7964
Lecture 1

This lecture introduces various concepts regarding statistics, focusing on the concept of "variables".

I. Terminology

Let's start with some terminology.

• Raw data: Raw data is a term for numbers and category labels that have been collected, but not have been processed in any way. For instance, if I were to conduct a survey across students in 7964, the raw data would be the answers -- fixed response or open response -- to the survey questions.
  
  
• Variable: A variable is a characteristic that can differ (vary) from one individual to the next. For instance, a person's sex (can be either male or female), the number of classes students have had in statistics prior to 7964, and so on.
  
  
• units of analysis are the things that you are studying. So, if you are studying legislators, and you have a database that has a number of characteristics for each legislator, then the units of analysis are the legislators. If you are studying arrests, the units of analysis might be the individual arrests.
  
  
• A population is the collection of all the cases (or units) that you are interested in. Political pollsters, for instance, may be interested in all eligible voters in the New Orleans mayoral election. The size of the population--or the number of cases in the population--is denoted by N (note-- upper case).
  
  
  
• A sample is a smaller subset of the population--since it is often prohibitively time consuming and costly to study the entire population, researchers often study samples. We'll talk more about how to draw samples from a population later on. The size of the sample is denoted by n (note -- lower case). n is always smaller than N.

II. Types of variables

• A.Levels: Categorical, Ordinal, Interval
  
  
  • categorical variable: categorical variables do not have any logical ordering. An example would be the variable of religion: specific values for cases could be Christian, Jewish, Muslim, etc. Categorical variables are sometimes called "nominal variables".
    
    
  • ordinal level variable: ordinal level variables have an order, but the distance between each possible value or each level is not necessarily the same. For instance, state newspapers sometimes release rankings of state legislators by effectiveness-- effectiveness is a variable (it varies across cases of legislators). But the difference in effectiveness between the most effective legislator and the second most effective legislator is not necessarily the same as the distance between the 5th most effective legislator and the 6th most effective legislator. The legislators can be ordered, but one doesn't assume that the ordering is an interval level scale.
    
    
  • Interval level variable: interval level variables have an order, and the distance between each possible value or each level is the same. For instance, seniority in legislatures, or number of years of schooling--the distance between one year and two years is the same as the distance between four years and five years.
    
    

  B. Quantitative variables; continuous variables

  • quantitative variables: raw data for quantitative variables are recorded as numerical values (but they can be either ordinal, or interval level variables). Generally, categorical variables are not considered quantitative variables--even if they are coded as numbers (for instance, Jewish=1, Catholic=2, Protestant=3, Muslim=4, etc.)
    
    
    • Other ways to refer to "quantitative variable" would include measurement variable and numerical variable.
    
    
    
  • A continuous variable is one in which every value within some interval is a possible result. So, for instance, height can be thought of as a continuous variable-- every possible value within some range is a possible height (of course, we can't measure height so precisely to capture every possible value, out to the infinite decimal point).

  C. Explanatory versus Dependent/Response Variables
  

  Whether one is dealing with a population or a sample (that is, a subset of a population), often researchers think in terms of what factors (or variables) might predict (or explain) variables of interest. What predicts the decision to turn out to vote? What predicts the decision to drop out of high school? Perhaps income, family attitudes toward education, family education, etc. Given that, we can think of variables in the following manner:
  
  
  • An explanatory variable is a variable which is thought to partially explain-- or predict--the value of another variable. Generally, explanatory variables (or independent variables, or exogenous variables) are thought to be variables that are not influenced by other variables in the research model. So, for instance, if a researcher examines whether partisanship influences voting behavior--partisanship is seen as an "exogeneous", "explanatory", or "independent" variable. So, family education is an "independent" variable; in the simple model predicting dropping out of high school, family education is not influenced by other variables in the model.
    
    
  • A response variable is the variable that "responds to" or is influenced by the (or several) explanatory variable(s). Response variables--sometimes called endogenous variables or dependent variables--are influenced by other variables in the model. So "dropped out of high school" is a dependent variable.
  
  

III. Questions

• 1. What are some variables that might be commonly encountered in your own field? How would you classify them -- given the above classifications and definitions?
  
  
• 2. Is a social security number a quantitative variable? Why or why not?
  
  
• 3. Define the following terms:
  • raw data
  • variable
  • categorical variable
  • ordinal variable
  • interval variable
  • continuous variables
  • explanatory variable or independent variable
  • response or dependent variable