer case characteristic variables than the Booker Report

model and also includes some additional variables that were not included in that analysis. 

 The following case characteristic variables were used in the refined model: (1) the 

“presumptive sentence”76 (i.e., the bottom of the applicable sentencing guideline range, including 

 

75 Id. at B-24.

76 See supra note 74. 
A-3 

the effect of any statutory mandatory minimum penalty or consecutive sentencing enhancement); 

(2) the type of offense (violent, sexual abuse, pornography, drug, immigration, white collar, and 

“other”); (3) the offender’s departure status (upward, substantial assistance departure, below 

range, or none); (4) whether the offender went to trial (as opposed to pleading guilty); 

(5) whether the offender was subject to a mandatory minimum statutory sentence; and (6) the 

offender’s bail status. 

 The case characteristic variables used in the approach discussed in the Booker Report but 

which were excluded from the refined model include: (1) the number of criminal history points; 

(2) whether the offender received a “safety valve” adjustment (in drug cases); (3) whether the 

offender was convicted of an offense under 18 U.S.C. § 924(c); (4) whether the offender 

received a specific offense characteristic (“SOC”) enhancement for use of a weapon; (5) whether 

the Career Offender enhancement applied; (6) whether the Armed Career Criminal enhancement 

applied; and (7) the offender’s role, if any, in the offense (mitigating role adjustment, 

aggravating role adjustment, or no role adjustment). These guideline factors directly contribute 

to or are highly correlated with the presumptive sentence variable used in the analysis. Including 

these variables in the Booker Report approach allowed the Commission to examine the influence 

of these variables over and above their respective contributions to the presumptive sentence. To 

accomplish this, however, required that the regression analysis be “restricted” by artificially 

setting (or restricting) the coefficient for the presumptive sentence variable to a value of one.77 

The refined model uses an “unrestricted” methodology which does not constrain any of the 

coefficients. As a result, each variable in the refined model has a coefficient value attributed to it 

that reflects the contribution of that variable to the overall sentence. 

 With respect to demographic variables, the refined model paired the traditional race and 

gender variables to create eight “race/gender” pairings: (1) white males; (2) white females; (3) 

black males; (4) black females; (5) Hispanic males; (6) Hispanic females; (7) “other” males; and 

(8) “other” females. Additional demographic variables include age of the offender (i.e., whether 

the offender was over 25 years of age); level of education (i.e., whether the offender attended 

any college); and whether the offender was a U.S. citizen. 

 As with the multivariate analysis employed by the Booker Report, the level of statistical 

significance was determined at p<0.01. The R2 for the refined model was 71.7 percent for the 

Post-PROTECT Act Period, 67.4 percent for the Post-Booker Period, and 61.8 percent for the 

Post-Gall Period. 

 Finally, attached at Appendix C is a list of the variables used in the Refined Model. Also 

included in Appendix C is Table C-1, similar to Table B-1 in Technical Appendix to the 2006 

Booker Report (at B-30-B-31). Table C-1 corresponds to Figure C above. 

 

77 See Shawn D. Bushway & Anne M. Phiel, Judging Judicial Discretion: Legal Factors and Racial Discrimination 

in Sentencing, 35 LAW & SOC’Y REV. 733, 748 (2001). 
A-4

Table A

Descriptive Statistics

Post-PROTECT Act, Post-Booker, and Post-Gall Periods

Booker Model Variables

Race and Gender Number Percent

Sentence Imposed Presumptive Sentence

Mean Median Mean Median

Post-PROTECT Act

Total 63,750 100.0 54 30 60 37

White 19,896 31.2 48 27 55 30

Black 15,797 24.8 78 48 88 57

Hispanic 25,464 39.9 44 30 49 33

Other 2,593 4.1 44 24 49 27

Male 55,040 86.3 58 36 65 37

Female 8,710 13.7 25 12 32 15

Post-Booker

Total 178,418 100.0 56 33 64 37

White 52,118 29.2 51 30 60 37

Black 44,333 24.8 82 57 95 60

Hispanic 74,338 41.7 44 27 50 33

Other 7,629 4.3 49 27 56 33

Male 154,863 86.8 60 37 69 41

Female 23,555 13.2 27 12 35 18

Post-Gall

Total 119,443 100.0 52 30 62 37

White 34,341 28.8 49 27 61 37

Black 27,919 23.4 82 60 96 63

Hispanic 52,490 44.0 39 24 45 24

Other 4,693 3.9 45 24 55 33

Male 104,491 87.5 56 32 66 37

Female 14,952 12.5 26 12 36 18
A-5

Table A (cont.)

Descriptive Statistics

Post-PROTECT Act, Post-Booker, and Post-Gall Periods

Revised Model Variables

Race and Gender Number Percent

Sentence Imposed Presumptive Sentence

Mean Median Mean Median

Post-PROTECT Act

Total 63,750 100.0 54 30 60 37

White Male 16,528 25.9 53 30 59 33

White Female 3,368 5.3 27 12 34 15

Black Male 13,346 20.9 88 60 98 63

Black Female 2,451 3.8 24 8 30 12

Hispanic Male 23,079 36.2 45 30 51 33

Hispanic Female 2,385 3.7 26 15 31 18

Other Male 2,087 3.3 50 27 54 30

Other Female 506 0.8 22 8 28 12

Post-Booker

Total 178,418 100.0 56 33 64 37

White Male 43,161 24.2 56 33 65 37

White Female 8,957 5.0 28 12 38 21

Black Male 38,339 21.5 91 63 105 70

Black Female 5,994 3.4 26 10 34 15

Hispanic Male 67,246 37.7 45 30 52 36

Hispanic Female 7,092 4.0 26 13 33 18

Other Male 6,117 3.4 54 30 62 37

Other Female 1,512 0.8 26 12 34 18

Post-Gall

Total 118,741 100.0 52 30 62 37

White Male 28,036 23.6 55 30 66 39

White Female 5,911 5.0 26 12 38 18

Black Male 24,354 20.5 90 63 105 70

Black Female 3,401 2.9 26 12 35 18

Hispanic Male 47,805 40.3 40 24 46 27

Hispanic Female 4,574 3.8 25 12 33 18

Other Male 3,778 3.2 50 27 59 37

Other Female 882 0.7 25 12 38 24
B-1

APPENDIX B

BOOKER REPORT MODEL LIST OF VARIABLES

Dependent Variable

Length of confinement: The length of confinement imposed (including any alternative

incarceration), with a cap of 470 months (for example, a sentence imposed of life was coded as

470). The logarithm was used, with all sentences of zero months given the value of 0.01 months

as the logarithm of zero is not mathematically possible. This variable was used for the ordinary

least squares analyses. The variable used was SENSPLT0.

Independent Variables

Guideline minimum: The minimum sentence, in months, the offender was subject to, taking into

account all guideline, statutory and mandatory minimums. The logarithm of this variable was

used, with all minimums of zero months given the value of 0.01 months, as the logarithm of zero

is not mathematically possible. Minimums of life imprisonment were coded as 470 months. The

variable used was GLMIN.

Type of offense committed (the variable used was GDLINEHI):

Violent offense: Offenders whose guideline sentence was controlled by the following

guidelines were considered violent offenders: Chapter Two Part K offenders (“Offenses

involving Public Safety”), USSG §§2A1.1-2A1.5, 2A2.1-2A2.4, 2A4.1-2A4.2, 2A5.1-

2A5.3, 2A6.1, 2A6.2, 2E1.3, 2E1.4, 2E2.1, 2B3.1, 2B3.2, and 2B3.3. 

Sexual abuse offense: Offenders whose guideline sentence was controlled by the

following guidelines: USSG §§2A3.1-2A3.4, 2G1.1-2G1.3, and 2G2.1-2G2.5.

Drug trafficking offense: Offenders whose guideline sentence was controlled by the

following guidelines: USSG §§2D1.1, 2D1.2, 2D1.5, 2D1.6, 2D1.7, 2D1.8, 2D1.9,

2D1.10, 2D1.11, 2D1.12, and 2D1.13.

Other drug offenses: Offenders whose guideline sentence was controlled by the following

guidelines: USSG §§2D2.1 and 2D2.2.

White collar offenses: Offenders whose guideline sentence was controlled by the

following guidelines: USSG §§2B1.1, 2B1.6, 2B4.1, 2B5.1, 2B5.3, 2F1.1, 2F1.2, 2R1.1,

Chapter Two Part S offenses (“Money Laundering and Monetary Transaction

Reporting”), and Chapter Two Part T offenses (“Offenses Involving Taxation”).

Immigration offenses: Offenders whose guideline sentence was controlled by offenses in

Chapter Two Part L (“Offenses Involving Immigration, Naturalization and Passports”).
B-2

Other type offenses: Offenders whose guideline sentence was controlled by offenses not

in the violent, sexual abuse, drug trafficking, other drug offenses, white collar offenses,

and immigration offenses.

Criminal History Points: The number of criminal history points assigned to the offender. The

variable used was SORCHPT.

Conviction for 18 U.S.C. § 924(c): Conviction by the court under this statute carries a

consecutive mandatory minimum. The variable used was IS924C.

Weapon SOC enhancement: The application of an enhancement for use or possession of a

weapon during the offense. The variable used was WEAPSOC.

Mandatory minimum application: If the statutory minimum for the offense was greater than zero,

a mandatory minimum applies in the case. The variable used was STATMIN.

Career offender applied: Whether the offender was subject to the enhanced criminal history level

and offense level under USSG §4B1.1. The variable used was CAROFFAP.

Armed career criminal application: Whether the offender was subject to the enhanced criminal

history level and offense level under USSG §4B1.4. The variable used was ACCAP.

Sentence placement relative to guideline range: Prior to the Booker decision, this was more

commonly referred to as “departure status.” Pre-Booker the variable used was DEPART. 

Upward departures were coded as “above range sentence”, downward departures were coded as

“below range sentence” and substantial assistance departures retained their identity. PostBooker, the variable BOOKERCD was used. “Above range sentence” was coded if the values

were “upward departure - guideline reason,” “upward departure - guideline and 18 U.S.C. §3553

(3553) reason,” “above range with Booker and 3553 reason,” and “other above range.” “Below

range - Court” was coded if the values were“downward departure",” downward departure - with

Booker," “below range with Booker,” and “remaining other below range.” Below range -

government" was coded if the values were “early disposition/§5K3.1" and “government

sponsored - below range.” Substantial assistance departures retained their identity. 

Safety valve: The application of safety valve under USSG §5C1.2 (Limitation of Applicability of

Statutory Minimum Sentences in Certain Cases). The variable used was SAFE.

Trial: Whether the offender was tried either by jury or by the court. The variable used was

NEWCNVTN.

Mitigating role: Court determination that the offender had a minor or minimal role in the offense

according to USSG §3B1.2 in the guidelines manual. The variable used was MITROLHI.

Aggravating role: Court determination that the offender had an aggravating role in the offense
B-3

according to USSG §3B1.1 in the guidelines manual. The variable used was AGGROLHI.

Race of offender: The variable NEWRACE (race or ethnicity of the offender) was used.

Gender of offender: The variable MONSEX (gender of the offender) was used.

Age of offender: This was coded as a dichotomous variable, separating those who were 25 years

of age and younger from the those older than 25 years of age. The variable used was AGE.

Educational attainment: This was coded as a dichotomous variable, separating those offenders

who attended college for any period of time and those who never attended college. The variable

used was EDUCATN.

Citizenship: The variable NEWCIT was used.
B-4

Table B-1

Booker Report Model

Post-PROTECT Act, Post-Booker, and Post-Gall

Variable

Post-PROTECT Post-Booker Post-Gall

Percent Difference Percent Difference Percent Difference

R2 65.3 62.4 53.8

Demographic Variables

Race of offender (reference category = White offenders)78

Black NS 7.4 10.0

Hispanic NS NS NS

“Other” NS 5.2 NS

Other Demographic Variables

Male (Female)79 17.0 12.3 17.7

Attending College (No college) -8.4 -9.3 -9.6

Over 25 Years of age (25 and younger) -10.3 -10.1 -14.6

Non United States Citizen (U.S. Citizen) 33.9 35.6 48.5

))))))))))))))

78 The reference category for all races is white offenders. This should be interpreted as, for example, in the PostBooker Period black offenders received sentences 7.4 percent longer than white offenders after controlling for all

variables in the model, while in the Post-Gall Period, black offenders received sentences 10.0 percent longer than

white offenders.

79 Reference categories are in parentheses. This should be interpreted as, for example, in the Post-PROTECT Act

Period, male offenders are sentenced 17.0 percent longer than female offenders after controlling for all variables in

the model, while in the Post-Booker Period male offenders received sentences 12.3 percent longer than female

offenders, and in the Post-Gall Period, male offenders received sentences 17.7 percent longer than female offenders.
B-5

Table B-1 (cont.)

Booker Report Model

Post-PROTECT Act, Post-Booker, and Post-Gall

Variable

Post-PROTECT Post-Booker Post-Gall

Percent Difference Percent Difference Percent Difference

R2 65.3 62.4 53.8

Case Characteristic Variables

Offense Type (reference category = Drug Trafficking)80

Violent -9.5 -10.5 -9.3

Sexual Abuse -20.5 -8.9 NS

Other Drug 367.7 160.9 143.2

Immigration 43.0 41.2 77.2

White Collar NS -12.9 -16.1

Other offenses -12.4 -17.8 -25.2

Criminal History

Career Offender application81 30.4 27.7 52.3

Criminal History Points81 -1.5 -0.6 -1.8

Armed Career Criminal application81 NS 11.2 27.6

Role in the Offense82

Aggravating Role81 NS NS NS

Mitigating Role81 -15.1 -15.2 -19.6

))))))))))))))

80 The reference category for all offense types is drug trafficking offenses. This should be interpreted as, for

example, in the Post-PROTECT Act Period, offenders convicted of violent offenses received sentences 9.5 percent

shorter than those convicted of drug trafficking offenses after controlling for all variables in the model, while in the

Post-Booker Period violent offenders received sentences 10.5 percent shorter than drug trafficking offenders, and in

the Post-Gall Period violent offenders received sentences 9.3 percent shorter than drug trafficking offenders.

81 This is a variable that is part of the calculation of the presumptive sentence. Therefore, the percent difference for

these variables should be interpreted as that variable’s contribution to the sentence above or below the amount it

already contributes to the presumptive sentence.

82 The reference category for role in the offense is “no role in the offense.”
B-6

Table B-1 (cont.)

Booker Report Model

Post-PROTECT Act, Post-Booker, and Post-Gall

Variable

Post-PROTECT Post-Booker Post-Gall

Percent Difference Percent Difference Percent Difference

R2 65.3 62.4 53.8

Case Characteristic Variables

Place in Range (reference category = Within Range)83

Above Range 383.8 429.8 401.1

Below Range - Court -73.0 -73.0 -77.0

Below Range - Government -66.8 -68.5 -76.7

Substantial Assistance -79.9 -79.2 -81.8

Other Case Characteristic Variables

Trial84 (Plea) -10.6 NS NS

18 U.S.C. § 924(c) conviction84 NS NS NS

Weapon SOC84 NS NS NS

Mandatory Minimum Applied84 6.0 15.3 22.3

Safety Valve84 -17.8 -11.0 -19.5

))))))))))))))

83 The reference category for all place in range variables is within range sentences. 

84 This is a variable that is part of the calculation of the presumptive sentence. Therefore, the percent difference for

this variable should be interpreted as that variable’s contribution to the sentence above or below the amount it

already contributes to the presumptive sentence.

SOURCE: U.S. Sentencing Commission, 2003 - 2009 Datafiles, USSCFY03-USSCFY09.
B-7

 Booker Report Model

 Post-PROTECT

 The REG Procedure

 Model: MODEL1

 Dependent Variable: logsplit

NOTE: Restrictions have been applied to parameter estimates.

 Number of Observations Read 68203

 Number of Observations Used 68203

 Analysis of Variance

 Sum of Mean

 Source DF Squares Square F Value Pr > F

 Model 27 271433 10053 4760.99 <.0001

 Error 68176 143957 2.11155

 Corrected Total 68203 415390

 Root MSE 1.45312 R-Square 0.6534

 Dependent Mean 2.79776 Adj R-Sq 0.6533

 Coeff Var 51.93871

 Parameter Estimates

 Parameter Standard Standardized

 Variable DF Estimate Error t Value Pr > |t| Estimate

 Intercept 1 0.24040 0.02690 8.94 <.0001 0

 logmin 1 1.00000 0 Infty <.0001 1.05953

 violent 1 -0.10001 0.02163 -4.62 <.0001 -0.01468

 sexual 1 -0.22936 0.04538 -5.05 <.0001 -0.01233

 drug 1 1.54266 0.04932 31.28 <.0001 0.07461

 immigration 1 0.35779 0.02419 14.79 <.0001 0.05797

 othtype 1 -0.13196 0.03313 -3.98 <.0001 -0.01017

 whitecoll 1 -0.04478 0.02175 -2.06 0.0396 -0.00710

 sorchpt 1 -0.01509 0.00121 -12.48 <.0001 -0.03358

 IS924C 1 -0.04925 0.03445 -1.43 0.1528 -0.00346

 WEAPSOC 1 0.01557 0.02788 0.56 0.5767 0.00131

 valve 1 -0.19592 0.02072 -9.46 <.0001 -0.02809

 ACCAP 1 0.13800 0.06286 2.20 0.0281 0.00530

 CAROFFAP 1 0.26512 0.03449 7.69 <.0001 0.01862

 upward 1 1.57658 0.04787 32.94 <.0001 0.07499

 downgovt 1 -1.10299 0.02398 -45.99 <.0001 -0.11021

 downcourt 1 -1.31031 0.02369 -55.32 <.0001 -0.12636

 subasst 1 -1.60618 0.01602 -100.26 <.0001 -0.24106

 mandmin 1 0.05801 0.01806 3.21 0.0013 0.01053

 NEWCNVTN 1 -0.11256 0.02680 -4.20 <.0001 -0.00974

 mitigate 1 -0.16379 0.02064 -7.94 <.0001 -0.01981

 aggravate 1 -0.03416 0.02542 -1.34 0.1791 -0.00312

 black 1 0.01877 0.01551 1.21 0.2262 0.00330

 hisp 1 -0.01009 0.01757 -0.57 0.5658 -0.00200
B-8

 Booker Report Model

 Post-PROTECT

 The REG Procedure

 Model: MODEL1

 Dependent Variable: logsplit

 Parameter Estimates

 Parameter Standard Standardized

 Variable DF Estimate Error t Value Pr > |t| Estimate

 other 1 -0.03405 0.02957 -1.15 0.2496 -0.00273

 agedummy 1 -0.11580 0.01376 -8.42 <.0001 -0.01957

 educ 1 -0.08743 0.01476 -5.92 <.0001 -0.01453

 male 1 0.15663 0.01715 9.13 <.0001 0.02188

 NEWCIT 1 0.29181 0.01751 16.67 <.0001 0.05543

 RESTRICT -1 -78790 733.02136 -107.49 <.0001* .

 * Probability computed using beta distribution.
B-9

 Booker Report Model

 Post-Booker

 The REG Procedure

 Model: MODEL1

 Dependent Variable: logsplit

NOTE: Restrictions have been applied to parameter estimates.

 Number of Observations Read 179872

 Number of Observations Used 179872

 Analysis of Variance

 Sum of Mean

 Source DF Squares Square F Value Pr > F

 Model 27 620558 22984 11039.1 <.0001

 Error 179844 374439 2.08202

 Corrected Total 179871 994997

 Root MSE 1.44292 R-Square 0.6237

 Dependent Mean 2.92128 Adj R-Sq 0.6236

 Coeff Var 49.39356

 Parameter Estimates

 Parameter Standard Standardized

 Variable DF Estimate Error t Value Pr > |t| Estimate

 Intercept 1 0.17987 0.01704 10.56 <.0001 0

 logmin 1 1.00000 0 Infty <.0001 1.00374

 violent 1 -0.11086 0.01334 -8.31 <.0001 -0.01686

 sexual 1 -0.09362 0.02375 -3.94 <.0001 -0.00626

 drugposs 1 0.95902 0.04726 20.29 <.0001 0.03011

 immigration 1 0.34541 0.01469 23.52 <.0001 0.06145

 othtype 1 -0.19540 0.02046 -9.55 <.0001 -0.01572

 whitecoll 1 -0.13777 0.01360 -10.13 <.0001 -0.02200

 totchpts 1 -0.00580 0.00073239 -7.92 <.0001 -0.01373

 is924c 1 0.00003799 0.01983 0.00 0.9985 0.00000300

 weapsoc 1 -0.00203 0.01480 -0.14 0.8907 -0.00020902

 valve 1 -0.11669 0.01304 -8.95 <.0001 -0.01735

 accap 1 0.10575 0.03693 2.86 0.0042 0.00445

 caroffap 1 0.24420 0.01998 12.22 <.0001 0.01909

 upward 1 1.66727 0.02385 69.90 <.0001 0.10219

 downgovt 1 -1.15400 0.01189 -97.09 <.0001 -0.15279

 downcourt 1 -1.30961 0.01062 -123.36 <.0001 -0.18518

 subasst 1 -1.57106 0.01023 -153.54 <.0001 -0.24209

 mandmin 1 0.14229 0.01091 13.05 <.0001 0.02799
B-10

 Booker Report Model

 Post-Booker

 The REG Procedure

 Model: MODEL1

 Dependent Variable: logsplit

 Parameter Estimates

 Parameter Standard Standardized

 Variable DF Estimate Error t Value Pr > |t| Estimate

 newcnvtn 1 -0.03379 0.01652 -2.05 0.0408 -0.00306

 mitigate 1 -0.16557 0.01277 -12.96 <.0001 -0.02078

 aggravate 1 0.02618 0.01662 1.58 0.1151 0.00235

 black 1 0.07117 0.00972 7.32 <.0001 0.01308

 hisp 1 -0.02578 0.01092 -2.36 0.0183 -0.00540

 other 1 0.05125 0.01774 2.89 0.0039 0.00441

 male 1 0.11600 0.01064 10.90 <.0001 0.01675

 agedummy 1 -0.10697 0.00874 -12.24 <.0001 -0.01828

 educ 1 -0.09738 0.00920 -10.58 <.0001 -0.01681

 newcit 1 0.30425 0.01084 28.08 <.0001 0.06145

 RESTRICT -1 -171107 1071.22223 -159.73 <.0001* .

 * Probability computed using beta distribution.
B-11

 Booker Report Model

 Post-Gall

 The REG Procedure

 Model: MODEL1

 Dependent Variable: logsplit

NOTE: Restrictions have been applied to parameter estimates.

 Number of Observations Read 119443

 Number of Observations Used 119443

 Analysis of Variance

 Sum of Mean

 Source DF Squares Square F Value Pr > F

 Model 27 360537 13353 5145.60 <.0001

 Error 119415 309891 2.59507

 Corrected Total 119442 670428

 Root MSE 1.61092 R-Square 0.5378

 Dependent Mean 2.81236 Adj R-Sq 0.5377

 Coeff Var 57.28019

 Parameter Estimates

 Parameter Standard Standardized

 Variable DF Estimate Error t Value Pr > |t| Estimate

 Intercept 1 0.22303 0.02395 9.31 <.0001 0

 logmin 1 1.00000 0 Infty <.0001 1.04036

 violent 1 -0.09746 0.01870 -5.21 <.0001 -0.01431

 sexual 1 -0.00027857 0.02991 -0.01 0.9926 -0.00002063

 drugposs 1 0.88860 0.07266 12.23 <.0001 0.02458

 immigration 1 0.57224 0.02021 28.32 <.0001 0.10765

 othtype 1 -0.29109 0.02857 -10.19 <.0001 -0.02292

 whitecoll 1 -0.17582 0.01889 -9.31 <.0001 -0.02691

 totchpts 1 -0.01871 0.00102 -18.27 <.0001 -0.04304

 is924c 1 -0.04251 0.02885 -1.47 0.1406 -0.00313

 weapsoc 1 -0.00631 0.02023 -0.31 0.7552 -0.00064959

 valve 1 -0.21730 0.01862 -11.67 <.0001 -0.03120

 accap 1 0.24361 0.05055 4.82 <.0001 0.01016

 caroffap 1 0.42065 0.02751 15.29 <.0001 0.03270

 upward 1 1.61167 0.03045 52.92 <.0001 0.10546

 downgovt 1 -1.45869 0.01537 -94.92 <.0001 -0.20262

 downcourt 1 -1.46897 0.01338 -109.79 <.0001 -0.22857

 subasst 1 -1.70152 0.01476 -115.30 <.0001 -0.25053
B-12

 Booker Report Model

 Post-Gall

 The REG Procedure

 Model: MODEL1

 Dependent Variable: logsplit

 Parameter Estimates

 Parameter Standard Standardized

 Variable DF Estimate Error t Value Pr > |t| Estimate

 mandmin 1 0.20157 0.01482 13.60 <.0001 0.03889

 newcnvtn 1 -0.00593 0.02494 -0.24 0.8120 -0.00048280

 mitigate 1 -0.21759 0.01840 -11.83 <.0001 -0.02620

 aggravate 1 0.06020 0.02338 2.58 0.0100 0.00523

 black 1 0.09550 0.01382 6.91 <.0001 0.01706

 hisp 1 0.02129 0.01461 1.46 0.1449 0.00446

 other 1 -0.04593 0.02527 -1.82 0.0691 -0.00377

 male 1 0.16325 0.01497 10.90 <.0001 0.02280

 agedummy 1 -0.15755 0.01215 -12.97 <.0001 -0.02632

 educ 1 -0.10108 0.01287 -7.85 <.0001 -0.01707

 newcit 1 0.39523 0.01518 26.03 <.0001 0.08123

 RESTRICT -1 -148022 1012.58565 -146.18 <.0001* .

 * Probability computed using beta distribution.
C-1

APPENDIX C 

REFINED MODEL LIST OF VARIABLES

Dependent Variable

Length of confinement: The length of confinement imposed (including any alternative

incarceration), with a cap of 470 months (for example, a sentence imposed of life was coded as

470). The logarithm was used, with all sentences of zero months given the value of 0.01 months

as the logarithm of zero is not mathematically possible. This variable was used for the ordinal

least squares analyses. The variable used was SENSPLT0.

Independent Variables

Guideline minimum: The minimum sentence, in months, the offender was subject to, taking into

account all guideline, statutory and mandatory minimums. The logarithm of this variable was

used, with all minimums of zero months given the value of 0.01 months, as the logarithm of zero

is not mathematically possible. Minimums of life imprisonment were coded as 470 months. The

variable used was GLMIN.

Type of offense committed (the variable used was GDLINEHI):

Violent offense: Offenders whose guideline sentence was controlled by the following

guidelines were considered violent offenders: Chapter Two Part K offenders (“Offenses

involving Public Safety”), USSG §§2A1.1-2A1.5, 2A2.1-2A2.4, 2A4.1-2A4.2, 2A5.1-

2A5.3, 2A6.1, 2A6.2, 2E1.3, 2E1.4, 2E2.1, 2B3.1, 2B3.2, and 2B3.3. 

Sexual abuse offense: Offenders whose guideline sentence was controlled by the

following guidelines: USSG §§2A3.1-2A3.4, and 2G1.1-2G1.3.

Pornography offense: Offenders whose guideline sentence was controlled by the

following guidelines: USSG §§ 2G2.1-2G2.5.

Drug trafficking offense: Offenders whose guideline sentence was controlled by the

following guidelines: USSG §§2D1.1, 2D1.2, 2D1.5, 2D1.6, 2D1.7, 2D1.8, 2D1.9,

2D1.10, 2D1.11, 2D1.12, and 2D1.13.

White collar offenses: Offenders whose guideline sentence was controlled by the

following guidelines: USSG §§2B1.1, 2B1.6, 2B4.1, 2B5.1, 2B5.3, 2F1.1, 2F1.2, 2R1.1,

Chapter Two Part S offenses (“Money Laundering and Monetary Transaction

Reporting”), and Chapter Two Part T offenses (“Offenses Involving Taxation”).

Immigration offenses: Offenders whose guideline sentence was controlled by offenses in

Chapter Two Part L (“Offenses Involving Immigration, Naturalization and Passports”).
C-2

Other type offenses: Offenders whose guideline sentence was controlled by offenses not

in the violent, sexual abuse, pornography, drug trafficking, white collar offenses, and

immigration offenses.

Sentence placement relative to guideline range: Prior to the Booker decision, this was more

commonly referred to as “departure status.” Pre-Booker the variable used was DEPART. 

Upward departures were coded as “above range sentence”, downward departures were coded as

“below range sentence” and substantial assistance departures retained their identity. PostBooker, the variable BOOKERCD was used. “Above range sentence ” was coded if the values

were “upward departure - guideline reason,” “upward departure - guideline and 18 U.S.C. §3553

(3553) reason,” “above range with Booker and 3553 reason,” and “other above range.” “Below

range sentence” was coded if the values were“downward departure - guideline reason,”

downward departure - guideline and 3553 reason,” “below range with Booker and 3553 reason,”

“other below range,” “other below range,” “early disposition/§5K3.1" and “government

sponsored - below range.” Substantial assistance departures retained their identity. 

Trial: Whether the offender was tried either by jury or by the court. The variable used was

NEWCNVTN.

Mandatory minimum application: If the statutory minimum for the offense was greater than zero,

a mandatory minimum applies in the case. If the sentencing court was relieved from application

of the mandatory either via a substantial assistance departure or application of safety valve, the

mandatory minimum does not apply and this variable was coded as “0.” The variables used were

STATMIN, BOOKERCD, DEPART and SAFE.

Pre-sentence custody status: The offender’s pre-sentence detention status. The variable used was

PRESENT.

Race and gender of offender: The variables NEWRACE (race or ethnicity of the offender) and

MONSEX (gender of the offender) were merged to form one value for each offender.

Age of offender: This was coded as a dichotomous variable, separating those who were 25 years

of age and younger from the those older than 25 years of age. The variable used was AGE.

Educational attainment: This was coded as a dichotomous variable, separating those offenders

who attended college for any period of time and those who never attended college. The variable

used was EDUCATN.

Citizenship: The variable NEWCIT was used.
C-3

Table C-1

Refined Model

Post-PROTECT Act, Post-Booker, and Post-Gall

Variable

Post-PROTECT Post-Booker Post-Gall

Percent Difference Percent Difference Percent Difference

R2 71.7 67.4 61.8

Demographic Variables

Race and Gender of offender (reference category = White Male offenders)85

White Female -23.1 -19.0 -27.8

Black Male 5.5 15.2 23.3

Black Female -34.5 -24.9 -29.1

Hispanic Male -4.4 NS 6.8

Hispanic Female -23.1 -23.1 -13.9

“Other” Male -8.0 NS NS

“Other” Female -43.4 -22.8 -36.7

Other Demographic Variables

Attending College (No college)86 -3.9 -5.4 -3.9

Over 25 Years of age (25 and younger) NS 3.1 NS

Non United States Citizen (U.S. Citizen) NS 8.5 11.2

))))))))))))))

85 The reference category for all races and gender pairings is white male offenders. This should be interpreted as, for

example, in the Post-PROTECT Act Period, white females received sentences 23.1 percent shorter than white males

after controlling for all variables in the model, while in the Post-Booker Period white female offenders received

sentences 19.0 percent shorter than white male offenders, and in the Post-Gall Period white female offenders receive

sentences 27.8 percent shorter than white male offenders.

86 Reference categories are in parenthesis. This should be interpreted as, for example, in the Post-PROTECT Act

period, offenders who attended college had sentences 3.9 percent shorter than offenders who did not attend college

after controlling for all variables in the model, while in the Post-Booker Period those who attended college received

sentences 5.4 percent shorter than those who did not attend college, and in the Post-Gall Period 3.9 percent shorter.
C-4

Table C-1 (cont.)

Refined Model

Post-PROTECT Act, Post-Booker, and Post-Gall

Variable

Post-PROTECT Post-Booker Post-Gall

Percent Difference Percent Difference Percent Difference

R2 71.7 67.4 61.8

Case Characteristic Variables

Presumptive Sentence 101.6 102.2 90.6

Trial (Plea)87 24.2 36.2 51.0

In Pre-conviction Custody (not in custody) 98.9 107.1 131.5

Sentence subject to Mandatory Minimum 40.8 38.7 60.2

Offense Type (reference category = Violent)88

Drug Trafficking 14.1 15.0 8.5

Sexual Abuse NS NS NS

Pornography NS 38.0 56.6

Immigration 22.0 11.7 8.0

White Collar -29.7 -31.5 -34.4

Other offenses -34.8 -37.9 -50.2

Place in Range (reference category = Within Range)89

Below Range -60.6 -59.7 -62.1

Substantial Assistance -72.0 -68.6 -68.5

Above Range 207.0 274.6 249.7

))))))))))))))

87 Reference categories are in parenthesis. This should be interpreted as, for example, in the Post-PROTECT Act

Period, offenders who went to trial had sentences 24.2 percent longer than offenders who pled guilty after

controlling for all variables in the model, while in the Post-Booker Period those who went to trial received sentences

36.2 percent longer than those who pled guilty, and in the Post-Gall Period those who went to trial received

sentences 51.0 percent longer than those who pled guilty.

88 The reference category for all offense types is violent offenders. This should be interpreted as, for example, drug

trafficking offenders in the Post-PROTECT Act Period received sentences 14.1 percent longer than offenders

convicted of violent offenses after controlling for all variables in the model, while in the Post-Booker Period drug

trafficking offenders received sentences 15.0 percent longer than offenders convicted of violent offenses, and in the

Post-Gall Period drug trafficking offenders received sentences 8.5 percent longer than offenders convicted of violent

offenses.

89 The reference category for place in range are offenders with sentences within the guideline range.

SOURCE: U.S. Sentencing Commission, 2003 - 2009 Datafiles, USSCFY03-USSCFY09.
C-5

 Refined Model

 Post-PROTECT

 The REG Procedure

 Model: MODEL1

 Dependent Variable: logsplit

 Number of Observations Read 63750

 Number of Observations Used 63750

 Analysis of Variance

 Sum of Mean

 Source DF Squares Square F Value Pr > F

 Model 23 262379 11408 7006.62 <.0001

 Error 63726 103755 1.62814

 Corrected Total 63749 366133

 Root MSE 1.27599 R-Square 0.7166

 Dependent Mean 2.85964 Adj R-Sq 0.7165

 Coeff Var 44.62052

 Parameter Estimates

 Parameter Standard Standardized

 Variable DF Estimate Error t Value Pr > |t| Estimate

 Intercept 1 0.61972 0.02795 22.17 <.0001 0

 logmin 1 0.70087 0.00254 275.64 <.0001 0.73059

 drugtraff 1 0.13157 0.01707 7.71 <.0001 0.02685

 sexual2 1 0.14899 0.06296 2.37 0.0180 0.00516

 porn 1 0.12196 0.05021 2.43 0.0151 0.00539

 immigration 1 0.19885 0.02163 9.19 <.0001 0.03356

 othtype 1 -0.42711 0.02997 -14.25 <.0001 -0.03379

 whitecoll 1 -0.35248 0.01971 -17.88 <.0001 -0.05714

 upward 1 1.12157 0.04604 24.36 <.0001 0.05174

 downdep 1 -0.93116 0.01614 -57.70 <.0001 -0.12854

 subasst 1 -1.27297 0.01460 -87.19 <.0001 -0.19978

 mandmin2 1 0.34250 0.01665 20.57 <.0001 0.05174

 newcnvtn 1 0.21649 0.02471 8.76 <.0001 0.01899

 custody 1 0.68759 0.01331 51.66 <.0001 0.13279

 whitefemale 1 -0.26209 0.02455 -10.67 <.0001 -0.02446

 blackmale 1 0.05346 0.01536 3.48 0.0005 0.00907

 blackfemale 1 -0.42348 0.02813 -15.06 <.0001 -0.03398

 hispmale 1 -0.04531 0.01689 -2.68 0.0073 -0.00909

 hispfemale 1 -0.26309 0.02893 -9.09 <.0001 -0.02083

 othermale 1 -0.08359 0.03026 -2.76 0.0057 -0.00621

 otherfemale 1 -0.56858 0.05780 -9.84 <.0001 -0.02105

 agedummy 1 0.01955 0.01242 1.57 0.1154 0.00340

 educ 1 -0.03990 0.01338 -2.98 0.0029 -0.00680

 citizen 1 -0.02114 0.01626 -1.30 0.1935 -0.00416
C-6

 Refined Model

 Post-Booker

 The REG Procedure

 Model: MODEL1

 Dependent Variable: logsplit

 Number of Observations Read 178418

 Number of Observations Used 178418

 Analysis of Variance

 Sum of Mean

 Source DF Squares Square F Value Pr > F

 Model 23 644083 28004 16031.0 <.0001

 Error 178394 311627 1.74685

 Corrected Total 178417 955709

 Root MSE 1.32168 R-Square 0.6739

 Dependent Mean 2.95157 Adj R-Sq 0.6739

 Coeff Var 44.77895

 Parameter Estimates

 Parameter Standard Standardized

 Variable DF Estimate Error t Value Pr > |t| Estimate

 Intercept 1 0.55903 0.01786 31.30 <.0001 0

 logmin 1 0.70384 0.00171 412.35 <.0001 0.70205

 drugtraff 1 0.14012 0.01072 13.07 <.0001 0.02949

 sexual2 1 0.05343 0.03813 1.40 0.1611 0.00196

 porn 1 0.32204 0.02565 12.56 <.0001 0.01861

 immigration 1 0.11072 0.01320 8.39 <.0001 0.02007

 othtype 1 -0.47651 0.01875 -25.41 <.0001 -0.03900

 whitecoll 1 -0.37897 0.01255 -30.21 <.0001 -0.06158

 upward 1 1.32065 0.02210 59.76 <.0001 0.08187

 downdep 1 -0.90906 0.00795 -114.34 <.0001 -0.16695

 subasst 1 -1.16007 0.00956 -121.39 <.0001 -0.18196

 mandmin2 1 0.32716 0.00989 33.06 <.0001 0.05362

 newcnvtn 1 0.30897 0.01511 20.45 <.0001 0.02841

 custody 1 0.72786 0.00852 85.41 <.0001 0.14086

 whitefemale 1 -0.21120 0.01563 -13.51 <.0001 -0.01993

 blackmale 1 0.14130 0.00968 14.59 <.0001 0.02508

 blackfemale 1 -0.28593 0.01858 -15.39 <.0001 -0.02226

 hispmale 1 -0.00996 0.01071 -0.93 0.3523 -0.00209

 hispfemale 1 -0.26311 0.01757 -14.98 <.0001 -0.02221

 othermale 1 0.02567 0.01832 1.40 0.1611 0.00202

 otherfemale 1 -0.25818 0.03473 -7.43 <.0001 -0.01023

 agedummy 1 0.03029 0.00797 3.80 0.0001 0.00526

 educ 1 -0.05544 0.00844 -6.57 <.0001 -0.00971

 citizen 1 -0.08864 0.01003 -8.84 <.0001 -0.01823
C-7

 Refined Model

 Post-Gall

 The REG Procedure

 Model: MODEL1

 Dependent Variable: logsplit

 Number of Observations Read 118741

 Number of Observations Used 118741

 Analysis of Variance

 Sum of Mean

 Source DF Squares Square F Value Pr > F

 Model 23 402618 17505 8344.26 <.0001

 Error 118717 249052 2.09787

 Corrected Total 118740 651671

 Root MSE 1.44840 R-Square 0.6178

 Dependent Mean 2.83456 Adj R-Sq 0.6178

 Coeff Var 51.09791

 Parameter Estimates

 Parameter Standard Standardized

 Variable DF Estimate Error t Value Pr > |t| Estimate

 Intercept 1 0.63754 0.02456 25.96 <.0001 0

 logmin 1 0.64491 0.00219 295.12 <.0001 0.66895

 drugtraff 1 0.08163 0.01479 5.52 <.0001 0.01672

 sexual2 1 0.05923 0.05163 1.15 0.2513 0.00213

 porn 1 0.44858 0.03099 14.47 <.0001 0.02977

 immigration 1 0.07655 0.01788 4.28 <.0001 0.01458

 othtype 1 -0.69802 0.02572 -27.13 <.0001 -0.05562

 whitecoll 1 -0.42206 0.01737 -24.30 <.0001 -0.06541

 upward 1 1.25204 0.02766 45.27 <.0001 0.08244

 downdep 1 -0.96985 0.01024 -94.68 <.0001 -0.18725

 subasst 1 -1.15429 0.01350 -85.48 <.0001 -0.17214

 mandmin2 1 0.47111 0.01338 35.21 <.0001 0.07625

 newcnvtn 1 0.41221 0.02233 18.46 <.0001 0.03397

 custody 1 0.83958 0.01177 71.31 <.0001 0.15461

 whitefemale 1 -0.32638 0.02116 -15.43 <.0001 -0.03030

 blackmale 1 0.20955 0.01337 15.67 <.0001 0.03612

 blackfemale 1 -0.34452 0.02688 -12.82 <.0001 -0.02453

 hispmale 1 0.06546 0.01401 4.67 <.0001 0.01370

 hispfemale 1 -0.14940 0.02384 -6.27 <.0001 -0.01227

 othermale 1 0.01706 0.02541 0.67 0.5019 0.00128

 otherfemale 1 -0.45668 0.04971 -9.19 <.0001 -0.01674

 agedummy 1 0.02346 0.01084 2.16 0.0304 0.00396

 educ 1 -0.04022 0.01158 -3.47 0.0005 -0.00686

 citizen 1 -0.11857 0.01370 -8.65 <.0001 -0.02467