1. Chapter 1 Spring 13

2. 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

3. 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

4. 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

5. 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

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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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.

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

14. 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

15. 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

16. 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

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

18. 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

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
Mutually Exclusive

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

23. 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 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

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

29. 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

30. 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

31. 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

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

33. 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 = x
1973. Purpose is to demonstrate the importance of graphing data and the effect of outliers

35. 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

36. 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