Chapter 1
Overview of Statistics &
Definition of Key Terms &
Concepts
Definition

Statistics=set of tools and techniques
used to describe, organize, and interpret
information
– Provides a vehicle to understand the world
around us
– Provides a way to investigate questions using a
potentially objective method

Statistics depend on data
– Data=a set of observations or events (datum)
– E.g., Scores on a test, ages of students at
CSULA, # times victimized, # times stopped
by the police
Brief Background
The possibility of statistics began when
humans learned to count things
 As areas of study began to develop in the
17th century, individuals of many
disciplines needed a way to measure the
relationship between phenomena; hence,
the birth of statistics
 20th century brought forth tremendous
growth in the conceptual and technological
development of statistics
 As a result, most areas of study use some
type and level of statistics to explore
research questions and build knowledge

Purpose of Statistics

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Statistics are ultimately used to measure and
assess the relationship between an independent
(X) and dependent variable (Y)
Independent Variable=The factor that you believe
relates to/causes the problem of interest (must
occur before the dependent variable)—X
Dependent Variable=The factor/problem that you
are trying to explain—Y
Both the independent and dependent variables
should be clear in your research question:
– XY
Testing XY
A primary purpose of statistics is to
measure the relationship between X
causes Y…does X cause Y?
 In order to determine causation, a
researcher must assess whether the
relationship meets following criteria:

– Correlation: x and y are related in a meaningful way
– Temporal ordering: x must come before y
– Non-spuriousness: relationship between x and y must
not be due to chance or a third, unaccounted for
variable
Types of Statistics

Descriptive statistics-organizes and
summarizes data
– Basic understanding of the data

Inferential statistics-interpreting data
– The next step after descriptive statistics
– Used to make inferences from a smaller group
(sample) to a larger group (population)
– More complex examination and comparison of
the data
Building Blocks of Statistics

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Research Question=What you are interested in
knowing
Research Hypotheses=Possible answers to the
question
Research Methods=Framework for collecting
data—ensures that the data meets high
standards of quality
Data=The information that is used in the
computation of statistics—captures meaning in
numerical form
Statistics=Analysis of data to test the hypotheses
in order to answer a research question
Chapter 6:
Building Research Questions
& Hypotheses
Research Question
 What
is it?
– A research question is a question about
the relationship between two or more
concepts
 Why
is it important?
– A research question is the foundation of
the research study. Everything revolves
around it
– It is the first step in any research
project
Evaluating Your Research
Question

Research questions can be exploratory or
directed:
 Exploratory:
Why is violent crime increasing?
 Directed: Is violent crime more likely to increase
during economical difficult times?

A directed research question specifies a
relationship between two concepts and
ultimately becomes the study’s
independent variable and dependent
variable
The Next Step: Hypothesis

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Hypotheses are used to guide the testing of your research
question.
It is an educated guess as to the answer to your research
question
Example:
– RQ: Do female offenders receive harsher outcomes than male
offenders?
– H: Female offenders will receive harsher outcomes than male
offenders.
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It is a reflection of the problem statement that motivates the
research question—it is the testable form of the research question
It is essential that your hypothesis is precise and clear.
If your research question is not precise and clear, it will be difficult
to create clear a hypothesis related to the research question &
difficult to discern how to use statistics to answer the research
question
Types of Hypotheses

Every research question provides the foundation for two
types of hypotheses:
– The null hypothesis
– The research hypothesis

Null Hypothesis (H0)
– Assumes equality and represents no relationship between
variables (x and y)
– Provides starting point: Accepted as true given no other
information (i.e., no evidence to the contrary)
– Operates as the comparison (or benchmark) for the research
hypothesis

For example: Female offenders do not receive different treatment
than male offenders.
– The null hypothesis is often implied rather than directly stated
in research articles
Types of Hypotheses, Cont’d.

Research Hypothesis (H1)
– A definitive statement that there is a relationship
between x and y
 Non-directional: posits a difference but no specific
direction is implied (yes/no)
– Female offenders receive different treatment than male
offenders.
 Directional:
posits a specific type of difference (more
than/less than)
– Female offenders receive harsher treatment than male
offenders.
– In either case, the point of statistical analysis is to
empirically compare the research hypothesis to the null
hypothesis

Empirical comparison determines which explanation for the
relationship is supported by the data
Another Example

Are drug courts more effective than traditional probation at
reducing recidivism?
– Null (H0): Recidivism among drug court participants will
not differ from recidivism among non-drug court
offenders on traditional probation.
– Non-Directional (H1): Recidivism among drug court
participants will differ from recidivism among non-drug
court offenders on traditional probation.
– Directional (H2): Recidivism among drug court
participants will be lower than recidivism among nondrug court offenders on traditional probation.
Criteria for a Good Hypothesis
1.
2.
3.
4.
5.
Should be declarative statement—not a
question
Proposes a specific relationship between
the independent (x) variable and the
dependent (y) variable
Reflects the theory/literature on the topic
area—it is a substantive link to previous
literature and theory
Is brief and to the point—easy to
understand and evaluate
Must be testable—can carry out the
intention of the research question
Using Statistics to Test
Hypotheses
Using Statistics to Test Your
Hypotheses
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Purpose of statistics is to test your research
question
The best way to accomplish this is to collect data
from a sample that represents the larger
population that you are interested in.
Sampling is the process of selecting part of a
population
Population represents everyone or everything
that you are interested in studying
Population v. Sample
Population
Probability Sampling:
No or limited bias
between the Population
& Sample
Non-Probability Sampling:
Bias exists between
Population & Sample
Sample
Sampling
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Research Goals for Sampling
1. Select a sample that represents the larger
population
2. Generalize from a sample to an
unobserved population the sample is
intended to represent
Target populations are implied in your
research question:
–
Do female juvenile offenders receive harsher
punishments than male juvenile offenders?
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–
Target population=?
Does parent supervision reduce juvenile
delinquency?

Target population=?
Sampling Bias
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Sampling bias refers to selecting subjects in a
way that will not provide assurances that the
sample is representative of the population
Examples:
– Selecting the first 100 males encountered in
a mall to represent all males
– Interviewing judges that have viewpoints
consistent with a research question and not
interviewing judges with inconsistent
viewpoints
Unless a researcher uses probability sampling
from the population, it is impossible to declare
that your sample is representative of that
population
Probability Sampling

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To meet the goals of sampling, it is best to use
probability sampling
Probability sampling is a method of sampling
in which each member of a population has a
known chance or probability of being selected
A sample is representative if the aggregate
characteristics of the sample closely
approximate those same aggregate
characteristics in the population
– Sampling error=the difference between the values of
the sample statistic and the population parameter
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Probability sampling helps researchers achieve
a representative sample
It protects a sample from sampling bias
Non-Probability Sampling
Probability sampling designs are not
possible in many situations
 Non-probability sampling is an
alternative; however, the samples are
not representative of the population
from which they are drawn
 Non-probability sampling designs are
prone to selection bias
 Non-Probability sampling designs are,
therefore, weaker than probability
sampling designs

Populations, Samples, &
Hypotheses,

Null hypotheses refer to the population
– Null hypotheses are indirectly tested because
samples mirror but are not 100% identical to
the sample

Research hypotheses refer to the sample
– Research hypotheses are directly tested in
order to infer (using the sample to generalize
back to the population) the results back to the
population
Exercise for Next Class
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1.
2.
3.
4.
5.
Using the reserve article (password=student)…
Identify the research question, null hypotheses,
and research hypotheses proposed/inferred in
the article
Indicate whether each research hypothesis is
directional or non-directional
Identify the type of data and how it was
retrieved for the study
List the measures (names of) used for the
independent variables and dependent variables
Indicate whether the study supported or
refuted each of the research hypotheses
Helpful Information
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Sample=The source of the data used to test the
hypotheses in a study—e.g., A random sample of
high school seniors at 12 high schools for a total
sample size of 3,000
Method=How was the data derived from the
source? Were surveys used? Were the data
retrieved from case files?
Independent Variables=The factors that
potentially relate to/cause the problem of interest
(most occur before the dependent variable)
Dependent Variables=The factor that the
researcher is trying to explain
Find & Assess Hypotheses
Either copy and paste provided tables into WORD or create
similar types of tables in WORD to complete the assignment.
Hypotheses
H0/H1
H0/H2
H0/H3
H0/H4
H0/H5
H0/H6
H0/H8
H0/H8
Type
Support/Refute
Identify the Data & Measures
Description of Sampling and Data Used:
Independent Variables
Dependent Variables
List
List