Demographic Differences in Federal Sentencing Practices: An Update of the Booker Report’s Multivariate Regression Analysis, US Sentencing Commission, 2010

• Feb. 19, 2016 • Locations: United States of America • Topics: Sentencing

Download original document:
Brief thumbnail

This text is machine-read, and may contain errors. Check the original document to verify accuracy.

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)

DEMOGRAPHIC DIFFERENCES IN FEDERAL SENTENCING PRACTICES:
AN UPDATE OF THE BOOKER REPORT’S
MULTIVARIATE REGRESSION ANALYSIS

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.

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.

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

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.

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.

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-a3

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.”

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.

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

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.

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.

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.

The Commission’s Office of Research and Data staff use Statistical Analysis System (“SAS”) software
to conduct regression analyses.

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).

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.”).

Id. at 121-25, 191-94.

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.

See generally id. at 354-59.

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

“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.

Adrian E. Raftery, Bayesian Model Selection in Social Research, 25 SOCIOLOGICAL METHODOLOGY
111, 141 (1995).
24

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

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.

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

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

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.

FJC Reference Manual, supra note 6, at 216.

Id.

Finkelstein, supra note 5, at 370.

“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.

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.

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

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).

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.

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.

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.

“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).

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.

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”).

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.

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

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:

Booker Report, supra note 3, at 107.

Booker Report, supra note 3, at 109.

Figure A
Figure 12
Differences in Sentence Length for Demographic Factors
Results of Multivariate Analysis
Post-PROTECT Act - Post-Booker
40

Percentage Difference in Sentence Length

Post-PROTECT Act

33.9

Post-Booker

35.7

17.0 16.2
10.8

10
4.9

-10

Black
vs.
White

“Other”
Race
vs.
White

Male
vs.
Female

Non-U.S.
Citizen
vs.
U.S. Citizen

-4.6
-8.4

-10.3 -9.0

Any College
vs.
No College

-20

Over 25 Years of Age
vs.
25 Years of Age and
Younger

-30
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.

Figure 13
Differences in Sentence Length by Race and Gender
Results of Multivariate Analysis
FY1999 – Post-Booker
30.0

Percentage Difference in Sentence Length
27.6

25.0
18.6

20.0
15.0

16.8

17.0

15.6

14.2

16.2

13.2
10.2

10.0

10.7

10.8

8.2
4.9

5.0
0.0
FY1999

FY2000

FY2001

-5.0
-10.0

FY2002

Pre-PROTECT
Act

-7.6

PostPROTECT
Act

Booker

-13.2

-15.0
Hispanic vs. W hite

Black vs. White

O the r vs. White

Male vs. Fe male

-20.0
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.

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.

Id.

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.

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.

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

Figure B provides the results of the analysis for the three time periods: PostPROTECT Act, Post-Booker, and Post-Gall. 55
Figure B
Booker Report Model: Data Through FY2009
Differences in Sentence Length for Demographic Factors
Results of Multivariate Regression Analysis
Post-PROTECT Act, Post-Booker, and Post-Gall

Percentage Difference in Sentence Length

• Poa-PROTKt..."'T

• PoIl.Boobr

.Patt.OeU

30
20
10.0

• • •

0
-10

Over 25 Years of Age
vs.
25 Years of Age or Younger

Black vs. White

Non-U.S.Citizen
“Other” Race vs. White
vs.
Male vs. Female U.S. Citizen
Hispanic vs. White
Any College
vs.
No College

~O
•signifies that there was no statistically significant difference between the two groups.
SOURCE: U.S. Sentencing Commission, 2003-2009 Datafiles, USSCFY03-USSCFY09.

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.

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.

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

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.

The presumptive sentence is the bottom of the applicable sentencing guideline range that applies in a
case. See supra note 46.

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.

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.

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.

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

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

See USSG §4B1.1.

See USSG §4B1.4.

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.

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.

Figure C sets forth the results of the refined model for the following three periods:
Post-PROTECT Act, Post-Booker, and Post-Gall.71

Figure C
Refined Model
Differences in Sentence Length for Demographic Factors
Results of Multivariate Regression Analysis
Post-PROTECT Act, Post-Booker, and Post-Gall

----~==----

25 t-

D .3

Percentage Difference in Sentence Length

15
.J>oet.Od

Other Female
vs.
White Male

5
-S

Black Male
vs.
White Male

-15

Hispanic Male
vs.
White Male
Other Male
vs.
White Male

-25
-35
White Female
vs.
White Male

Hispanic Female
vs.
White Male

Black Female
vs.
White Male

-2:L1

-36..7

•Indicates that the difference between the two groups was not statistically significant.
SOURCE: U.S. Sentencing Commission, 2003-2009 Datafiles, USSCFY03-USSCFY09.

Refined Model
Differences in Sentence Length for Demographic Factors
Results of Multivariate Regression Analysis
Post-PROTECT Act, Post-Booker, and Post-Gall

Percentage Difference in Sentence Length

• Post.-PROTECT
• Post.-Booker
.Post.-GaJl
_

11.2

-5

-10

Non-U.S.Citizen
vs.
U.S. Citizen

Over 25 Years of Age
vs.
25 Years of Age or Younger

Any College
vs.
No College

•Indicates that the difference between the two groups was not statistically significant.
SOURCE: U.S. Sentencing Commission, 2003-2009 Datafiles, USSCFY03-USSCFY09.

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

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

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).

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

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-1

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.

See supra note 74.

A-2

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.

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-3

Table A
Descriptive Statistics
Post-PROTECT Act, Post-Booker, and Post-Gall Periods
Booker Model Variables
Sentence Imposed
Race and Gender

Number

Percent

Mean

Presumptive Sentence

Median

Mean

Median

Post-PROTECT Act
Total

63,750

100.0

White

19,896

31.2

Black

15,797

24.8

Hispanic

25,464

39.9

Other

2,593

4.1

Male

55,040

86.3

8,710

13.7

Female

Post-Booker
Total

178,418

100.0

White

52,118

29.2

Black

44,333

24.8

Hispanic

74,338

41.7

Other

7,629

4.3

Male

154,863

86.8

23,555

13.2

Female

Post-Gall
Total

119,443

100.0

White

34,341

28.8

Black

27,919

23.4

Hispanic

52,490

44.0

Other

4,693

3.9

Male

104,491

87.5

14,952

12.5

Female

A-4

Table A (cont.)
Descriptive Statistics
Post-PROTECT Act, Post-Booker, and Post-Gall Periods
Revised Model Variables
Sentence Imposed
Race and Gender

Number

Percent

Mean

Presumptive Sentence

Median

Mean

Median

Post-PROTECT Act
Total

63,750

100.0

White Male

16,528

25.9

3,368

5.3

13,346

20.9

Black Female

2,451

3.8

Hispanic Male

23,079

36.2

Hispanic Female

2,385

3.7

Other Male

2,087

3.3

506

0.8

White Female
Black Male

Other Female

Post-Booker
Total

178,418

100.0

43,161

24.2

8,957

5.0

38,339

21.5

105

Black Female

5,994

3.4

Hispanic Male

67,246

37.7

Hispanic Female

7,092

4.0

Other Male

6,117

3.4

Other Female

1,512

0.8

White Male
White Female
Black Male

Post-Gall
Total

118,741

100.0

28,036

23.6

5,911

5.0

24,354

20.5

105

Black Female

3,401

2.9

Hispanic Male

47,805

40.3

Hispanic Female

4,574

3.8

Other Male

3,778

3.2

882

0.7

White Male
White Female
Black Male

Other Female

A-5

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, 2A5.12A5.3, 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-1

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-2

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-3

Table B-1
Booker Report Model
Post-PROTECT Act, Post-Booker, and Post-Gall

Variable

Post-PROTECT

Post-Booker

Post-Gall

Percent Difference

65.3

62.4

53.8

Demographic Variables
Race of offender (reference category = White offenders)78
Black

7.4

10.0

Hispanic

“Other”

5.2

Other Demographic Variables
Male (Female)79

17.0

12.3

17.7

Attending College (No college)

-8.4

-9.3

-9.6

-10.3

-10.1

-14.6

33.9

35.6

48.5

Over 25 Years of age (25 and younger)
Non United States Citizen (U.S. Citizen)

))))))))))))))
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.

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-4

Table B-1 (cont.)
Booker Report Model
Post-PROTECT Act, Post-Booker, and Post-Gall

Variable

Post-PROTECT

Post-Booker

Post-Gall

Percent Difference

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

Other Drug

367.7

160.9

143.2

Immigration

43.0

41.2

77.2

White Collar

-12.9

-16.1

-12.4

-17.8

-25.2

Other offenses

Criminal History
Career Offender application81

30.4

27.7

52.3

Criminal History Points81

-1.5

-0.6

-1.8

11.2

27.6

-15.1

-15.2

-19.6

Armed Career Criminal application81

Role in the Offense82
Aggravating Role81
Mitigating Role81

))))))))))))))
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.

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.

The reference category for role in the offense is “no role in the offense.”

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

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

-77.0

Below Range - Government

-66.8

-68.5

-76.7

Substantial Assistance

-79.9

-79.2

-81.8

-10.6

18 U.S.C. § 924(c) conviction84

Weapon SOC84

Mandatory Minimum Applied84

6.0

15.3

22.3

-17.8

-11.0

-19.5

Other Case Characteristic Variables
Trial84 (Plea)

Safety Valve84

))))))))))))))
83

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

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-6

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
Number of Observations Used

68203
68203

Analysis of Variance
DF

Sum of
Squares

Mean
Square

27
68176
68203

271433
143957
415390

10053
2.11155

Root MSE
Dependent Mean
Coeff Var

1.45312
2.79776
51.93871

Source
Model
Error
Corrected Total

R-Square
Adj R-Sq

F Value

Pr > F

4760.99

<.0001

0.6534
0.6533

Parameter Estimates
Variable
Intercept
logmin
violent
sexual
drug
immigration
othtype
whitecoll
sorchpt
IS924C
WEAPSOC
valve
ACCAP
CAROFFAP
upward
downgovt
downcourt
subasst
mandmin
NEWCNVTN
mitigate
aggravate
black
hisp

Parameter
Estimate

Standard
Error

t Value

Pr > |t|

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

0.24040
1.00000
-0.10001
-0.22936
1.54266
0.35779
-0.13196
-0.04478
-0.01509
-0.04925
0.01557
-0.19592
0.13800
0.26512
1.57658
-1.10299
-1.31031
-1.60618
0.05801
-0.11256
-0.16379
-0.03416
0.01877
-0.01009

0.02690
0
0.02163
0.04538
0.04932
0.02419
0.03313
0.02175
0.00121
0.03445
0.02788
0.02072
0.06286
0.03449
0.04787
0.02398
0.02369
0.01602
0.01806
0.02680
0.02064
0.02542
0.01551
0.01757

8.94
Infty
-4.62
-5.05
31.28
14.79
-3.98
-2.06
-12.48
-1.43
0.56
-9.46
2.20
7.69
32.94
-45.99
-55.32
-100.26
3.21
-4.20
-7.94
-1.34
1.21
-0.57

<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.0396
<.0001
0.1528
0.5767
<.0001
0.0281
<.0001
<.0001
<.0001
<.0001
<.0001
0.0013
<.0001
<.0001
0.1791
0.2262
0.5658

B-7

Standardized
Estimate
0
1.05953
-0.01468
-0.01233
0.07461
0.05797
-0.01017
-0.00710
-0.03358
-0.00346
0.00131
-0.02809
0.00530
0.01862
0.07499
-0.11021
-0.12636
-0.24106
0.01053
-0.00974
-0.01981
-0.00312
0.00330
-0.00200

Booker Report Model
Post-PROTECT
The REG Procedure
Model: MODEL1
Dependent Variable: logsplit
Parameter Estimates
Variable

Parameter
Estimate

Standard
Error

t Value

Pr > |t|

Standardized
Estimate

other
agedummy
educ
male
NEWCIT
RESTRICT

1
1
1
1
1
-1

-0.03405
-0.11580
-0.08743
0.15663
0.29181
-78790

0.02957
0.01376
0.01476
0.01715
0.01751
733.02136

-1.15
-8.42
-5.92
9.13
16.67
-107.49

0.2496
<.0001
<.0001
<.0001
<.0001
<.0001*

-0.00273
-0.01957
-0.01453
0.02188
0.05543
.

* Probability computed using beta distribution.

B-8

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
Number of Observations Used

179872
179872

Analysis of Variance
DF

Sum of
Squares

Mean
Square

27
179844
179871

620558
374439
994997

22984
2.08202

Root MSE
Dependent Mean
Coeff Var

1.44292
2.92128
49.39356

Source
Model
Error
Corrected Total

R-Square
Adj R-Sq

F Value

Pr > F

11039.1

<.0001

0.6237
0.6236

Parameter Estimates
Variable
Intercept
logmin
violent
sexual
drugposs
immigration
othtype
whitecoll
totchpts
is924c
weapsoc
valve
accap
caroffap
upward
downgovt
downcourt
subasst
mandmin

Parameter
Estimate

Standard
Error

t Value

Pr > |t|

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

0.17987
1.00000
-0.11086
-0.09362
0.95902
0.34541
-0.19540
-0.13777
-0.00580
0.00003799
-0.00203
-0.11669
0.10575
0.24420
1.66727
-1.15400
-1.30961
-1.57106
0.14229

0.01704
0
0.01334
0.02375
0.04726
0.01469
0.02046
0.01360
0.00073239
0.01983
0.01480
0.01304
0.03693
0.01998
0.02385
0.01189
0.01062
0.01023
0.01091

10.56
Infty
-8.31
-3.94
20.29
23.52
-9.55
-10.13
-7.92
0.00
-0.14
-8.95
2.86
12.22
69.90
-97.09
-123.36
-153.54
13.05

<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.9985
0.8907
<.0001
0.0042
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001

B-9

Standardized
Estimate
0
1.00374
-0.01686
-0.00626
0.03011
0.06145
-0.01572
-0.02200
-0.01373
0.00000300
-0.00020902
-0.01735
0.00445
0.01909
0.10219
-0.15279
-0.18518
-0.24209
0.02799

Booker Report Model
Post-Booker
The REG Procedure
Model: MODEL1
Dependent Variable: logsplit
Parameter Estimates
Variable

Parameter
Estimate

Standard
Error

t Value

Pr > |t|

Standardized
Estimate

newcnvtn
mitigate
aggravate
black
hisp
other
male
agedummy
educ
newcit
RESTRICT

1
1
1
1
1
1
1
1
1
1
-1

-0.03379
-0.16557
0.02618
0.07117
-0.02578
0.05125
0.11600
-0.10697
-0.09738
0.30425
-171107

0.01652
0.01277
0.01662
0.00972
0.01092
0.01774
0.01064
0.00874
0.00920
0.01084
1071.22223

-2.05
-12.96
1.58
7.32
-2.36
2.89
10.90
-12.24
-10.58
28.08
-159.73

0.0408
<.0001
0.1151
<.0001
0.0183
0.0039
<.0001
<.0001
<.0001
<.0001
<.0001*

-0.00306
-0.02078
0.00235
0.01308
-0.00540
0.00441
0.01675
-0.01828
-0.01681
0.06145
.

* Probability computed using beta distribution.

B-10

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
Number of Observations Used

119443
119443

Analysis of Variance
DF

Sum of
Squares

Mean
Square

27
119415
119442

360537
309891
670428

13353
2.59507

Root MSE
Dependent Mean
Coeff Var

1.61092
2.81236
57.28019

Source
Model
Error
Corrected Total

R-Square
Adj R-Sq

F Value

Pr > F

5145.60

<.0001

0.5378
0.5377

Parameter Estimates
Variable
Intercept
logmin
violent
sexual
drugposs
immigration
othtype
whitecoll
totchpts
is924c
weapsoc
valve
accap
caroffap
upward
downgovt
downcourt
subasst

Parameter
Estimate

Standard
Error

t Value

Pr > |t|

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

0.22303
1.00000
-0.09746
-0.00027857
0.88860
0.57224
-0.29109
-0.17582
-0.01871
-0.04251
-0.00631
-0.21730
0.24361
0.42065
1.61167
-1.45869
-1.46897
-1.70152

0.02395
0
0.01870
0.02991
0.07266
0.02021
0.02857
0.01889
0.00102
0.02885
0.02023
0.01862
0.05055
0.02751
0.03045
0.01537
0.01338
0.01476

9.31
Infty
-5.21
-0.01
12.23
28.32
-10.19
-9.31
-18.27
-1.47
-0.31
-11.67
4.82
15.29
52.92
-94.92
-109.79
-115.30

<.0001
<.0001
<.0001
0.9926
<.0001
<.0001
<.0001
<.0001
<.0001
0.1406
0.7552
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001

B-11

Standardized
Estimate
0
1.04036
-0.01431
-0.00002063
0.02458
0.10765
-0.02292
-0.02691
-0.04304
-0.00313
-0.00064959
-0.03120
0.01016
0.03270
0.10546
-0.20262
-0.22857
-0.25053

Booker Report Model
Post-Gall
The REG Procedure
Model: MODEL1
Dependent Variable: logsplit
Parameter Estimates
Variable

Parameter
Estimate

Standard
Error

t Value

Pr > |t|

Standardized
Estimate

mandmin
newcnvtn
mitigate
aggravate
black
hisp
other
male
agedummy
educ
newcit
RESTRICT

1
1
1
1
1
1
1
1
1
1
1
-1

0.20157
-0.00593
-0.21759
0.06020
0.09550
0.02129
-0.04593
0.16325
-0.15755
-0.10108
0.39523
-148022

0.01482
0.02494
0.01840
0.02338
0.01382
0.01461
0.02527
0.01497
0.01215
0.01287
0.01518
1012.58565

13.60
-0.24
-11.83
2.58
6.91
1.46
-1.82
10.90
-12.97
-7.85
26.03
-146.18

<.0001
0.8120
<.0001
0.0100
<.0001
0.1449
0.0691
<.0001
<.0001
<.0001
<.0001
<.0001*

0.03889
-0.00048280
-0.02620
0.00523
0.01706
0.00446
-0.00377
0.02280
-0.02632
-0.01707
0.08123
.

* Probability computed using beta distribution.

B-12

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, 2A5.12A5.3, 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-1

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-2

Table C-1
Refined Model
Post-PROTECT Act, Post-Booker, and Post-Gall

Variable

Post-PROTECT

Post-Booker

Post-Gall

Percent Difference

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

5.5

15.2

23.3

Black Female

-34.5

-24.9

-29.1

Hispanic Male

-4.4

6.8

-23.1

-13.9

-8.0

-43.4

-22.8

-36.7

-3.9

-5.4

-3.9

Over 25 Years of age (25 and younger)

3.1

Non United States Citizen (U.S. Citizen)

8.5

11.2

Black Male

Hispanic Female
“Other” Male
“Other” Female

Other Demographic Variables
Attending College (No college)86

))))))))))))))
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.

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-3

Table C-1 (cont.)
Refined Model
Post-PROTECT Act, Post-Booker, and Post-Gall
Post-PROTECT

Post-Booker

Post-Gall

Percent Difference

71.7

67.4

61.8

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

14.1

15.0

8.5

Sexual Abuse

Pornography

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

Variable
R2

Case Characteristic Variables
Presumptive Sentence

Offense Type (reference category = Violent)88
Drug Trafficking

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.

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.

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-4

Refined Model
Post-PROTECT
The REG Procedure
Model: MODEL1
Dependent Variable: logsplit
Number of Observations Read
Number of Observations Used

63750
63750

Analysis of Variance
DF

Sum of
Squares

Mean
Square

23
63726
63749

262379
103755
366133

11408
1.62814

Root MSE
Dependent Mean
Coeff Var

1.27599
2.85964
44.62052

Source
Model
Error
Corrected Total

R-Square
Adj R-Sq

F Value

Pr > F

7006.62

<.0001

0.7166
0.7165

Parameter Estimates
Variable
Intercept
logmin
drugtraff
sexual2
porn
immigration
othtype
whitecoll
upward
downdep
subasst
mandmin2
newcnvtn
custody
whitefemale
blackmale
blackfemale
hispmale
hispfemale
othermale
otherfemale
agedummy
educ
citizen

Parameter
Estimate

Standard
Error

t Value

Pr > |t|

Standardized
Estimate

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

0.61972
0.70087
0.13157
0.14899
0.12196
0.19885
-0.42711
-0.35248
1.12157
-0.93116
-1.27297
0.34250
0.21649
0.68759
-0.26209
0.05346
-0.42348
-0.04531
-0.26309
-0.08359
-0.56858
0.01955
-0.03990
-0.02114

0.02795
0.00254
0.01707
0.06296
0.05021
0.02163
0.02997
0.01971
0.04604
0.01614
0.01460
0.01665
0.02471
0.01331
0.02455
0.01536
0.02813
0.01689
0.02893
0.03026
0.05780
0.01242
0.01338
0.01626

22.17
275.64
7.71
2.37
2.43
9.19
-14.25
-17.88
24.36
-57.70
-87.19
20.57
8.76
51.66
-10.67
3.48
-15.06
-2.68
-9.09
-2.76
-9.84
1.57
-2.98
-1.30

<.0001
<.0001
<.0001
0.0180
0.0151
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.0005
<.0001
0.0073
<.0001
0.0057
<.0001
0.1154
0.0029
0.1935

0
0.73059
0.02685
0.00516
0.00539
0.03356
-0.03379
-0.05714
0.05174
-0.12854
-0.19978
0.05174
0.01899
0.13279
-0.02446
0.00907
-0.03398
-0.00909
-0.02083
-0.00621
-0.02105
0.00340
-0.00680
-0.00416

C-5

Refined Model
Post-Booker
The REG Procedure
Model: MODEL1
Dependent Variable: logsplit
Number of Observations Read
Number of Observations Used

178418
178418

Analysis of Variance
DF

Sum of
Squares

Mean
Square

23
178394
178417

644083
311627
955709

28004
1.74685

Root MSE
Dependent Mean
Coeff Var

1.32168
2.95157
44.77895

Source
Model
Error
Corrected Total

R-Square
Adj R-Sq

F Value

Pr > F

16031.0

<.0001

0.6739
0.6739

Parameter
Estimate

Standard
Error

t Value

Pr > |t|

Standardized
Estimate

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

0.55903
0.70384
0.14012
0.05343
0.32204
0.11072
-0.47651
-0.37897
1.32065
-0.90906
-1.16007
0.32716
0.30897
0.72786
-0.21120
0.14130
-0.28593
-0.00996
-0.26311
0.02567
-0.25818
0.03029
-0.05544
-0.08864

0.01786
0.00171
0.01072
0.03813
0.02565
0.01320
0.01875
0.01255
0.02210
0.00795
0.00956
0.00989
0.01511
0.00852
0.01563
0.00968
0.01858
0.01071
0.01757
0.01832
0.03473
0.00797
0.00844
0.01003

31.30
412.35
13.07
1.40
12.56
8.39
-25.41
-30.21
59.76
-114.34
-121.39
33.06
20.45
85.41
-13.51
14.59
-15.39
-0.93
-14.98
1.40
-7.43
3.80
-6.57
-8.84

<.0001
<.0001
<.0001
0.1611
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.3523
<.0001
0.1611
<.0001
0.0001
<.0001
<.0001

0
0.70205
0.02949
0.00196
0.01861
0.02007
-0.03900
-0.06158
0.08187
-0.16695
-0.18196
0.05362
0.02841
0.14086
-0.01993
0.02508
-0.02226
-0.00209
-0.02221
0.00202
-0.01023
0.00526
-0.00971
-0.01823

C-6

Refined Model
Post-Gall
The REG Procedure
Model: MODEL1
Dependent Variable: logsplit
Number of Observations Read
Number of Observations Used

118741
118741

Analysis of Variance
DF

Sum of
Squares

Mean
Square

23
118717
118740

402618
249052
651671

17505
2.09787

Root MSE
Dependent Mean
Coeff Var

1.44840
2.83456
51.09791

Source
Model
Error
Corrected Total

R-Square
Adj R-Sq

F Value

Pr > F

8344.26

<.0001

0.6178
0.6178

Parameter
Estimate

Standard
Error

t Value

Pr > |t|

Standardized
Estimate

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

0.63754
0.64491
0.08163
0.05923
0.44858
0.07655
-0.69802
-0.42206
1.25204
-0.96985
-1.15429
0.47111
0.41221
0.83958
-0.32638
0.20955
-0.34452
0.06546
-0.14940
0.01706
-0.45668
0.02346
-0.04022
-0.11857

0.02456
0.00219
0.01479
0.05163
0.03099
0.01788
0.02572
0.01737
0.02766
0.01024
0.01350
0.01338
0.02233
0.01177
0.02116
0.01337
0.02688
0.01401
0.02384
0.02541
0.04971
0.01084
0.01158
0.01370

25.96
295.12
5.52
1.15
14.47
4.28
-27.13
-24.30
45.27
-94.68
-85.48
35.21
18.46
71.31
-15.43
15.67
-12.82
4.67
-6.27
0.67
-9.19
2.16
-3.47
-8.65

<.0001
<.0001
<.0001
0.2513
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.5019
<.0001
0.0304
0.0005
<.0001

0
0.66895
0.01672
0.00213
0.02977
0.01458
-0.05562
-0.06541
0.08244
-0.18725
-0.17214
0.07625
0.03397
0.15461
-0.03030
0.03612
-0.02453
0.01370
-0.01227
0.00128
-0.01674
0.00396
-0.00686
-0.02467

C-7