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CJ StatisticsJanuary 30th, 2012

Chapter 1

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We study statistics because…1. Data are everywhere,

2. statistical techniques are used to make many decisions that affect our lives, and

3. no matter what your career, you will make professional decisions that involve data.

-Understanding statistical methods will help you make these decisions more effectively-Furthers develop critical thinking and analytical skills and act as an informed customer

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What is theory??

• A statement about relationships among social phenomena

• Goal is to develop explanations of:– Why things are as they appear– Their meaning

• Driven by observation and reason

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ReasoningDeductive Reasoning Inductive Reasoning

-Moves from theory to data (general to specific)-Data tests theory-“Why something happens” -> “Whether it actually does”

-Moves from data to theory (specific to general)-Makes sense of data through theory-“Why something happens” <- “Whether it actually does”-Grounded theory

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The Hypothesis

• A testable statement of a predicted relationship or difference among selected variables.

• Two forms– Research Hypothesis (H1)

• States the expected outcome

– Null Hypothesis (Ho)• States there is no statistically significant difference between

comparison groups and the general population• Differences due to random error• Only used for statistical purposes

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Conceptualization and Operationalization

• Conceptualization– Specifying precisely what is meant when a

particular term is used– Derives concepts from research questions• Concepts represent a characteristic, phenomena, or

group of interrelated phenomena

• Operationalization– The process of developing operational definitions– Indicting the value/measure

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The Variables

• Variables are factors that influence something else• Within the hypothesis is the independent and

dependent variable• Independent Variable– Presumed cause– Must precede the dependent variable (time order)– May have multiple levels of the IV

• Dependent Variable: Presumed effect the IV has• If X occurs, then Y

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• A teacher is doing a study of Instructional Methods and corresponding grades.– One class was taught only with lecture and no visuals– Another class was taught using the book and worksheets– A third class was taught only using PowerPoint

• In this example there is only one independent variable – Instructional Methods; but there are three levels of that variable. – IV: Instructional Methods– DV: Grades

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Original Hypothesis Independent Variable

Dependent Variable

If-then statement

Females use seatbelts more than males.

Gender Seatbelt usage

If the individual is a female, then she is more likely to use a seatbelt.

One parent households generates higher rates of delinquency.

Family structure Delinquency If the household has only one parent, then the rate of delinquency is higher.

As unemployment increases in the United States, larceny-theft increases.

Unemployment Rate of larceny-theft

If unemployment is higher, then the rate of theft is higher.

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The Experiment

• Type of research where the researcher manipulates one (or more) of the independent variables

• Experimental Group – Group that is manipulated• Control Group – Group that is not manipulated• Requires randomization of both groups

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The Quasi-Experiment

• Due to ethical and practical reasons, quasi-experiments are used much more often

• Lacks a control group• May compare the experimental group with a

comparison group who are matched base on their characteristics in respect to the experimental group

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The Survey

• Retrospective research– Effects of the IV on the DV are recorded later

• Includes questionnaires and interviewsBenefits Limitations

Cost effective Lack of tight control

Ability to generalize / more representative

Cause and effect

Investigate numerous IVs at once

Time order

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Content Analysis• Describes the content of previously produced messages• May include books, magazines, newspapers, films, music, etc• Benefits:

– May be the only method available– Broad range of “texts”– Access to deeper contextualized meanings

• Limitations:– Time consuming– Tedious– Interpretation– Small sample size

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Secondary Analysis

• Research using data collected by another researcher

• Cost effective• Limited to what the original researcher

examined• No control over what was asked, how, or why

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Data Sources in Criminal Justice

• Universal Crime Report (UCR)• National Crime Victimization Survey (NCVS)• National Incident Based Reporting System

(NIBRS)

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Five Steps of Research

1. The problem must be reduced to a testable hypothesis

2. Develop measures and instrumentation3. Collect data4. Analyze data5. Results of the analysis are interpreted and

communicated whether supported or not

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Quiz Time: Identify the IV and DV• A study examining the impact of drug usage upon crime.

• Students who are able to distinguish between the IV and DV will score higher on their exam than students who cannot distinguish between the two variables.

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Quiz Time: Identify the IV and DV

• A researcher wanted to identify how to increase response rates to surveys and was curious if a monetary incentive would influence response rates. Half the respondents were included in a raffle for $100 while the others were not offered any incentive.

• A student who studies more on an exam will earn a better grade.

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Levels of Measurement • Problems in data analysis must be confronted in the

planning stages of a research project, because they have a bearing on the nature of decisions at all other stages

• Levels of measurement dictate which statistical procedures we may rightfully employ in our analyses

• The mathematical precision with which the values of a variable can be expressed is the level of measurement

• Measurement – assigning a characteristic to a series of numbers according to a set of rules

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Levels of Measurement

• Nominal• Ordinal• Interval• Ratio

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Nominal Measure• The nominal level of measurement classifies or

categorizes variables whose values have no mathematical interpretation and counting the frequency of occurrence

• Data cannot be ranked or scaled for comparison• Examples: Gender, ethnicity, country of origin• Mutually Exhaustive– All possible measures must be included in the attributes

• Mutually Exclusive– Can only be identified by one attribute– No overlap between attributes/categories

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Mutually Exclusive and ExhaustiveAnnual Income ReligionLess than $5,000$5,000 - $10,000$10,001 - $20,000$20,001 - $50,000$50,001 - $100,000$100,000+

CatholicJewishMuslimProtestantNoneOther

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Ordinal Measures

• Only the order of the cases is specified in “greater than” and “less than” directions

• Scores cannot be assigned• May be expressed as a range• Prisons may operate using minimum, medium or

maximum security. Maximum security is greater than medium security, but there is no mathematical measure of exactly how much greater.

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Rank of Professor Do you support capital punishment? Distinguished professor Full professor Associate professor Assistant professor Instructor Lecturer Teaching assistant

1. Strongly agree2. Agree3. No opinion4. Disagree5. Strongly disagree

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Interval Measures

• Numbers represent fixed measurement units but lack an absolute zero point

• Zero point on an interval scale is arbitrary and negative scores can be used

• Examples:– Fahrenheit / Celsius– IQ– Prison terms

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Ratio Measures• Based on an absolute zero• Ratios can be formed between the numbers• Ratios can be added and subtracted as they begin at an

absolute zero point as well multiplied and divided• Note: For all practical purposes, interval and ratio data are

treated the same statistically

• Examples:– Kelvin– Age– Exam score

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Ordinal Data as Interval

• Levels of measurement vary in their degree of sophistication

• Ordinal data may be treated as interval when ordered categories have roughly equal intervals

• Allows for more powerful statistical procedures

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Which may be considered as interval?Scale Value Rank of Professor Attitude toward Professor

1 Distinguished professor Very favorable

2 Full professor Favorable

3 Associate professor Somewhat favorable

4 Assistant professor Neutral

5 Instructor Somewhat unfavorable

6 Lecturer Unfavorable

7 Teaching assistant Very unfavorable

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Function of Statistics

• When researchers quantify their data at the nominal, ordinal, or interval/ratio level of measurement, statistics is used as a tool of eitherI. Description, II. Decision making, orIII. Correlation

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Description

• Allows for overall tendencies or group characteristics to be easily observed and easily communicated

• Graphs are commonly used

98 44 6287 89 7692 86 7280 84 75

Final Exam Grades

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Midterm Grades F (frequency)

90-100 2

80-89 5

70-79 3

60-69 1

< 59 1

< 59 60-69 70-79 80-89 90-1000

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6Final Exam Grades

# of Students

Anscombe's quartet I II III IV

x y x y x y x y

10.0 8.04 10.0 9.14 10.0 7.46 8.0 6.58

8.0 6.95 8.0 8.14 8.0 6.77 8.0 5.76

13.0 7.58 13.0 8.74 13.0 12.74 8.0 7.71

9.0 8.81 9.0 8.77 9.0 7.11 8.0 8.84

11.0 8.33 11.0 9.26 11.0 7.81 8.0 8.47

14.0 9.96 14.0 8.10 14.0 8.84 8.0 7.04

6.0 7.24 6.0 6.13 6.0 6.08 8.0 5.25

4.0 4.26 4.0 3.10 4.0 5.39 19.0 12.50

12.0 10.84 12.0 9.13 12.0 8.15 8.0 5.56

7.0 4.82 7.0 7.26 7.0 6.42 8.0 7.91

5.0 5.68 5.0 4.74 5.0 5.73 8.0 6.89

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Anscombe’s quartetProperty Value

Mean of x 9

Variance of x 11

Mean of y 7.5

Variance of y 4.122

Correlation between x and y 0.816

Linear regression Y = 3.00 + 0.5x

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Decision Making

• Almost always, it is necessary to go beyond mere description.

• Allows researchers to draw inferences from the sample to the population

• Allows for generalizing• Statistics is a set of decision-making techniques

that aid researchers in drawing inferences from samples to populations and, hence, in testing hypotheses regarding the nature of social reality.

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Correlation• Describes the relationship between two more variables• Correlation does not lead to causation