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

PADM 582 Quantitative and Qualitative Research Methods

Basic Concepts of Statistics Soomi Lee, Ph.D

Outline

• Syllabus• Why of Statistics?• Basic Concepts

• 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?

• 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?

• Design– Determining the best way to obtain data

• Description– Summarizing and exploring the data

• Inference– Determining causality– Making predictions

Purpose of Statistics

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?

Why should we care?

• Misleading measurement1. No child left behind and

standardized tests–Atlanta cheating scandal–Houston miracle

2. Measuring well-being–GDP?–Happiness?

Example

• Misleading samples• Gun ownership–USA today: 89%–General Social Survey: 35%

• Misleading correlations• Ice cream sales and crime rate

Example

Why should we care?

• Population vs. Sample• Parameter vs. Statistic• Variables

Basic Concepts

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

Why should we care?Basic Concepts

Population vs. Sample


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


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.


Who Cares?

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

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


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 01 M 45 Republican 60,000

Person 02 F 52 Independent 22,000

Person 03 F 28 Republican 42,000

Person 04 M 66 Democrat 580,000


Person 06 F 31 Democrat 33,000


Level of Variables

• Quantitative • Ordinal • Qualitative (nominal)

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

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

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…

Why should we care?Practice Questions

• Identify the types of variables below:1. Race and ethnicity: White, Black, Asian,

Latino, Other2. Incarceration rate by county in California3. Satisfaction with local public service: very

satisfied, satisfied, neutral, unsatisfied, very unsatisfied

4. Marital status: married, single5. Marital status: married, separated, divorced,

widowed, never married6. Perceived success of animal rights association

in advocacy: very high, high, moderate, low, very low

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 Ordinal4. Marital status: married, single Nominal5. Marital status: married, separated, divorced, widowed,

never married Nominal6. Perceived success of animal rights association in

advocacy: very high, high, moderate, low, very low Ordinal

Why should we care?Group Work

• Give two examples of the following types of variables1. Nominal2. Quantitative discrete3. Quantitative continuous4. Ordinal

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.


Subject ID Variable 1: gender

Variable 2: age

Variable 3: party ID

Variable 4: income

Person 01 M 45 Republican 60,000

Person 02 F 52 Independent 22,000

Person 03 F 28 Republican 42,000



Person 06 F 31 Democrat 33,000


Subject ID

Variable 4: income

(quantitative variable)

Income level

(ordinal variable)

Proposed tax reform

affected

Person 01 60,000 2 0

Person 02 22,000 1 0

Person 03 42,000 2 0

Person 04 580,000 3 1

Person 05 79,000 2 0

Person 06 33,000 1 0

• 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.


• 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.

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.

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

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