Chapter 1: The What and the Why of Statistics Leon-Guerrero and Frankfort-Nachmias, Essentials of Statistics for a Diverse Society

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: “Are women paid less than men for the same types of work?” Not Empirical: “Is racial equality good for society?”

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.

Formulating the 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 Examples: Social class, age, gender, income

Units of Analysis The 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 Independent The variable to be explained (the “effect”). Independent The variable expected to account for (the “cause” of) the dependent variable.

Cause and Effect Relationships Cause and effect relationships between variables are not easy to infer in the social sciences. Causal relationships must meet three criteria: The cause has to precede the effect in time There has to be an empirical relationship between the cause and effect This relationship cannot be explained by other factors Don’t include in PFP version!!

Guidelines for Independent and Dependent Variables The dependent variable is always the property you are trying to explain; it is always the object of the research. The independent variable usually occurs earlier in time than the dependent variables. The independent variable is often seen as influencing, directly or indirectly, the dependent variable.

Example 1 Research Question: People 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 variables Gender 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, Jewish, Methodist, Islamic…) Political party identification

Example 2 Number of books read independent variable: Research Question: The number of books read to a child per day positively affects a child’s word recognition. Identify the IV and DV Identify possible control variables Are the causal arguments sound? 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 her/his parent reads to her/him. Number of books read Older siblings Word recognition Health status Birth order

Collecting Data THEORY Develop a research design Asking the Research Question Formulating the Hypotheses 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

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 Measurement Nominal Ordinal Interval-Ratio Not every statistical operation can be used with every variable. The type of statistical operations we employ will depend on how our variables are measured. Variables are measured in three ways: Nominal Ordinal Interval-Ratio Nominal -- means “in name only.” Also known as categorical or qualitative. Ask them for examples of nominal variables: gender, religion, type of company (manufacturing, retail, health services, etc.) Ordinal -- e.g., attitudinal variables (views on abortion) Interval-Ratio -- can ask how much more of X (temperature, income, test scores)

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: Age Income SAT 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 can’t be measured at higher levels. Level Different or Equivalent Higher or Lower How Much Higher Nominal Yes No Ordinal Interval-ratio

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 the Hypotheses 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

Begin the Process Again... Asking the Research Question Formulating the Hypotheses 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