Chapter 1: The What and the Why of Statistics

• The Research Process• Asking a Research Question• The Role of Theory• Formulating the Hypotheses

– Independent & Dependent Variables: Causality– Independent & Dependent Variables: Guidelines

• Collecting Data – Levels of Measurement– Discrete and Continuous Variables

• Analyzing Data & Evaluating Hypotheses– Descriptive and Inferential Statistics

• Looking at Social Differences

The Research Process

Asking the Research Question

Formulating theHypotheses

Evaluating the Hypotheses

Analyzing Data

Develop a research design

Contribute new evidence to literature and begin again

THEORY

Examine a social relationship, study the relevant literature

Collecting Data

The Role of Theory

• A theory is an explanation of the relationship between two or more observable attributes of individuals or groups.

• Social scientists use theory to attempt to establish a link between what we observe (the data) and our understanding of why certain phenomena are related to each other in a particular way.

Asking a Research Question What is Empirical Research?

• Research based on information that can be verified by using our direct experience.

• To answer research questions we cannot rely on reasoning, speculation, moral judgment, or subjective preference

• Empirical (fact): – “Are women paid less than men for the same types of

work?”

• Not Empirical /Normative (value):– “Is racial equality good for society?”

• Hypotheses: – Tentative answers to research questions (subject to

empirical verification)

– A statement of a relationship between characteristics that vary (variables)

• Variable:– A property of people or objects that takes on two or more

values

– Must include categories that are both exhaustive and mutually exclusive

Formulating the Hypotheses

Example

Variable Categories

Religion

Christian

Jewish

Muslim

Monthly Income ($)

0-1999

2000-2999

2000-& above

Marital Status

Single

Married

Divorced

Widowed

Units of AnalysisThe level of social life on which social scientists focus

(individuals, groups). Examples:

• Individual as unit of analysis:– What are your political views?

• Family as unit of analysis:– Who does the housework?

• Organization as unit of analysis:– What is the gender composition?

• City as unit of analysis:– What was the crime rate last year?

Types of Variables

• Dependent The variable to be explained (the “effect”).

• Independent The variable expected to account for (the “cause”

of) the dependent variable.

IV DV

Cause and effect relationships between variables are not easy to infer in the social sciences. Causal relationships must meet three criteria:

1. The cause has to precede the effect in time

2. There has to be an empirical relationship between the cause and effect

3. This relationship cannot be explained by other factors

Cause and Effect Relationships

Guidelines for Independent and Dependent Variables

1. The dependent variable is always the property you are trying to explain; it is always the object of the research.

2. The independent variable usually occurs earlier in time than the dependent variables.

3. The independent variable is often seen as influencing, directly or indirectly, the dependent variable.

Example 1People who attend church regularly are more likely to oppose abortion than people who do not attend church regularly.

• Identify the IV and DV– independent variable:– dependent variable:

• Identify possible control variablesGender

• Are the causal arguments sound?– e.g. does party id affect abortion views or vice versa?

Church attendance

Age

Attitudes toward abortion

Religious affiliation (Catholic, Baptist, Islamic…)Political party identification

Example 2

• Identify the IV and DV

• Identify possible control variables

• Are the causal arguments sound?

The number of books read to a child per day positively affects a child’s word recognition.

– independent variable:– dependent variable:

Gender

– Most likely. It is hard to construct an argument where a 36 month old child affects the number of books his or her parent reads to him/her.

Number of books read

Older siblings

Word recognition

Health status Birth order

Collecting Data

Ask the Research Question

Formulating theHypotheses

Evaluating the Hypotheses

Analyzing Data

Develop a research design

Contribute new evidence to literature and begin again

THEORY

Collecting Data

Examine a social relationship, study the relevant literature

Collecting Data

Researchers must decide three things:

– How to measure the variables of interest

– How to select the cases for the research

– What kind of data collection techniques to use

Levels of MeasurementNot every statistical operation can be used with every variable. The type of statistical operations we employ will depend on how our variables are measured.

Nominal

Ordinal

Interval-Ratio

Nominal Level of Measurement

Numbers or other symbols are assigned to a set of categories for the purpose of naming, labeling, or classifying the observations.

• Examples:Political Party (Democrat, Republican)Religion (Catholic, Jewish, Muslim, Protestant)Race (African American, Latino, Native

American)

Ordinal Level of Measurement

Nominal variables that can be ranked from low to high.

• Example: Social Class

Upper Class

Middle Class

Working Class

Interval-Ratio Level of Measurement

Variables where measurements for all cases are expressed in the same units. (Variables with a natural zero point, such as height and weight, are called ratio variables.)

• Examples: AgeIncomeSAT scores

Cumulative Property of Levels of Measurement

• Variables that can be measured at the interval-ratio level of measurement can also be measured at the ordinal and nominal levels.

• However, variables that are measured at the nominal and ordinal levels cannot be measured at higher levels.

Different or Higher or How Much

Level Equivalent Lower Higher

Nominal Yes No No

Ordinal Yes Yes No Interval-ratio Yes Yes Yes

Cumulative Property of Levels of Measurement

There is one exception, though• Dichotomous variables

– Because there are only two possible values for a dichotomy, we can measure it at the ordinal or the interval-ratio level (e.g., gender)

– There is no way to get them out of order– This gives the dichotomy more power than other

nominal level variables

Discrete and Continuous Variables

• Discrete variables: variables that have a minimum-sized unit of measurement, which cannot be sub-divided

– Example: the number children per family

• Continuous variables: variables that, in theory, can take on all possible numerical values in a given interval

– Example: length

Analyzing Data: Descriptive and Inferential Statistics

• Population: The total set of individuals, objects, groups, or events in which the researcher is interested.

• Sample: A relatively small subset selected from a population.

• Descriptive statistics: Procedures that help us organize and describe data collected from either a sample or a population.

• Inferential statistics: The logic and procedures concerned with making predictions or inferences about a population from observations and analyses of a sample.

Analyze Data & Evaluate Hypotheses

Asking the Research Question

Formulating theHypotheses

Evaluating the Hypotheses

Analyzing Data

Develop a research design

Contribute new evidence to literature and begin again

THEORY

Collecting Data

Examine a social relationship, study the relevant literature

Begin the Process Again...

Asking the Research Question

Formulating theHypotheses

Evaluating the Hypotheses

Analyzing Data

Develop a research design

Contribute new evidence to literature and begin again

THEORY

Collecting Data

Examine a social relationship, study the relevant literature