CJ 301 CHAPTER 1 NOTES It is important for everyone to become familiar with the language of research as we begin this statistics course, so follow along and try to absorb the information below.  This module is intended to accompany Chapter 1 of the Adventures in Criminal Justice Research text (4th edition): This textbook introduces you to the logic of theory, research, and practice in criminal justice and gives you some practical experience through the use of the SPSS for Windows computer program. WHAT DO WE MEAN WHEN WE SAY STATISTICS? The word statistics can have a variety of meanings.  1. It can refer to fragments of data or information. 2. To some it may mean the theories and procedures that are used for understanding data. 3. Statistics may also be defined as collections of facts expressed as numbers. -For example, in 1990, 341,387 full-time law enforcement officers were working in the U.S.; this is a statistic.  So is the fact that 7,830 bank robberies occurred in the same year (Crime in the U.S. 1990) and that four million offenders were under some form of correctional supervision (Sourcebook of Criminal Justice Statistics 1992).  The list of statistical facts about the criminal justice system may be regarded as statistics.  Your age, your shoe size, your height, your sex, your ethnicity are all statistics.  Indeed, any fact that can be expressed as a number, whether it is important or not, is a statistic. 4. For this class, we are going to use the following working definition of the term statistics.  Statistics is a set of problem-solving procedures that are used to analyze and interpret aggregate data. WHAT ARE SOME PRACTICAL APPLICATIONS OF STATISTICS? Criminal justice practitioners deal with a wide variety of problems that statistics can help solve. 1. Statistics can be used to describe crime in a city, or the composition of a police department or the overcrowding problem in a county jail, or the case processing rate of a criminal court. 2. Other problems that arise in criminal justice go beyond simple description and into areas such as prediction and evaluation.  -         For example, if a police department were to add 60 officers to its force, what would be the predicted impact on crime rates, staff morale, or gasoline consumption?  How many new probation officer positions would be required in the next five years to keep up with the current growth in caseloads?  If sentences to prison continue at their present rate, for how many new prison beds must the state plan?  Is probation more effective than prison?  Which community-based corrections programs work better than others?  How successful is community-oriented policing or judicial training or the public defender’s office?  Answering these types of question involves various statistical techniques that we will learn about during this semester. WHAT ARE THE TYPES OF STATISTICS? 1. Descriptive Statistics – These are statistics whose function it is to describe what data looks l.

1. CJ 301
CHAPTER 1
NOTES
It is important for everyone to become familiar with the
language of research as we begin this statistics course, so
follow along and try to absorb the information below. This
module is intended to accompany Chapter 1 of the Adventures
in Criminal Justice Research text (4th edition):
This textbook introduces you to the logic of theory, research,
and practice in criminal justice and gives you some practical
experience through the use of the SPSS for Windows computer
program.
WHAT DO WE MEAN WHEN WE SAY STATISTICS?
The word statistics can have a variety of meanings.
1. It can refer to fragments of data or information.
2. To some it may mean the theories and procedures that are
used for understanding data.
3. Statistics may also be defined as collections of facts
expressed as numbers.
-For example, in 1990, 341,387 full-time law enforcement
officers were working in the U.S.; this is a statistic. So is the
fact that 7,830 bank robberies occurred in the same year (Crime
in the U.S. 1990) and that four million offenders were under
some form of correctional supervision (Sourcebook of Criminal
Justice Statistics 1992). The list of statistical facts about the
criminal justice system may be regarded as statistics. Your age,
your shoe size, your height, your sex, your ethnicity are all
statistics. Indeed, any fact that can be expressed as a number,
whether it is important or not, is a statistic.
4. For this class, we are going to use the following working
definition of the term statistics. Statistics is a set of problem-
solving procedures that are used to analyze and interpret
aggregate data.
WHAT ARE SOME PRACTICAL APPLICATIONS OF

2. STATISTICS?
Criminal justice practitioners deal with a wide variety of
problems that statistics can help solve.
1. Statistics can be used to describe crime in a city, or the
composition of a police department or the overcrowding
problem in a county jail, or the case processing rate of a
criminal court.
2. Other problems that arise in criminal justice go beyond
simple description and into areas such as prediction and
evaluation.
- For example, if a police department were to add 60
officers to its force, what would be the predicted impact on
crime rates, staff morale, or gasoline consumption? How many
new probation officer positions would be required in the next
five years to keep up with the current growth in caseloads? If
sentences to prison continue at their present rate, for how many
new prison beds must the state plan? Is probation more
effective than prison? Which community-based corrections
programs work better than others? How successful is
community-oriented policing or judicial training or the public
defender’s office? Answering these types of question involves
various statistical techniques that we will learn about during
this semester.
WHAT ARE THE TYPES OF STATISTICS?
1. Descriptive Statistics – These are statistics whose function it
is to describe what data looks like, where the center is, how
broadly the data are spread, and how they are related in terms of
one aspect to another aspect of the same data. Descriptive
statistics might include how many officers completed a
questionnaire, the age, racial/ethnic composition, sex, and rank
of those who completed the questionnaire, the overall average
score for each organizational division, and the percentage of
officers extremely satisfied with a given aspect of the job as
opposed to the percentage extremely dissatisfied. These
statistics describe what the data look like.
2. Inferential Statistics – These are statistics that we use during

3. the research process that makes it possible to infer from a
sample to the entire population.
- For example, how might I determine the public opinion
of students at NMSU about the death penalty? One method
would be to physically ask each and every student at NMSU if
they favor or oppose the death penalty. That method is very
time consuming and potentially very expensive. A less
expensive and less time intensive method is to draw a
representative sample from the population of all NMSU
students, calculate my statistics and then use those statistics to
infer characteristics of that sample back to the population of all
NMSU students. If the sampling procedure is done correctly
one can be very confident that the statistics calculated from the
sample will be representative of the same information in the
general population. Think back to the 2000 presidential
election. What did the pollsters tell us about the potential
outcome of that election prior to the actual election? They told
us the outcome was too close to call. They based their
information on the statistical analysis a sample of a little more
than 1,500 eligible voters from the total population of eligible
voters? Were they correct? You bet they were!
DATA versus VARIABLE
The word data is the plural of datum, which is defined as an
individual piece of information. However, we typically use the
plural form data because we rarely deal with only a single or
isolated fact. Data may be defined as the units of information
we collect and analyze.
- For example, the FBI collects the number and types of
criminal offenses that occur every month. This is data.
A variable is defined as a characteristic or attribute that is not
the same for all the persons, objects, or events being studied.
- For example, the racial or ethnic composition of students
in an introductory criminal justice course would be a variable.
- Criminal justice is concerned with an almost endless list
of variables that includes persons, objects, or events as the unit
of analysis. Persons can include criminals, inmates,

4. correctional officers, judges, attorneys, police officers, and
court clerks. Objects can include police cars, felony cases,
jails, prisons, judges’ chambers, guns, and bodies. Events can
include crimes, sentences, incarcerations, victimizations, and
executions.
- In criminal justice research, we do not study any of these
persons, objects, or events in a general or abstract way.
Instead, we focus on specific characteristics or attributes. If we
studied a group of offenders, for example, we might record age,
race, sex, and number of convictions. In a general study of
criminal offenders, most are not the same age, have not
committed the same offense, and have not used a weapon.
Similarly, most police officers differ in their job satisfaction,
and most felony cases are not disposed of in equal lengths of
time. These different characteristics are called variables
because their values are not the same for each member of the
group. Because the characteristics or attributes of persons,
objects, or events are not the same for all members of a group
under study, that is, they vary, they are called variables.
VARIABLES AND ATTRIBUTES –
Research methods are written in a variable language, and people
get involved mostly as the carriers of those variables.
VARIABLES - logical grouping of attributes. Example:
“gender” is variable composed of logical grouping of “male”
and “female” attributes. “Occupation” is a variable compose of
“dentist”, “teacher”, “plumber”, “janitor”, and etc. attributes.
(Please see the figure 1.2)
Marital status is a variable; it can take on the value of never
married single, married, divorced, or widowed. Type of crime
committed is a variable; it can take on values of robbery,
burglary, theft, murder, and so forth. Family income is a
variable; it can take on values from zero to billions of dollars.
A person’s attitude toward abortion is a variable; it can range
from strongly favoring legal abortion to strongly believing that
abortion should be a crime.
ATTRIBUTES – categories that make up a variable. The values

5. or the categories of a variable are its attributes. It is easy to
confuse variables and attributes.
For example, “male” is not a variable; it describes a category of
sex and is an attribute of the variable “sex”. Yet, a related idea,
“degree of masculinity,” is a variable. It describes the intensity
or strength of attachment to attitudes, beliefs, and behaviors
associated with the concept of “masculine” within a culture.
“Married” is not a variable; it is an attribute of the variable
“marital status.” Related ideas such as “number of years
married” or “depth of commitment to a marriage” are variables.
Likewise, “robbery” is not a variable; it is an attribute of the
variable “type of crime.” “Number of robberies,” “robbery
rate,” “amount taken during the robbery,” and “type of robbery”
are all variables because they vary or take on a range of values.
INDEPENDENT AND DEPENDENT VARIABLE –
Scientists use an experiment to search for cause and effect
relationships in nature. In other words, they design an
experiment so that changes to one item cause something else to
vary in a predictable way.
In CAUSE-AND-EFFECT term, the independent variable is
THE CAUSE, and dependent variable is the EFFECT.
Research focusing on causal relations usually begins with an
effect, then searches for its causes. Variables are classified
depending on their location in a causal relationship. The cause
variable, or the one that identifies forces or conditions that act
on something else, is the independent variable. The variable that
is the effect or is the result or outcome of another variable is
the dependent variable. The independent variable is independent
of prior causes that act on it, whereas the dependent variable
depends on the cause.
It is not always easy to determine whether a variable is
independent or dependent. Answering two questions helps you
identify the independent variable.
First, does it come before other variables in time? Independent
variables come before any other type.
Second, if the variables occur at the same time, does the author

6. suggest that one variable has an impact on another variable?
Independent variables affect or have an impact on other
variables.
Research topics are often phrased in terms of the dependent
variables because dependent variables are the phenomenon or
object or study to be explained. For example, suppose a
researcher examines the reasons for an increase in the crime
rate in Dallas, Texas; the dependent variable is the crime rate.
LEVEL OF MEASUREMENT FOR VARIABLES
Variables can be classified according to how they are
measured. This is an extremely important distinction as some
statistics can only be used when variables are measured in a
specific way. I will describe each level of measurement (also
sometimes referred to as scale) below going from least
sophisticated to most sophisticated level of measurement.
1. Nominal Level of Measurement (sometimes referred to as
categorical) – Variables measured at this level have categories
that are different and mutually exclusive in that each item
measured can be placed into one and only one category.
Furthermore, placement into a category does not indicate
possession of more or less of the variable in question.
- For example the variable sex has two categories, male
and female. One is either male or female and being in one
category or another does not imply possession of more or less of
the variable sex. Similarly, religious preference may have many
categories such as Baptist, Methodist, Lutheran, Episcopalian,
Catholic, Jewish, Agnostic, etc. and each individual can be
placed into one and only one category. The category of
religious preference does not imply possession of more or less
of the variable in question. We refer to these measurements as
nominal because they name, simply name the different
categories constituting them.
3. Ordinal Level of Measurement – Variables measured at this
level have categories that are different and mutually exclusive
but the various categories indicate possession of more or less of
the variable in question. However, it is not possible to

7. determine the exact distance between each category.
- For example, if I attempt to measure the level of
satisfaction of our MCJ distance students with the distance
program I might ask a question such as: How satisfied are you
with the MCJ Online Program? And I might have categories
that range between 1 and 5 where 1 refers to Very Unsatisfied, 2
refers to Unsatisfied, 3 refers to Neutral, 4 refers to Satisfied,
and 5 refers to Very Satisfied. In my analysis I would know for
certain that those responding with a 1 possess less of the
variable “satisfaction with MCJ Online Program than those
responding with a 5. I would not know exactly home much
more satisfaction, but I am confident that they are more
satisfied.
4. Interval Level of Measurement – Variables at this level of
measurement have categories that are mutually exclusive,
indicate possession of more or less of the variable, and the
precise distance between each category is measurable. The one
unique factor associated with variables measured at the interval
level is that there is no true zero point.
- For example, the variable IQ is often used to represent a
variable measured at the interval level. Assuming that IQ is
measured by the score on a standardized IQ examination we can
conclude that each category of the variable is mutually
exclusive (each person scores one and only one of the many
possible scores); each category indicates possession of more or
less of the variable IQ (a person with a score of 100 is assumed
to possess more IQ than a person with a score of 50); and the
exact distance between each category is measurable ( a person
with a score of 100 has scored precisely 50 points higher than a
person with a score of 50). However, if assume that it is not
possible for a living human being to have zero IQ, there is no
true zero. Consequently, we cannot say that a person who
scores 100 is twice as smart as a person who scores 50.
5. Ratio Level of Measurement – Variables at this level of
measurement have all of the characteristics of variables at the
interval level of measurement except that variables at the ratio

8. level of measurement have a true zero point.
- For example, the variable annual income is often used to
represent a variable measured at the ratio level. Each category
is mutually exclusive. Each category indicates possession of
more or less of the variable annual income. The distance
between each category is known and can be precisely
measured. Finally, it is possible to have zero annual income.
Consequently, we can say that a person who earns $100,000 per
year has an annual income precisely twice as high as a person
who earns $50,000 per year.
Important: Sometimes you will have options regarding the
levels of measurement to be created in variables. For instance,
although age qualifies as a ratio variable (e.g., 1-10, 11-20, 21-
30, 31-40, 41-50, 51-60, 61-over), it could be measured as an
ordinal (e.g., young, middle-aged, old) or even as a nominal
(e.g., baby boomer, not baby boomer) variable. Similarly, the
amount of time served in prison might be considered a ratio
variable (e.g., 3 years, 2 days and 2 hours…) but it could be
measured as an ordinal (e.g., greater than average for a
particular prison, less then or equal to that average) variable.
BASIC versus APPLIED RESEARCH
Basic research is research for the sake of research. This type of
research is undertaken for the primary reason of curiosity with
no specific goal beyond adding to the cumulative body of
knowledge being pursued.
Applied research is research that is geared toward a specific
purpose and the intent is that the results will be used by an
agency or organization to help that agency or organization
resolve problems and do planning.
THEORY
A theory is a set of interconnected statements or propositions
that explain how two or more events are related to one another.
- For example, once labeled as a troublemaker, juveniles
will tend to continue to engage in deviant behavior that violates
criminal statutes. This statement is descriptive of labeling
theory.

9. - Implicit in theory are statements that we refer to as
hypotheses. A hypothesis is a tentative statement about
empirical reality involving two or more variables. Those
variables are referred to as independent and dependent
variables. We say that the Independent Variable
(IV)INFLUENCES the Dependent Variable (DV). The IV
occurs prior to the DV in time. Throughout this statistics
course we will typically refer to the IV as “X” and the DV as
“Y”. We will frequently be attempting to explain the influence
of X on Y.
VALIDITY
Validity is concerned with the question; does an indicator really
measure what it is intended to measure?
- For example, if we are attempting to measure a concept
such as “political orientation” what indicator best captures the
total meaning of the concept, political party ID, race/ethnicity,
age, sex, union status. There are a variety of justifications that
any of these variables can be used to predict, to some degree,
one’s political orientation. But, which one is most valid? I
don’t really know. Maybe for this concept it is better to use
multiple indicators because there is no single indicator that
adequately enables us to explain any given individual’s or
group’s political orientation.
- One way to help us understand if an indicator is valid is
to consider the indicator’s face validity. Does the indicator as
it appears seem to be related to the concept in question?
RELIABILITY
Reliability is concerned with the question, will a measure
produce the same results when used repeatedly.
- This concern is especially true of surveys. Can we trust
the answers people give to us on questions such as: what is
your income? Or how many miles have you driven in the past
year? Or what grade did you make on your last exam? One way
that researchers deal with this problem is to provide individuals
with categories that represent ranges: a series of income ranges
to choose among; a series of mile ranges to choose among; or a

10. series of test score ranges to choose among.
Example from the textbook: The difference between reliability
and validity can be seen most clearly in reference to a simply
bathroom scale. If you step on a scale repeatedly (scales do not
remember) and it gives you a different weight each time, the
scale has a reliability problem.
Conversely, if the scale tells you that you weight 125 pounds
every time you step on it, it is pretty reliable, but if you
actually weight 225 pounds, the scale has a problem in the
validity department: It does not indicate your weight accurately.
Hypothesis = a specified expectation about empirical reality,
derived from propositions. Ex: working-class youths have
higher delinquent rates than upper-class youths.