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 17 th century, individuals of many disciplines needed a way to measure the relationship between phenomena; hence, the birth of statistics  20 th 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  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  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  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.  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 (H 0 ) –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 (H 1 ) –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 ( H 0 ): Recidivism among drug court participants will not differ from recidivism among non-drug court offenders on traditional probation. –Non-Directional ( H 1 ): Recidivism among drug court participants will differ from recidivism among non-drug court offenders on traditional probation. –Directional ( H 2 ): Recidivism among drug court participants will be lower than recidivism among non- drug court offenders on traditional probation.

Criteria for a Good Hypothesis 1. Should be declarative statement—not a question 2. Proposes a specific relationship between the independent (x) variable and the dependent (y) variable 3. Reflects the theory/literature on the topic area—it is a substantive link to previous literature and theory 4. Is brief and to the point—easy to understand and evaluate 5. Must be testable—can carry out the intention of the research question

Using Statistics to Test Hypotheses

Using Statistics to Test Your Hypotheses  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 Sample Population Probability Sampling: No or limited bias between the Population & Sample Non-Probability Sampling: Bias exists between Population & Sample

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

Sampling Bias  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  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  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  Using the reserve article (password=student)… 1. Identify the research question, null hypotheses, and research hypotheses proposed/inferred in the article 2. Indicate whether each research hypothesis is directional or non-directional 3. Identify the type of data and how it was retrieved for the study 4. List the measures (names of) used for the independent variables and dependent variables 5. Indicate whether the study supported or refuted each of the research hypotheses

Helpful Information  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. HypothesesTypeSupport/Refute H 0 /H 1 H 0 /H 2 H 0 /H 3 H 0 /H 4 H 0 /H 5 H 0 /H 6 H 0 /H 8

Identify the Data & Measures Description of Sampling and Data Used: Independent Variables Dependent Variables ListList