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# Chapter 1

Chapter 1. Overview of Statistics &amp; Definition of Key Terms &amp; Concepts. Definition. Statistics=set of tools and techniques used to describe, organize, and interpret information Provides a vehicle to understand the world around us

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## Chapter 1

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1. Chapter 1 Overview of Statistics & Definition of Key Terms & Concepts

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. Chapter 6: Building Research Questions & Hypotheses

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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 non-drug court offenders on traditional probation.

15. Criteria for a Good Hypothesis • 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

16. Using Statistics to Test Hypotheses

17. 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

18. Population v. Sample Population Probability Sampling: No or limited bias between the Population & Sample Non-Probability Sampling: Bias exists between Population & Sample Sample

19. Sampling • Research Goals for Sampling • Select a sample that represents the larger population • 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=?

20. 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

21. 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

22. 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

23. 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

24. Exercise for Next Class • 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

25. 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

26. Find & Assess Hypotheses

27. Identify the Data & Measures

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