Justice Research and Statistics Association 720 7th Street, NW, Third Floor Washington, DC 20001

I. Introduction and Overview of Descriptive Statistics

Erin J. Farley Ph.D. &

Stan Orchowsky Ph.D.

Justice Research and Statistics Association 1/14/2016

Training and Technical Assistance Webinar Series

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Justice Research and Statistics Association 720 7th Street, NW, Third Floor Washington, DC 20001

Training and Technical Assistance Webinar Series

Justice Research and Statistics Association 720 7th Street, NW, Third Floor Washington, DC 20001

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Objectives

• Define key concepts in descriptive statistics

• Demonstrate how to run descriptive statistics in Excel and SPSS

Area of Interest, idea, or theory

Conceptualization Specify the meaning of the

concepts to be studied

Operationalization How will we actually

measure the variables under study?

Choice of Research Method

Experiments Survey Research Field Research

Content analysis Existing data research Comparative research Evaluation research

Population & Sampling

Whom do we want to be able to draw conclusions about? Who will be

observed for that purpose?

Observations Collecting data for analysis & interpretation

Analysis Analyzing data drawing conclusions

Application Reporting results & assessing their

implications

Maxfield & Babbie (2012) Basics of Research Methods

Descriptive and Inferential Statistics

• Summarize, organize, and make sense of a set of scores or observations

• Describe characteristics of a sample Descriptive

• Allows us to take measurements from a sample and to “infer”, or use this information to estimate the unknown characteristics of a larger population

Inferential

Data Types

•Measures •Methods

Quantitative

•Measures •Methods

Qualitative

Data Types

Variables: Any characteristic or attribute of persons,

objects, or events that can take on different

numerical values

Latent : Not observable & can only be measured

indirectly

Manifest : A variable that can be observed

Independent: Variable that is manipulated to determine

impact (x)

Dependent: Variable influenced by another(y)

Validity: Degree to which variable accurately reflects

the concept it is intended to measure

Reliability: Refers to the consistency or “repeatability” of

the operationalization of the concept

Collecting Quantitative Data

Unit of Analysis

• Objective for observation • Individuals • Towns • States

Measurement

• Process of assigning numbers to observations

• EX: • Likert-scale

Missing Data

• No meaningful information for a given observation

• ≠ 0 • -99

Levels of Measurement

Nominal • Qualitative, categorical variable

Ordinal • Quantitative, categorical variable • Rank-ordered categories

Interval • Quantitative, continuous variable • Distance between values is known and constant

Ratio

• Quantitative, continuous variable • Distance between values is known and equal w/ true zero pt

Frequency & Distribution

• A table of response categories of a variable and the number of times each outcome is observed

Frequency Distribution

• For a given score the total number of cases in a distribution at or below that value

Cumulative Frequency

• For a give score the percentage of cases in a distribution at or below that value

Cumulative Percent

recode avergrade (1 thru 9 eq copy)(-99 eq sysmiss) into avegd. exe. value labels avegd 1 'D' 2 'C-' 3 'C' 4 'C+' 5 ' B-' 6 'B' 7 'B+' 8 'A-' 9 'A'. exe. freq avegd. exe.

Begin Excel Example

Measures of Central Tendency

Mean • Average of a group of scores

Median • The exact middle score in a distribution

of ranked scores

Mode • Most frequent score in distribution of

scores

freq offense_1_sum /stats = mean median mode. exe.

temporary. select if state ne 21. freq offense_1_sum /format=notable /stats = mean median mode.

freq offense_1_sum /format=notable /stats = mean median mode.

Begin Excel Example

Measures of Dispersion

Range Mean Deviation Variance &

Standard Deviation

Skewness

Example 1

Freq =offense_1_sum /format=notable /stats= stddev range minimum.

Example 2

Example 3

Begin Excel Example

Future Topics in the Statistical Analysis for Criminal Justice Research Series

• Sampling Basics • Significance Testing: Comparing Proportions • Significance Testing: Comparing Means • Correlation and Simple Linear Regression • Displaying Data • Multiple Linear Regression • Logistic Regression • Exploratory Data Analysis