+1443 776-2705 panelessays@gmail.com


Graphs represent data in an engaging manner and make comparisons and analyses easier. For example, a graph depicting the number of crimes committed each year over a decade is easier to comprehend visually than reading the numerical values for each year. Before creating a graph, however, it is important to choose one that appropriately represents the data. A histogram, rather than a pie chart, is appropriate for depicting the age groups (e.g., 15–24, 25–34) of murder victims in a city. Histograms are designed to be used with variables that are categorized, but pie charts plot each value. Therefore, it would be easier to read a histogram showing bars for age groups of murder victims than a pie chart in which every single age would have to be plotted. In the past, creating graphs was cumbersome and time consuming, but present-day software programs such as Microsoft Word and Excel provide tutorials that walk you through the process. With knowledge of these software programs, you can create customized charts and figures to represent your research data in visually interesting ways. In this Assignment, you create at least two different graphs in Excel or Word that can be used to illustrate hypothetical data related to six incidents of crime.

· Create at least two different graphs in Excel or Word using the data provided in the table below:      


Type of Crime

Offender’s Age

Offender’s Gender

Time of the Incident





Early morning


Possession of drugs



Late evening





Late evening







Possession of drugs





Possession of drugs



Early morning

· Briefly describe the data represented in the graphs and/or charts you created.

· Explain why the graphs and/or charts you created best represent the data compared to other options. Be specific.

Submit the graphs you created in a document that is separate from your written Assignment.

Bachman, R. D., & Schutt, R. K. (2019). The practice of research in criminology and criminal justice (7th ed.). Thousand Oaks, CA: SAGE Publications.

· Chapter 4, “Conceptualization and Measurement” (pp. 86–116)

The Practice of Research in Criminology and Criminal Justice, 7th Edition by Bachman, R. D. & Schutt, R. K. Copyright 2019 by SAGE Publications, Inc. Reprinted by permission of SAGE Publications, Inc via the Copyright Clearance Center.

Bachman, R. D., & Schutt, R. K. (2019). The practice of research in criminology and criminal justice (7th ed.). Thousand Oaks, CA: SAGE Publications.

· Chapter 14, “Analyzing Quantitative Data” (pp. 404–415 and 426–444)

The Practice of Research in Criminology and Criminal Justice, 7th Edition by Bachman, R. D. & Schutt, R. K. Copyright 2019 by SAGE Publications, Inc. Reprinted by permission of SAGE Publications, Inc via the Copyright Clearance Center.

Trochim, W. M. K. (2006). Levels of measurement. In Research methods knowledge base. Retrieved from http://www.socialresearchmethods.net/kb/measlevl.php

Walden University: Academic Skill Center. (n.d.). ASC software assistance: Microsoft Excel. Retrieved March 15, 2019, from https://academicguides.waldenu.edu/ASCsoftware/msoffice/excel

Microsoft Office Online. (n.d.). Excel help center. Retrieved March 30, 2019, from https://support.office.com/en-us/excel

Navigate to the tables and charts section of this page to access the applicably level of training you may need for creating charts and graphs in Excel.

Lynda.com. (2019). Excel: Introduction to charts and graphs. Retrieved from https://www.lynda.com/Excel-tutorials/Excel-Introduction-Charts-Graphs/802837-2.html

Lynda.com. (2018). Excel 2019 essential training. Retrieved from https://www.lynda.com/Excel-tutorials/Excel-2019-Essential-Training/728368-2.html

Lynda.com. (2016). Excel 2016 essential training with Dennis Taylor. Retrieved from https://www.lynda.com/Excel-tutorials/Excel-2016-Essential-Training/376985-2.html

,i." Define a

My research methods class has already helped me. I am taking a human development class and u)e are writing annotations and a syn- thesis for three different studies and it's so easy to understand all the studies and data posted from SPSSI I'm euenhelping out a few class- mates so they can include information in their annotations that thE didn' t understand b efor e,

Emma T., Stu dent

a ubstance abuse is a social problem of remarkable proportions. About 18 , million Americans have an alcohol use disorder (Grant et aL.2004; Hasin, Stinson, Ogburn, and Grant 2007 ; National Instirute on Ncohol Abuse and AIco- holism hTIAAAI 2018), and about 80,000 die every year from alcohol-related causes O{IAAA 2018). While in college, four out of ten students binge drink ftVechsler et aL.2002), and about one out of three could be diagnosed as alcohol abusers (Knight et aL. 2002). Drinking is a factor in almost half of on-campus sexual assaults (Sinozich and Langton20L+), and almost one in four victims of violence in the general population perceive their attackers to have been under the influence of drugs and/or alcohol. And finally, almost half of jail inmates report having alcohol dependence or abuse problems (Karberg and James 2005). Nl told, the annual costs of prevention and treatrment for alcohol and drug abuse exceed $340 billion in the United States (Miller and Hendrie 2008). Across the globe, alcohol misuse results in about}.5 million deaths annually OVorld Health Organi zatton [WHO) 201 3 ).

Within all of these facts, we have presented several concepts, including alcobol, college students, and ahohol dependence. While we all have our own ideas about what these concepts mean, do we all have the same idea in mind when we hear these terms? For exampl q are community colleges classified within the term college? How is alcohol abuse drfferent from dependence?

Whether your goal is to examine the factors related to criminal offending, to deliver useful services, or to design effective social policies, at some point, you will probably need to read the research literature on substance abuse. Every time you begin to review or design relevant research, you will have to answer two questions: The first concerns concepnaLization: "What is meant by sub- stance abuse in this research? " The second concerns measurement: "FIow was substance abuse measured?" Both questions must be answered to evaluate the validity of substance abuse research. You cannot make sense of the results of a study until you know how the concepts were defined and measured. Nor are you


ready to begin a research project until you have defined your concepts and constructed valid measures of them. Measurement validity is essential to successful research; in fact, without valid measures, it is fruitless to attempt to achieve the other two aspects of validity: causal validity (see Chapter 6) and generalizabtliry (see Chapter 5).

In this chapter, we first address the issue of concep- anlization, using substance abuse and related concepts as examples. We also provide examples of the conceptualtza- tion process for other terms such as street gangs and inmnte miscondua.We then focus on measurement, reviewing first how measures of substance abuse have been constructed using available data (i.e., arrest data), questions on surveys, observa- tions, and less direct and unobtrusive measures. Then we explain how to assess the validity and reliability of these measures. The final topic is the level of measurement reflected in dif- ferent measures. By chapter's end, you should have a good understanding of measurement, the first of the three legs on which a research project's validity rests.


Every concept requires an explicit definition before it is used in research, because we cannot otherwise be certain tllat all readers will share the same definition. It is even more important to define concepts that are somewhat abstract or unfamiliar. When we refer to concepts such as ploerty, social control, or strain, we cannot be certain that others know exacdy what we mean.

Many high school and college students have become familiar with the term binge drink- ingbutyou may be surprised to learn t-hat even researchers do not agree on how to measure it. The definition that Henry Wechsler et al. (2002) used is "heavy episodic drinking"; more specifically, "we defined binge drinking as the consumption of at least 5 drinks in a row for men or 4 drinks in a row for women during the 2 weeks before completion of the question- naire" (205). While this definition is widely accepted among social researchers, the NIAAA (College Alcohol Study 2008) provides a more precise definition: 'A pattern of drinking alco- hol that brings blood alcohol concentration to 0.08 grams percent or above." Most research- ers consider the so-called 5/4 definition (5 drinls for men, 4 for women) to be a reasonable approximation to this more precise definition. We cant say either of these definitions is cor- rect or even that one is better. IIowever, ifwe were to conduct research on the topic ofbinge drinking, we would need to specifi, what we mean when we use the term and be sure that others know that definition. And ofcourse, the definition has to be useful for our purposes: A definition based solely on blood alcohol concentration will not be usefirl if we are not taking blood measures.

We call binge drinking a concept-a mental image that summarizes a set of similar observations, feelings, or ideas. To make that concept usefirl in research (and even in ordinary discourse), we have to define it. Many concepts are used in weryday discourse without consis- tent definition; sometimes definitions of concepts are themselves the object of intense debate, and the meanings of concepts may change over time.

Conceptualization in Practice If we are to do an adequate job of conceptualization, we must do more than think up some definition-any definition-for our concepts. We may need to distinguish subconcepts (diruensions) of the concept. We also should ask how the concept's definition fits within the theoretical framework g"rding the research and what assumptions underlie this framework.


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DefiningYouth Gangs Do you have a clear image in mind when you hear rhe term youth gangs? Nthorgh this is a very ordinary term, social scientists' attempts to define precisely the concept,yoath gang, have not yet succeeded: "Neither gang researchers nor law enforcement agencies can agree onacoillmondefinition…andaconcertednationaleffort…failedtoreachaconsensus" (Ilowell 2003,7 5). Exhibit 4.1 lists a few of the many alternative definitions of youth gangs.

What is the basis of this conceptual difficulty? Howell Q003,27-28) suggests that defin- ing the tennylath gangshas been difficult for four reasons:

Youth gangs are not particularly cohesive.

Individual gangs change their focus over time.

Many have a "hodgepodge of features," with diverse members and unclear rules.

There are many incorrect but popular myths about yourh gangs.

In addition, youth gangs are only one type of social group, and it is important to define youth gangs in a way that distinguishes them from other types of groups (childhood play groups, youth subculture groups, delinquent groups, and adult criminal organizations). You can think of so cial group as a broader concept that has multiple dimensions, one of which may be a youth gang. In the same rvay, you can think of sabstance abuse as a concept with three dimensions: alcohol abuse, drug abuse, and polysubstance abuse. Whenever you define a







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concept, you need to consider whether the concept is unidimensional or multidimensional. If it is multidimensional, your job of conceptualization is not complete until you have specified the related subconcepts that belong under the umbrella of the larger concept. And finally, the conceptyou define must capture an idea that is distinctly separate from related ideas.


Defi ning Substance Abuse

What observations or images should we associate with the concept substance abwe? Some- one leaning against a building with a liquor bottle, barely able to speak coherendy? College students drinking heavily at a parLy and passing out? Someone in an Alcoholics Anonymous group drinking one beer? A 12-year-old boy drinking a small glass of wine in an alley? A t2-yearold boy drinking a small glass of wine at the dinner table in France? Do all these images have something in common that we should use as a definition of substance abuse for the purposes of a particular research study? Do some of them? Should we take into account cultural differences? Social situations? Physical tolerance for alcohol? Individual standards?

MarD, researchers now use the definition of sabstance abuse contairted in the American Psy- chiatric Association's Q000) Diagnostic and. Statistical Manual of Mmtal Disorderc, Text RnNun (DSM-IV-TR): "a maladaptive pattern of substance use manifested by recurrent and significant adverse consequences related to the repeated use ofsubstances . . . musthave occurred repeatedly during the same l2-month period or been persistenr" (DSM-IV-T& Subsance Abuse Features section, 198). But, despite its popularity among professionals, we cannot judge the DSM-IV-TR definition ofsubstance abuse as correct or incorrect. Each researcher has the right to conceptual- ize as he or she sees fit. Howeve! we can say that the DSM-I2-TR definition of substance abuse is useftrl, pardy because it has been widely adopted. It is also stated in a clear and precise language that minimizes differences in interpretation and maximizes understanding.

One caution is in order. The definition of any one concept rests on a shared understanding of the terms used in the definition. So, if our audience does not already have a shared understanding of terms such as adeqaate socialfunctioning,self-carefunctioning,xtdrEeatedwe,we must also define these terms before we are finished with the process of defining substance abuse.


Defining Poverty

Poverty is a very important variable in criminological research because of its relationship with many forms of offending and victimizaion,both at the aggregate level (i.e., city or state) and at the individual level. Decisions about how to define the concept of poaerty has always been somewhat controversial, however, because different notions of whai porrirty is shape estimates of how prevalent it is and what can be done about it.

Most of the statistics that you see in the newspaper about the poverty rate reflect a concep- tion of poverty that was formalized by Mollie Orshansky of the Social Security Administration in 1965 and subsequendy adopted by the federal government and many researchers @utram 1977). She defined poverty as an absolute standard, based on the amount of money required to purchase an emergency diet that is estimated to be nutritionally adequate for about two months. The idea is that people are truly poor if they can barely purchase the food they need and other essential goods.This poverty sandard is adjusted for household size and composition (number of children and adults), and the minimal amount needed for food is multiplied by three, because a 1 95 5 survey indicated that poor famiJies spend about one third of their incomes on food (Orshans$ 1977).


Does this sound straightforward? As is often the case with important concepts, the meaning of an absolute poverty standard has been the focus of a vigorous debate (Eckholm 2006). Although the traditional definition of absolute poverty accounts only for a family's cash income, some arg'ue that noncash benefits that low-income people can receive, such as food stamps, housing subsidies, and tax rebates, should be added to cash income before the level of poverty is calculated. Douglas Besharov of the American Enterprise Institute terms this approach "a much needed corrective" @ckholm 2006, A8). But some social scientists have proposed increasing the absolute standard for poverty so that it reflec* what a low-income family must spend to maintain a "socially acceptable sandard of living" that allows for a tele- phone, house repairs, and decent clothes (LJchitelle 1999). A new "multidimensional poverty index" (MPI) to aid international comparisons considers absolute deprivations in health, edu- cation, and living standards (Alkire, Roche, Santos, and Seth 2011). Others argue that the per- sistence of poverty should be considered, so someone who is poor for no more than ayea4for example, is distinguished from someone who is poor for manyyears @alker,Tomlinson, and Williams 2010). Any change in the definition of poverty will change eligibility for govern- ment benefits such as food stamps and Medicaid, so the feelings about this concept run deep.

Some social scientists disagree altogether with the absolute sandard and have instead urged adoption of a relatiae poverty standard (see Exhibit 4.2).They identify the poor as those in the lowest fifth or tenth of the income distribution or as those having some fraction of the average income. The idea behind this relative conception is that poverty should be defined in terms of what is normal in a given society at a particular time. "For example, while a car may be a luxury in some poor countries, in a county where most families own cars and public transportation is inadequate, a car is a basic necessity for finding and commuting to work" (Mayrl et al. 2004, 10).

Some social scientists prefer yet another conception of poverty. With the sabjeafue approach, pooerty is defined as what people think would be the minimal income they need to make ends meet. Of course, many have argued that this approach is influenced too much by the different standards that people use to estimate what they "need" (Ruggles 1990). There is a parallel debate about the concept of subjectioe utell-being,which is now measured annually with responses (on a l0-point scale) to four questions in the United Kingdom by its Office of National Statistics (Venkatapuram 2013).The four questions are (Venkatapuram 2013,9):

Overall, how satisfied are you with your life nowadays?

Overall, to what extent do you feel the things you do in your life are worthwhile?

Overall, how hrppy did you feel yesterday?

Overall, how anxious did you feel yesterday?

Which do you think is the most reasonable approach to defining poverty: some type of absolute standard, a relative standard, or a subjective standard? Be careful here: Conceptualization has consequencesl Research using the standard absolute concept ofpoverty indicated that the percentage ofAmericans in poverty declined by 1.7% in the 1990s, but use of a relative concept of poverty led to the conclusion that poverty increased by 2.7% (Mry.l et aL.2004). No matter which conceptuakzaton we decide to adopt, our understanding of the concept ofpoverty will be sharpened after we consider these alternative definitions.

From Concepts to Variables: Measurement Operations

After defining the concepts for a study, we can identifi,variables corresponding to the concepts and develop procedures to measure them. Recall that a variable is a characteristic or property that can vary (e.g., religion, alcohol use, victimization). This is an imporunt step. Consider the concept of social control, which Black (1984) defines as all of the processes by which people







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define and respond to deviant behavior. What variables do you think represent this conceptu- alization of social control? Proportion of persons amested in a community? Average length of sentences for crimes? Types of bystander reactions to public intoxication? Some combination of these?

Although we must proceed carefrrlly to speci!, what we mean by a concept such ts social control, some concepts are represented well by the specific variables in the study and need not be defined so carefully. We may define binge drinking as heary episodic drinking and measure it, as a variable, by asking people how many drinl,m they consumed in succession during one drinking episode (see Wechsleq Davenport, Dowdall, Moeykens, and Castillo 1994). That is pretty straightforward.

As we will see, some concepts are not so easy to measure, however. The goal is to devise mea- srrement procedures that actually measure the concepts we intend to measure-in other words, to achieve rileasaren ent oalidity. The operationalization process specifies the operations that will indicate the value ofa variable for each case. Exhibit 4.3 represens the operationalization


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Exhibit 4.2 Absolute, Relative, and Subjective Povertlr Standards

Binge drinking

Soc i.al,: cl,aS:s

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"How often within the past two weeks did you consume,flve or more drinks containing alcohol in a row?"

lncome + education + prestige

process in three studies. Researchers must provide anoperational definition, which includes what is measured, how it was measured, and the rules used to assign a value to what is observed and to interpret the value. For example, one researcher defines her concept (binge drinking) and chooses one variable (frequency ofheavy episodic drinking) to represent it. This variable is then measured with responses to a single question (or inditanr): "fIow often within the past two weela did you consume five or more drinks containing alcohol in a row?" Another researcher defines her concept(pwerty) as having two aspects or dimensions, subjective poverty and absolute poverty. Subjective poverty is measured with responses to a survey question: "Would you say you are poor?" Absolute poverty is measured by comparing family income to the poverty tlreshold. A third researcher decides that her concept (ncial class) can be indicated with three measured variables: income, education, and occupational prestige. The values of these three variables for each case studied are then combined into a singleindicator.

Good conceptualization and operationalization can prevent confusion later in the research process. For example, a researcher may find that substance abusers who join a self-help group are less likely to drink again than those who receive hospial-based substance abuse treaunent. But what is it about these treatrnent alternatives that is associated with successful abstinence? Level of peer support? Beliefs about the causes of alcoholism? Financial investrnent in the treatrnent? If the researcher had considered such aspecrc of the concept of subsance abuse ueaunent before collecting her data, she might have been able to measure different elements of treatrnent and then identify which, if any, were associated with differences in abstinence rates. Because she did not measure these variables, she will not contribute as much as she might have to our understanding of substance abuse treatrnent.

Social researchers have many options for operationrkzing their concepts. Measures can be based on activities as diverse as asking people questions, reading judicial opinions, observ- ing social interactions, coding words in books, checking census data, enumerating the contents of trash receptacles, or drawing urine and blood samples. We focus here on the operations of using published data, asking questions, observing behavior, and using unobtrusive means of measuring people's behavior and attitudes.

Using Available Data

Government reports are rich and readily accessible sources of criminal justice data, as are datasets available from nonprofit advocacy groups, university researchers, and some private businesses. For example, law enforcement and health satistics provide several community-level indicators of substance abuse (Gruenewald,Ti'eno,Thff, and l{Lruner 1997). Statistics on arrests for the sale and possession of drugs, drunk driving affests, and liquor


Exhibit 4.3 Goncepts, Variables, and Indicators

law violations (such as sales to minors) can usually be obtained on an annual basis (and often quarterly) from local police departrnents or state crime information centers.

Still, indicators such as these cannot be compared across communities or over time without a carefrrl review of how they were constructed in each community. The level of alcohol in the blood that is legally required to establish intoxication c:m vary among communities, creating the appearance ofdifferent rates ofsubsance abuse even though drinking and driving practices may be identical. Enforcement practices cxm vary among police jurisdictions and over time (Gruenewald et d,. 1997). We also crrnnot assume that available daa are accurate, even when they appear to measure the concept in which we are interested in a way that is consistent across communities. "Official" counts of homeless persons have been notoriously unreliable because of the difficulty of locating homeless persons on the strees, and government agencies have, at times, resorted to "guesstimates" by service providers @ossi 1989). Even available data for zuch seemingly straighdorward measures as cause of death can contain a surprising amount of error. For enample, between 30o/" and 40o/" of death certificates incorrecdy identifi, the cause of death (Altrnan 1 998).

Government statistics that are generated through a central agency such as the U.S. Bureau of the Census are often of high quality, but caution is warranted when using ofE- cial data collected by local levels of government. For example, the Uniform Crime Reports (tlCR) program administered by the Federal Bureau of Investigation @BI) imposes standard classification criteria, with explicit guidelines and regular training at the local level, but data are still inconsistent for many crimes. Consider only a few of the many sources of inconsis- tency between jurisdictions: variation in the classification of forcible rape cases due to differ- ences in what is considered to be "carnal lnowledge of a female"; different decisions about what is considered "more than necessary force" in the definition of strong-arm robberies; and, whether offenses in which threats were made but no physical injury occurred are classified as aggraaated. or siruple assaults (Mosher, Miethe, and Phillips 2002). A new National Inci- dent-Based Reporting System GIIBRS) corrects some of the problems with the UCR, but it requires much more raining and documentation and has not yet been widely used (Mosher et aL.2002). Moreover, as we learned in Chapter 1, both of these systems rely on victims to report their experiences to police in order to be counted.

In some cases, problems with an available indicator can be lessened by selecting a more precise indicator. For example, the number of single-vehicle nighttime crashes, whether fatal or not, is a more specific indicator of the frequency of drinking and driving than the number of single-vehiele fatal accidents alone (Gruenewald et al. 1997). Focusing on a different level of aggegation may also improve data quality, because procedures for data collection may dif- fer among cities, counties, states, and so on (Gruenewald eta,l. 1997).It is only after such fac- tors as legal standards, enforcement practices, and measurement procedures have been aken into account that comparisons among communities become credible,

Gonstructing Questions Asking people questions is the most common and probably the most versatile operation for measuring social variables. Most concepts about individuals can be defined in such a way that measurement with one or more questions becomes an option. In this section, we introduce some options for writing single questions; in Chapter 8, we explain why single questions can be inadequate measures of some concepts and then we examine approaches that rely on mul- tiple questions to measure a concept.

Measuring variables with single questions is very popular. Public opinion polls based on answers to single questions are reported frequendy in newspaper articles and TV newscasts: "Do you favor or oppose U.S. policy in . . . ?" "If you had to vote today, for which candidate would you vote?" Criminal justice surveys also rely on single questions to measure many vari- ables: "Overall, how satisfied are you with the police in your community?" "flow would you rate your current level ofsafety?"


CIosed-ended (fixed-choice)


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Single questions can be designed with or without explicit response choices. The question that follows is a closed-ended (fixed-choice) question, because respondents are offered explicit responses to choose from. It has been selected from the Core Alcohol and Drug Survey distributed by the Core Institute (1994) at Southern Illinois University for the Fund for the Improvement of Postsecondary Education (FIPSE) Core Analysis Grantee Group @resley, Meilman, and Lyerla 1994).

Compared to other campuses with which you are familiar, this campus's use of alcohol is…(Markone)

Greater than [that of] other campuses

Less than [that ofl other campuses


the same as [that of] other campuses

Response choices should be mutually exclusive and exhaustive, so every respondent can find one and only one choice that applies to him or her (unless the question includes a check all tbat apply option). To make response choices exhaustive, researchers may need to offer at least one option with room for ambiguity. For example, a questionnaire asking college students to indicate their school status shorld,notwefreshman,sophomore,junior,smior,and graduate smdmt as the only response choices. Most campuses also have students in a "special" category so you might add otber (please specify) to the five 6xed responses to this question. If respondents do not find a response option that corresponds to their answer to the question, they may skip the ques- tion entirely or choose a response option that does not indicate what they are really thinking.

Most zuwqzs of a large number of people contain primarily fixed-choice questions, which are easy to process with computers aind analyze with satistics. With fixed-choice questions, respondenm are also more Iikely to answer the question that the researcher really wants them to answer krcluding response choices reduces ambiguity and makes it easier for respondents to answer. Howwer, fixed-response choices can obscure what people really think if the choices do not match the range of possible responses to the question; many studies shorr that some reqpondents will choose response choices that do notapplyto them simplyto give some sortofanswer @eterson 2000). We will discuss question wording and response options in greater detail in Chapter 8.

Open-ended questions-namely, questions that have not previously been used in sur- veys, questions that are asked ofnew groups, and questions without explicit response choices, to which respondents write in their answers-are preferable vrhen the range of responses cannot adequately be anticipated. Open-ended questions can also lessen confusion about the meaning of responses involving complex concepts. The next question is an open-ended …


Identify the types of graphs and statistics that are appropriate for analysis of variables at each level of measurement.

I was fortunate enough to have an internship this summer at the Attorney General's office and work in their special crtmes untt, focus- ing on gang participatton, statistics 0n crtme, and preparing informa- tional booklets for the office,law enforcement, and the community. One of the main reasons I got this rnternship was because I took a research methods class and knew how to use SPSS to analyze and interpret data,

Ricky E., Stud,ent

"n h no, not dataanalysis and statistics!" We now hit the chapter thatyou r;, may have been fearing all along, the chapter on data analysis and the use of

statistics. This chapter describes what you need to do after your data have been collected. You noM need to analy ze what you have found, interpret it, and decide how to present your data so that you can most clearly make the points you wish to make.

What you probably dread about this chapter is something that you either sense or know from a previous course: Studying data analysis and statistics will lead you into that feared world of mathematics. We would like to state at the beginning, however, thatyou have relativelylittle to fear.The kind ofmathematics required to perform the data analysis tasks in this chapter is minimal. If you can add, subtract, multiply, and divide and are willing to pu