Chapter 1Chapter 1

Overview of Statistics & Overview of Statistics & Definition of Key Terms & Definition of Key Terms &

ConceptsConcepts

DefinitionDefinition Statistics=set of tools and techniques used Statistics=set of tools and techniques used

to describe, organize, and interpret to describe, organize, and interpret informationinformation– Provides a vehicle to understand the world Provides a vehicle to understand the world

around usaround us– Provides a way to investigate questions using a Provides a way to investigate questions using a

potentially objective methodpotentially objective method Statistics depend on dataStatistics depend on data

– Data=a set of observations or events (datum)Data=a set of observations or events (datum)– E.g., Scores on a test, ages of students at E.g., Scores on a test, ages of students at

CSULA, # times victimized, # times stopped by CSULA, # times victimized, # times stopped by the policethe police

Brief BackgroundBrief Background The possibility of statistics began when The possibility of statistics began when

humans learned to count thingshumans learned to count things As areas of study began to develop in the 17As areas of study began to develop in the 17thth

century, individuals of many disciplines needed century, individuals of many disciplines needed a way to measure the relationship between a way to measure the relationship between phenomena; hence, the birth of statisticsphenomena; hence, the birth of statistics

2020thth century brought forth tremendous growth century brought forth tremendous growth in the conceptual and technological in the conceptual and technological development of statistics development of statistics

As a result, most areas of study use some type As a result, most areas of study use some type and level of statistics to explore research and level of statistics to explore research questions and build knowledgequestions and build knowledge

Purpose of StatisticsPurpose of Statistics

Statistics are ultimately used to measure and Statistics are ultimately used to measure and assess the relationship between an independent assess the relationship between an independent (X) and dependent variable (Y)(X) and dependent variable (Y)

Independent VariableIndependent Variable=The factor that you believe =The factor that you believe relates to/causes the problem of interest (must relates to/causes the problem of interest (must occur before the dependent variable)—X occur before the dependent variable)—X

Dependent VariableDependent Variable=The factor/problem that you =The factor/problem that you are trying to explain—Y are trying to explain—Y

Both the independent and dependent variables Both the independent and dependent variables should be clear in your research question:should be clear in your research question:– X X Y Y

Testing XTesting XYY

A primary purpose of statistics is to A primary purpose of statistics is to measure the relationship between X measure the relationship between X causes Y…does X cause Y?causes Y…does X cause Y?

In order to determine causation, a In order to determine causation, a researcher must assess whether the researcher must assess whether the relationship meets following criteria:relationship meets following criteria:– Correlation: x and y are related in a meaningful wayCorrelation: x and y are related in a meaningful way– Temporal ordering: x must come before yTemporal ordering: x must come before y– Non-spuriousness: relationship between x and y must Non-spuriousness: relationship between x and y must

not be due to chance or a third, unaccounted for not be due to chance or a third, unaccounted for variablevariable

Types of StatisticsTypes of Statistics

Descriptive statistics-Descriptive statistics-organizes and organizes and summarizes datasummarizes data– Basic understanding of the dataBasic understanding of the data

Inferential statistics-Inferential statistics-interpreting data interpreting data – The next step after descriptive statisticsThe next step after descriptive statistics– Used to make inferences from a smaller group Used to make inferences from a smaller group

(sample) to a larger group (population)(sample) to a larger group (population)– More complex examination and comparison of More complex examination and comparison of

the datathe data

Building Blocks of StatisticsBuilding Blocks of Statistics Research Question=What you are interested in Research Question=What you are interested in

knowingknowing Research Hypotheses=Possible answers to the Research Hypotheses=Possible answers to the

questionquestion Research Methods=Framework for collecting dataResearch Methods=Framework for collecting data

—ensures that the data meets high standards of —ensures that the data meets high standards of qualityquality

Data=The information that is used in the Data=The information that is used in the computation of statistics—captures meaning in computation of statistics—captures meaning in numerical formnumerical form

Statistics=Analysis of data to test the hypotheses Statistics=Analysis of data to test the hypotheses in order to answer a research questionin order to answer a research question

Chapter 6:Chapter 6:Building Research Questions Building Research Questions

& Hypotheses& Hypotheses

Research QuestionResearch Question

What is it?What is it?– A research question is a question about A research question is a question about

the relationship between two or more the relationship between two or more concepts concepts

Why is it important?Why is it important?– A research question is the foundation of A research question is the foundation of

the research study. Everything revolves the research study. Everything revolves around itaround it

– It is the first step in It is the first step in anyany research research projectproject

Evaluating Your Research Evaluating Your Research QuestionQuestion

Research questions can be exploratory or Research questions can be exploratory or directed:directed:

Exploratory: Why is violent crime increasing? Exploratory: Why is violent crime increasing? Directed: Is violent crime more likely to increase Directed: Is violent crime more likely to increase

during economical difficult times? during economical difficult times?

A directed research question specifies a A directed research question specifies a relationship between two concepts and relationship between two concepts and ultimately becomes the study’s ultimately becomes the study’s independent variable and dependent independent variable and dependent variablevariable

The Next Step: HypothesisThe Next Step: Hypothesis Hypotheses are used to guide the testing of your research Hypotheses are used to guide the testing of your research

question. question. It is an educated guess as to the answer to your research questionIt is an educated guess as to the answer to your research question Example:Example:

– RQ: Do female offenders receive harsher outcomes than male RQ: Do female offenders receive harsher outcomes than male offenders?offenders?

– H: Female offenders will receive harsher outcomes than male H: Female offenders will receive harsher outcomes than male offenders. offenders.

It is a reflection of the problem statement that motivates the It is a reflection of the problem statement that motivates the research question—it is the testable form of the research questionresearch question—it is the testable form of the research question

It is essential that your hypothesis is precise and clear.It is essential that your hypothesis is precise and clear. If your research question is not precise and clear, it will be difficult If your research question is not precise and clear, it will be difficult

to create clear a hypothesis related to the research question & to create clear a hypothesis related to the research question & difficult to discern how to use statistics to answer the research difficult to discern how to use statistics to answer the research questionquestion

Types of HypothesesTypes of Hypotheses Every research question provides the foundation for two Every research question provides the foundation for two

types of hypotheses:types of hypotheses:– The null hypothesisThe null hypothesis– The research hypothesisThe research hypothesis

Null Hypothesis (HNull Hypothesis (H00))– Assumes equality and represents no relationship between Assumes equality and represents no relationship between

variables (x and y)variables (x and y)– Provides starting point: Accepted as true given no other Provides starting point: Accepted as true given no other

information (i.e., no evidence to the contrary)information (i.e., no evidence to the contrary)– Operates as the comparison (or benchmark) for the research Operates as the comparison (or benchmark) for the research

hypothesishypothesis For example: Female offenders do not receive different treatment For example: Female offenders do not receive different treatment

than male offenders.than male offenders.– The null hypothesis is often implied rather than directly stated The null hypothesis is often implied rather than directly stated

in research articlesin research articles

Types of Hypotheses, Cont’d.Types of Hypotheses, Cont’d. Research Hypothesis (HResearch Hypothesis (H11))

– A definitive statement that there is a relationship A definitive statement that there is a relationship between x and ybetween x and y

Non-directional: posits a difference but no specific Non-directional: posits a difference but no specific direction is implied (yes/no)direction is implied (yes/no)

– Female offenders receive different treatment than male Female offenders receive different treatment than male offenders. offenders.

Directional: posits a specific type of difference (more Directional: posits a specific type of difference (more than/less than)than/less than)

– Female offenders receive harsher treatment than male Female offenders receive harsher treatment than male offenders.offenders.

– In either case, the point of statistical analysis is to In either case, the point of statistical analysis is to empirically compare the research hypothesis to the null empirically compare the research hypothesis to the null hypothesishypothesis

Empirical comparison determines which explanation for the Empirical comparison determines which explanation for the relationship is supported by the datarelationship is supported by the data

Another ExampleAnother Example Are drug courts more effective than traditional probation at Are drug courts more effective than traditional probation at

reducing recidivism?reducing recidivism?– Null (Null (HH00):): Recidivism among drug court participants will Recidivism among drug court participants will

not differ from recidivism among non-drug court not differ from recidivism among non-drug court offenders on traditional probation. offenders on traditional probation.

– Non-Directional (Non-Directional (HH11):): Recidivism among drug court Recidivism among drug court participants will differ from recidivism among non-drug participants will differ from recidivism among non-drug court offenders on traditional probation. court offenders on traditional probation.

– Directional (Directional (HH22):): Recidivism among drug court Recidivism among drug court participants will be lower than recidivism among non-participants will be lower than recidivism among non-drug court offenders on traditional probation.drug court offenders on traditional probation.

Criteria for a Good HypothesisCriteria for a Good Hypothesis

1.1. Should be declarative statement—not a Should be declarative statement—not a questionquestion

2.2. Proposes a specific relationship between Proposes a specific relationship between the independent (x) variable and the the independent (x) variable and the dependent (y) variabledependent (y) variable

3.3. Reflects the theory/literature on the topic Reflects the theory/literature on the topic area—it is a substantive link to previous area—it is a substantive link to previous literature and theoryliterature and theory

4.4. Is brief and to the point—easy to Is brief and to the point—easy to understand and evaluateunderstand and evaluate

5.5. Must be testable—can carry out the Must be testable—can carry out the intention of the research questionintention of the research question

Using Statistics to Test Using Statistics to Test HypothesesHypotheses

Using Statistics to Test Your Using Statistics to Test Your HypothesesHypotheses

Purpose of statistics is to test your research Purpose of statistics is to test your research questionquestion

The best way to accomplish this is to collect data The best way to accomplish this is to collect data from a sample that represents the larger from a sample that represents the larger population that you are interested in.population that you are interested in.

Sampling is the process of selecting part of a Sampling is the process of selecting part of a populationpopulation

Population represents everyone or everything Population represents everyone or everything that you are interested in studyingthat you are interested in studying

Population v. SamplePopulation v. Sample

Sample

Population

Probability Sampling: No or limited bias between the Population & Sample

Non-Probability Sampling: Bias exists between Population & Sample

SamplingSampling Research Goals for SamplingResearch Goals for Sampling

1.1. Select a sample that represents the larger Select a sample that represents the larger populationpopulation

2.2. Generalize from a sample to an unobserved Generalize from a sample to an unobserved population the sample is intended to population the sample is intended to representrepresent

Target populations are implied in your research Target populations are implied in your research question:question:

– Do female juvenile offenders receive harsher Do female juvenile offenders receive harsher punishments than male juvenile offenders?punishments than male juvenile offenders?

Target population=?Target population=?– Does parent supervision reduce juvenile delinquency? Does parent supervision reduce juvenile delinquency?

Target population=?Target population=?

Sampling BiasSampling Bias Sampling bias refers to selecting subjects in a way Sampling bias refers to selecting subjects in a way

that that will notwill not provide assurances that the sample is provide assurances that the sample is representative of the populationrepresentative of the population

Examples:Examples:– Selecting the first 100 males encountered in a Selecting the first 100 males encountered in a

mall to represent all malesmall to represent all males– Interviewing judges that have viewpoints Interviewing judges that have viewpoints

consistent with a research question and not consistent with a research question and not interviewing judges with inconsistent viewpointsinterviewing judges with inconsistent viewpoints

Unless a researcher uses probability sampling from Unless a researcher uses probability sampling from the population, it is impossible to declare that your the population, it is impossible to declare that your sample is representative of that populationsample is representative of that population

Probability SamplingProbability Sampling To meet the goals of sampling, it is best to use To meet the goals of sampling, it is best to use

probability samplingprobability sampling Probability sampling is a method of sampling in which Probability sampling is a method of sampling in which

each member of a population has a known chance or each member of a population has a known chance or probability of being selectedprobability of being selected

A sample is representative if the aggregate A sample is representative if the aggregate characteristics of the sample closely approximate those characteristics of the sample closely approximate those same aggregate characteristics in the populationsame aggregate characteristics in the population– Sampling error=the difference between the values of the Sampling error=the difference between the values of the

sample statistic and the population parametersample statistic and the population parameter Probability sampling helps researchers achieve a Probability sampling helps researchers achieve a

representative samplerepresentative sample It protects a sample from sampling biasIt protects a sample from sampling bias

Non-Probability SamplingNon-Probability Sampling Probability sampling designs are not Probability sampling designs are not

possible in many situationspossible in many situations Non-probability sampling is an alternative; Non-probability sampling is an alternative;

however, the samples are not however, the samples are not representative of the population from which representative of the population from which they are drawnthey are drawn

Non-probability sampling designs are prone Non-probability sampling designs are prone to selection biasto selection bias

Non-Probability sampling designs are, Non-Probability sampling designs are, therefore, weaker than probability sampling therefore, weaker than probability sampling designsdesigns

Populations, Samples, & Populations, Samples, & Hypotheses, Hypotheses,

Null hypotheses refer to the population Null hypotheses refer to the population – Null hypotheses are indirectly tested because Null hypotheses are indirectly tested because

samples mirror but are not 100% identical to samples mirror but are not 100% identical to the samplethe sample

Research hypotheses refer to the sampleResearch hypotheses refer to the sample– Research hypotheses are directly tested in Research hypotheses are directly tested in

order to infer (using the sample to generalize order to infer (using the sample to generalize back to the population) the results back to the back to the population) the results back to the populationpopulation

Exercise for Next ClassExercise for Next Class Using the reserve article (password=student)…Using the reserve article (password=student)…1.1. Identify the research question, null hypotheses, Identify the research question, null hypotheses,

and research hypotheses proposed/inferred in and research hypotheses proposed/inferred in the articlethe article

2.2. Indicate whether each research hypothesis is Indicate whether each research hypothesis is directional or non-directionaldirectional or non-directional

3.3. Identify the type of data and how it was Identify the type of data and how it was retrieved for the studyretrieved for the study

4.4. List the measures (names of) used for the List the measures (names of) used for the independent variables and dependent variables independent variables and dependent variables

5.5. Indicate whether the study supported or refuted Indicate whether the study supported or refuted each of the research hypotheseseach of the research hypotheses

Helpful InformationHelpful Information SampleSample=The source of the data used to test the =The source of the data used to test the

hypotheses in a study—e.g., A random sample of hypotheses in a study—e.g., A random sample of high school seniors at 12 high schools for a total high school seniors at 12 high schools for a total sample size of 3,000sample size of 3,000

MethodMethod=How was the data derived from the =How was the data derived from the source? Were surveys used? Were the data source? Were surveys used? Were the data retrieved from case files?retrieved from case files?

Independent VariablesIndependent Variables=The factors that =The factors that potentially relate to/cause the problem of interest potentially relate to/cause the problem of interest (most occur before the dependent variable)(most occur before the dependent variable)

Dependent VariablesDependent Variables=The factor that the =The factor that the researcher is trying to explain researcher is trying to explain

Find & Assess HypothesesFind & Assess Hypotheses

Either copy and paste provided tables into WORD or create Either copy and paste provided tables into WORD or create similar types of tables in WORD to complete the assignment.similar types of tables in WORD to complete the assignment.

HypothesesHypotheses TypeType Support/RefuteSupport/Refute

HH00/H/H11

HH00/H/H22

HH00/H/H33

HH00/H/H44

HH00/H/H55

HH00/H/H66

HH00/H/H88

HH00/H/H88

Identify the Data & MeasuresIdentify the Data & Measures

Description of Sampling and Data Used:Description of Sampling and Data Used:

Independent VariablesIndependent Variables Dependent VariablesDependent Variables

List List ListList