Chapter 1 Spring 13

Why Analyze Data? Statistical analysis is about discovery Scientific inquiry: examining things that interest us in a systematic manner Requires evidence to support an argument Examine numbers associated with objects being studied

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

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

Reasoning Deductive 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

Induction: Find social phenomena and develop statements about why they work Deduction: Set out to develop statements and test them

Primary Questions Driving thought behind a research project Should represent the whole reason for the study How well researcher meets goals of the primary question will be criteria by which research is evaluated Should state the focus of the study

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

Conceptualization and Operationalization 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

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 Gender: Male and Female Dependent Variable: Presumed effect the IV has If X occurs, then Y Categorical vs Continuous

IV: Instructional Methods DV: Grades 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

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.

The Experiment Type of research where the researcher manipulates one (or more) of the independent variables Two types: True Experiment Quasi Experiment

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

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

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

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

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

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

Levels of Measurement Nominal Ordinal Interval Ratio

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 Mutually Exclusive

Mutually Exclusive and Exhaustive Type of Crime Sex Person Property Drug 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.

Rank of Professor Do you support capital punishment? Distinguished professor Full professor Associate professor Assistant professor Instructor Lecturer Teaching assistant Strongly agree Agree No opinion Disagree Strongly disagree

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

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

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

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

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 Description, Decision making, or Correlation

Description Final Exam Grades Allows for overall tendencies or group characteristics to be easily observed and easily communicated Graphs are commonly used Final Exam Grades 98 44 62 87 89 76 92 86 72 80 84 75

Midterm Grades F (frequency) 90-100 2 80-89 5 70-79 3 60-69 1 < 59

Anscombe’s quartet Property 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 1973. Purpose is to demonstrate the importance of graphing data and the effect of outliers

Anscombe's quartet I II III IV x y 10.0 8.04 9.14 7.46 8.0 6.58 6.95 8.14 6.77 5.76 13.0 7.58 8.74 12.74 7.71 9.0 8.81 8.77 7.11 8.84 11.0 8.33 9.26 7.81 8.47 14.0 9.96 8.10 7.04 6.0 7.24 6.13 6.08 5.25 4.0 4.26 3.10 5.39 19.0 12.50 12.0 10.84 9.13 8.15 5.56 7.0 4.82 7.26 6.42 7.91 5.0 5.68 4.74 5.73 6.89

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.

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