1. PADM 582 Quantitative and Qualitative Research Methods Basic Concepts of Statistics Soomi Lee, Ph.D

2. Outline Syllabus Why of Statistics? Basic Concepts

3. Information gathering – We use information gathering techniques to obtain observation (e.g. income growth, obesity rate). – The observations that are gathered are called data. Why Statistics?

4. Statistics is the scientific application of mathematical principles to the collection, analysis, and presentation of numerical data. – Definition by the American Statistics Association Examples of – Collecting data: telephone surveys – Analyzing data: analysis of variance, regression analysis – Presenting data: contingency tables, charts, graphs What is Statistics?

5. Design – Determining the best way to obtain data Description – Summarizing and exploring the data Inference – Determining causality – Making predictions Purpose of Statistics

6. Why should we care? Performance measurement Evaluation research Evidence based decision making May the best methodology win – Misleading measurement – Misleading samples – Misleading correlations Why Should We Care?

7. Why should we care? Misleading measurement 1.No child left behind and standardized tests – Atlanta cheating scandal – Houston miracle 2.Measuring well-being – GDP? – Happiness? Example

8. Misleading samples Gun ownership – USA today: 89% – General Social Survey: 35% Misleading correlations Ice cream sales and crime rate Example

9. Why should we care? Population vs. Sample Parameter vs. Statistic Variables Basic Concepts

10. Why should we care? Population Total set of subjects of interest in the study Ex. All residents in California Sample Subset of the population for which we collect data Ex. California’s Statewide Surveys (PPIC) Basic Concepts Population vs. Sample Basic Concepts Population vs. Sample

11. Why should we care? Basic Concepts Population vs. Sample Basic Concepts Population vs. Sample

12. Why should we care? Basic Concepts Population vs. Sample Basic Concepts Population vs. Sample

13. Why should we care? Basic Concepts Parameter and a Statistic Basic Concepts Parameter and a Statistic Parameter Numerical summary of population Ex. Governor’s job approval ratings for the whole residents in California Statistic Numerical summary of the sample of the population Ex. Governor’s job approval ratings in the Statewide Survey

14. Why should we care? Basic Concepts Who Cares? Basic Concepts Who Cares? We distinguish between a population and a sample because every sample will have an amount of error associated with it. In statistics, our goal is to gather a sample that best approximates the population.

15. Why should we care? Basic Concepts Who Cares? Basic Concepts Who Cares?

16. Why should we care? Does the decennial data collected by the U.S. Census reflect the U.S. population or a sample of the U.S. population? Practice Question

17. Why should we care? A recent PPIC Statewide survey indicated that 38% of the registered voters approve of the job that Governor Brown is doing. Is the value 38% a parameter of a statistic? Practice Question

18. Why should we care? Basic Concepts Variables Basic Concepts Variables A variable is a characteristic that can vary in value among subjects in a sample or population. Subject ID Variable 1: gender Variable 2: age Variable 3: party ID Variable 4: income Person 01M45Republican60,000 Person 02F52Independent22,000 Person 03F28Republican42,000 Person 04M66Democrat580,000 Person 05M53Democrat79,000 Person 06F31Democrat33,000

19. Why should we care? Basic Concepts Level of Variables Basic Concepts Level of Variables Quantitative Ordinal Qualitative (nominal)

20. Why should we care? Variables: Quantitative or interval The values of a variable vary in magnitude (you can actually count the number) Continuous if it can take an infinite continuum of possible real number Examples: income, housing price, crime rate Discrete if it can take on a finite number of values Examples: Years of education, number of children, number of Asians, number of arrests, number of policeofficers

21. Why should we care? Variables: Ordinal The ordinal variables consists of categorical scales that have a natural ordering of values. It does not have defined interval distances between the values. We “assign” numbers for each category for statistical purposes. Examples Socioeconomic status: low(1), middle (2), high (3) Political ideology: (1) extremely liberal, (2) liberal, (3) moderate, (4) conservative, (5) extremely conservative

22. Why should we care? Variables: Qualitative or nominal A scale for the measurement is a set of unordered categories. Differ in quality, not quantity or magnitude Examples Gender: female, male (dichotomous) States in the U.S.: CA, IL, FL… Cities in LA county: La Verne, Claremont, Pomona…

23. Why should we care? Practice Questions Identify the types of variables below: 1.Race and ethnicity: White, Black, Asian, Latino, Other 2.Incarceration rate by county in California 3.Satisfaction with local public service: very satisfied, satisfied, neutral, unsatisfied, very unsatisfied 4.Marital status: married, single 5.Marital status: married, separated, divorced, widowed, never married 6.Perceived success of animal rights association in advocacy: very high, high, moderate, low, very low

24. Why should we care? Practice Questions Identify the types of variables below: 1.Race and ethnicity: White, Black, Asian, Latino, Other  Nominal (qualitative) 2.Incarceration rate by county in California  Quantitative (continuous) 3.Satisfaction with local public service: very satisfied, satisfied, neutral, unsatisfied, very unsatisfied  Ordinal 4.Marital status: married, single  Nominal 5.Marital status: married, separated, divorced, widowed, never married  Nominal 6.Perceived success of animal rights association in advocacy: very high, high, moderate, low, very low  Ordinal

25. Why should we care? Group Work Give two examples of the following types of variables 1.Nominal 2.Quantitative discrete 3.Quantitative continuous 4.Ordinal

26. Why should we care? Who Cares? A higher level of variables has more flexibility because we can always transform it into variables at lower levels of measurement. The opposite is not true.

27. Why should we care? Who Cares? Subject ID Variable 1: gender Variable 2: age Variable 3: party ID Variable 4: income Person 01M45Republican60,000 Person 02F52Independent22,000 Person 03F28Republican42,000 Person 04M66Democrat580,000 Person 05M53Democrat79,000 Person 06F31Democrat33,000

28. Why should we care? Who Cares? Subject ID Variable 4: income (quantitative variable) Income level (ordinal variable) Proposed tax reform affected Person 0160,00020 Person 0222,00010 Person 0342,00020 Person 04580,00031 Person 0579,00020 Person 0633,00010 Want to construct an income level variable. Group 1: Under 50,000; Group 2: 50,001-100,000; Group 3: over 100,001 Want to construct a variable if a person’s income tax is affected by a proposed tax reform.

29. Why should we care? Who Cares? A higher level of variables has more flexibility because we can always transform it into variables at lower levels of measurement. The opposite is not true. We use different statistical technique to analyze different levels of measurement.

30. Next Week We will cover descriptive statistics. Read Salkind’s chapters 2 and 3. Pick your variable of interest. We will use excel in class exercise. Bring a calculator for in-class exercise. There is no homework assignment this week.