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### Chapter 1

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

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

- Research Hypothesis (H1)

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

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

The Experiment

- Type of research where the researcher manipulates one (or more) of the independent variables
- Three types:
- True Experiment
- Quasi Experiment
- Non Experiment

The Survey

- Retrospective research
- Effects of the IV on the DV are recorded later

- Includes questionnaires and interviews

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

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.

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

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

- Allows for overall tendencies or group characteristics to be easily observed and easily communicated
- Graphs are commonly used

Final Exam Grades

Anscombe's quartet

Anscombe’s quartet

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

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