CJ Statistics January 30 th, 2012 Chapter 1 1

We study statistics because… 2 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

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 3

Reasoning Deductive ReasoningInductive 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 4

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The Hypothesis A testable statement of a predicted relationship or difference among selected variables. Two forms – Research Hypothesis (H 1 ) States the expected outcome – Null Hypothesis (H o ) States there is no statistically significant difference between comparison groups and the general population Differences due to random error Only used for statistical purposes 6

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 7

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 8

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 9

Original HypothesisIndependent Variable Dependent Variable If-then statement Females use seatbelts more than males. GenderSeatbelt 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 structureDelinquencyIf the household has only one parent, then the rate of delinquency is higher. As unemployment increases in the United States, larceny-theft increases. UnemploymentRate of larceny-theft If unemployment is higher, then the rate of theft is higher. 10

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 11

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 12

The Survey Retrospective research – Effects of the IV on the DV are recorded later Includes questionnaires and interviews BenefitsLimitations Cost effectiveLack of tight control Ability to generalize / more representative Cause and effect Investigate numerous IVs at once Time order 13

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 14

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 15

Data Sources in Criminal Justice Universal Crime Report (UCR) National Crime Victimization Survey (NCVS) National Incident Based Reporting System (NIBRS) 16

Five Steps of Research 1.The problem must be reduced to a testable hypothesis 2.Develop measures and instrumentation 3.Collect data 4.Analyze data 5.Results of the analysis are interpreted and communicated whether supported or not 17

Quiz Time: Identify the IV and DV A study examining the impact of drug usage upon crime. 18 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.

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. 19

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 20

Levels of Measurement Nominal Ordinal Interval Ratio 21

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 22

Mutually Exclusive and Exhaustive 23 Annual IncomeReligion  Less than $5,000  $5,000 - $10,000  $10,001 - $20,000  $20,001 - $50,000  $50,001 - $100,000  $100,000+  Catholic  Jewish  Muslim  Protestant  None  Other

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. 24

Rank of ProfessorDo you support capital punishment?  Distinguished professor  Full professor  Associate professor  Assistant professor  Instructor  Lecturer  Teaching assistant 1.Strongly agree 2.Agree 3.No opinion 4.Disagree 5.Strongly disagree 25

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 26

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 27

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 28

Which may be considered as interval? Scale ValueRank of ProfessorAttitude toward Professor 1Distinguished professorVery favorable 2Full professorFavorable 3Associate professorSomewhat favorable 4Assistant professorNeutral 5InstructorSomewhat unfavorable 6LecturerUnfavorable 7Teaching assistantVery unfavorable 29

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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 either I.Description, II.Decision making, or III.Correlation 31

Description Allows for overall tendencies or group characteristics to be easily observed and easily communicated Graphs are commonly used Final Exam Grades

33 Midterm GradesF (frequency) < 591

Anscombe's quartet IIIIIIIV xyxyxyxy

Anscombe’s quartet PropertyValue Mean of x9 Variance of x11 Mean of y7.5 Variance of y4.122 Correlation between x and y0.816 Linear regressionY = x 35

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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. 37

Correlation Describes the relationship between two more variables Correlation does not lead to causation 38