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Unit 1

Introduction to Criminal Justice Statistics

Learning Objectives

-Describe the limited but crucial role of statistics in social research.

-Distinguish between three applications of statistics and identify situations in which each

is appropriate.

-Identify and describe three levels of measurement and cite examples of variables from

each.

Unit Outline

-Using Statistics

-Why Study Statistics?

-The Role of Statistics in Scientific Inquiry

-The Goals of This Text

-Descriptive and Inferential Statistics

Using Statistics

Statistics can be used to:

-Demonstrate the connection between smoking cigarettes and experiencing a stroke.

-Track the public approval rating of a President over time.

-Measure differences in attitudes towards tattoos and body piercings between people

in different age groups.

-Statistics are increasingly used in market research, social policy studies, and the

social sciences.

 Statistics are essential in the social sciences because they enable ideas to be evaluated and

theories to be tested.

 Quantitative Research projects use statistics to analyze numerical data.

 Statistics are mathematical techniques used by social scientists to analyze data in

order to answer questions and test theories.

The Role of Statistics in Scientific Inquiry

 The Research Process -A theory is an explanation of the relationships between phenomena.

-Theories are general. For example, consider Karl Marx’s theory of Economic Determinism.

Marx believed that economic relations influenced social and political spheres of life.

-Can you test that with statistics? Not easily!

-The Research Process -A hypothesis is derived from theory. It is a specific and exact statement about the relationship

between variables.

-Hypotheses are specific. Psychologist Thomas Pettigrew hypothesized that group prejudice

could be reduced when people were exposed to diverse others for a period of time under

certain specified conditions, such as those where individuals are treated equally regardless of

their race or ethnicity.

-Develop a hypothesis of your own.  Hypotheses are stated in terms of variables.

 A variable is any trait that can change values from case to case.

 Examples: age, income, religious affiliation, attitudes

toward some issue

 In Pettigrew’s hypothesis (previous slide), the variables

included level of prejudice, amount of time spent with

diverse others, and the presence of a situation where

people are treated equally.

 What are the variables in the hypothesis that you

created?  Science distinguishes between two types of variables: dependent

variables and independent variables.

 Independent variables are causes.

 Dependent variables are effects or outcomes.

 In Pettigrew’s hypothesis, an independent

variable was the amount of time spent with

diverse others.

 The dependent variable was the level of

prejudice.  To test a hypothesis, we must gather our data or observations.

 Things to consider:

 How many cases will we select?

 How will we measure our variables?

 How will we analyze the data?  After collecting data, we form empirical generalizations through

statistical analysis.

 At this point, we would revisit our theory.

 Do our results support our theory?

 Do our results suggest changes to our theory?  Statistics are useful tools, but not ends in themselves. Thus, we will not take a

“mathematical” approach to the subject.

 This text will help you to read and critique research literature in the social sciences.

 Learning how to use these tools will help you to carry out your own research.

 Descriptive Statistics  Univariate descriptive statistics summarize the distribution of a single variable.

 Percentages, rates, etc.

 Data reduction is a process of using a few numbers to summarize many.

 An example of a univariate statistic might be the percentage of

students who score an 80 or higher on an exam.

 Develop a univariate statistic of your own.  Bivariate descriptive statistics describe the relationship between two variables.

 Multivariate descriptive statistics describe the relationships among more than

two variables.

 Measures of association quantify the strength and pattern of a

relationship between two or more variables.

 For example, gender, race, and health behaviors are all

associated with life expectancy.

 Inferential Statistics  Inferential statistics are used to generalize sample information to its population.

 A population is a collection of all possible cases of interest.

 A sample is a carefully chosen subset of a population. It is the set of

cases used for study and analysis.

 For example, a hospital has a population of patients. A

researcher can use a probability technique to select a random

sample of 20% of the patients.

 Create your own example of a population and sample.

 Level of Measurement  Level of measurement refers to the mathematical characteristics of a

variable.

 There are three levels of measurement:

 Nominal

 Ordinal

 Interval-ratio

 The level of measurement of a variable guides our choice of statistic

and statistical technique.  Regardless of the level of measurement, variables should have categories that are:

 Mutually exclusive (No two cases should fit in one category)

 Exhaustive (All cases should fit in a category)

 Relatively homogenous (The categories must be similar)

 For the variable “political party affiliation,” think of a set of

categories that would be mutually exclusive, and homogenous.

 Nominal Variables:  Have categories that are non-numerical and cannot be

ranked.

 Are the lowest level of measurement available?

 Consist of categories that can only be compared by

considering how many cases fall under each one.

 Examples of nominal variables include gender and

religious affiliation.

 The Latin root word “nom” means “name”.

 Name five other nominal level variables.

 Ordinal Variables:  Have ‘scores’ or categories that can be ranked from high to low.

 Can be described as being “more or less” with respect to each other.

 Are limited because we do not know the exact distance from one score or

category to the next.

 Examples of ordinal variables include social class (lower,

working, middle, upper) and “Likert” items (strongly agree,

agree, disagree, strongly disagree).

 Name five other ordinal level variables.

 Ordinal Variables:  Have ‘scores’ or categories that can be ranked from high to low.

 Can be described as being “more or less” with respect to each other.

 Are limited because we do not know the exact distance from one score or

category to the next.

 Examples of ordinal variables include social class (lower,

working, middle, upper) and “Likert” items (strongly agree,

agree, disagree, strongly disagree).

 Name five other ordinal level variables.

 How to Quickly Determine Level of Measurement  Ask yourself two simple questions:

1. Can the categories of the variable be ranked based on value?

- If the answer is no, as in the case of gender, it is nominal.

- If the answer is yes, as in the case of age, go to question #2.

2. Can the distance between the categories be quantified?

- If the answer is yes, as in age, it is interval-ratio.

- If the answer is no, as in level of agreement (Strongly Agree, Agree, Disagree, Strongly

Disagree), it is ordinal.

 Some variables can be measured at multiple levels.

1. For example, educational attainment can be measured in the number of

years completed (0, 1, 2, 3, ..., 12, 13, etc. – an interval-ratio variable) or it

can be measured in the highest degree received (less than high school,

high school diploma, associates degree, bachelors degree, etc. – an ordinal

variable).

2. Think of another variable that can be measured at different levels?

Summary  The purpose of statistics is to organize, manipulate, and analyze data so that researchers

can test theories and answer questions. Along with theory and methodology, statistics are

a basic tool used by social scientists to enhance their understanding of the social world.

 There are two general classes of statistics. Descriptive statistics are used to summarize

the distribution of a single variable and the relationships between two or more variables.

We use inferential statistics to generalize to populations from random samples.

 Variables may be measured at any of the three different levels. At the nominal level, we

can compare category sizes. At the ordinal level, scores can be ranked from high to low.

At the interval-ratio level, all mathematical operations are permitted.

Basic Terms

 Data

 Data reduction

 Dependent variable

 Descriptive statistics

 Hypothesis

 Independent variable

 Inferential statistics

 Level of measurement

 Measures of association

 Population

 Quantitative research

 Research

 Sample

 Statistics

 Theory

 Variable