Costos terciarios

There are many ways to characterize variables: one of the most common is by the roles they play in a research design or data analysis.Using those criteria, a simple way to describe variables is as eitherdependent, if they represent some outcome of the study, or independent, if they are presumed to influence the value of the dependent variable(s).Many study designs include a third category,control vari-

ables, which may influence the dependent variable but are not the main focus of

interest.

Note that the labels “independent,” “dependent,” and “control” relate to the roles played by the variables in a given design or experiment.This is because a vari- able, for instance weight, could easily be an independent variable in one study, a dependent variable in another, and a control variable in a third.In addition, other labels are also used to describe dependent and independent variables, with some authors preferring to reserve specific labels for particular types of studies.Control variables are particularly problematic because many types of control variables have been defined, depending on their relationship to the independent and depen- dent variables of interest, and the type of study design employed.This discussion will concentrate on independent and dependent variables, and leave the discus- sion of control variables to the chapters relating to specific study designs.

We will use the example of a regression equation to illustrate the concept of inde- pendent and dependent variables.This is just a brief introduction: the topic of regression is covered in detail in Chapters 12 and 14.

In a standard linear model such as an OLS regression equation (OLS means Ordi- nary Least Squares; if not otherwise specified, this is what is meant by a regression equation), the outcome or dependent variable is customarily indicated by the letter Y, while the independent variables are indicated by X.Subscripts are used to identify each individual X variable: X1, X2, and so on.

This should be clear from the conventional way of notating a regression equation:

Theein this equation means “error” and refers to the fact that we don’t expect any regression equation to perfectly predictY.Note that eachXin the equation is preceded by aβ, which is called itsregression coefficient:β1is the regression coef- ficient forX1,β2is the regression coefficient forX2, and so on.These coefficients are determined through a mathematical process in order to make the best possible equation for predicting the value ofY from the value of theXs.

5 1     5! 1!5–1)! --- 5×4×3×2×1 1 4( ×3×2×1) --- 5 = = = P n( =1) = 5×(0. 5)×(0.5)4 = 0.156 Y = β0+β1X₁+β2X₂+β3X₃+…+e

Populations and Samples | 133

Inferential

Statistics

Because of this notational convention, the dependent variable is also referred to as the “Y variable” and the independent variables as the “X variables.” Other terms used for the dependent variable include theoutcome variable, theresponse vari- able, and theexplained variable.Other names for independent variables include

regressors,predictor variables, andexplanatory variables.

Some researchers believe that the terms independent and dependent should be reserved for experimental studies, in which case at least the primary independent variables have been manipulated in some way by the researcher, while the values for the dependent variable are merely observed and recorded.In this interpreta- tion, the terms “independent” and “dependent” imply causality, i.e., that the value of the dependent variabledependsat least in part on the values of the inde- pendent variables, a statement that is impossible to establish in many nonexperimental designs.This may be illustrated by comparing a randomized controlled trial (an experimental design) with a cross-sectional survey (an observa- tional design).

In a randomized clinical trial of the effects of a new drug on hypertension, if the correct procedures are followed and significant results are achieved, the researcher can be comfortable (or as comfortable as one can ever be when dealing with infer- ential statistics, whose conclusions are inherently probabilistic rather than absolute) in asserting that changes in blood pressure observed were caused or influenced by the new drug.

In a cross-sectional survey of juvenile delinquency and drug use, however, it is impossible to establish a causal effect because either variable could cause the other, and any relationships found could be due to other variables.For instance, children who use drugs may be more likely to become delinquent, or delinquents may be more likely to use drugs.Even if this issue is resolved by including tempo- rality in these questions (it might be possible to determine which came first, drug use or delinquency) the explanation cannot be discarded that those who use drugs (a self-selected group) differ in other ways from those who do not.For instance, the drug users may be less intelligent, or more intelligent, than the nondrug users, or may have different family circumstances, and either of those variables could influence delinquency independently of drug use.

Populations and Samples

The concept of populations and samples, discussed briefly in Chapter 4, is crucial to understanding inferential statistics.The process of defining the population and selecting an appropriate sampling method can be quite complex (in fact, many doctoral-level statisticians specialize in just that type of work) and requires more study than can be covered here.Instead, the basic issues and concepts will be discussed, and the reader interested in further information on the subject should consult a specialized textbook (several are listed in Appendix C).

The population of interest (often called merely “the population”) consists of all the people or other units (for instance, airplane parts or Atlantic salmon) that the researchers would like to study, if they had infinite resources.To put it another way, the population of interest is all the units to which the researchers would like to be able to generalize their results.Defining the population of interest is the first

step in drawing a sample: it may be very broad, such as everyone living in the United States in 2007, or narrow, such as Canadian men aged 65–75 with a diag- nosis of congestive heart failure.

Almost all research is based on a study sample drawn from a population, rather than the population itself, for practical reasons.The rare exceptions are studies such as those based on the U.S. census, which intends to collect data from every individual living in the United States in a particular year.