Variables can be related to each other in many ways. Obviously, when more than a few variables are involved, the patterns of relationship can become quite complex. What I want to do here is talk about some of the most simple relationships involving only 2 or 3 variables.  

       1. Causal   

     This is what we would always like to find, some variable that causes change in some other variable as it changes in some specified way. If the change in the first variable is enough by itself to cause the change in the second variable, we can say that this variable is sufficient to cause a change in the second variable. One thing that social scientists look for as evidence of a causal relationship is the time relationship between the changes that occur in the variables. If the change in the second one consistently follows the change in the first, you have pretty good evidence for a causal relationship.  

     A useful way to talk about these relationships is to use diagrams, sometimes called "arrow diagrams," or path diagrams.  A causal relationship where a change in variable A is sufficient for a change in variable B is shown below.

                            A ‑‑‑‑‑‑‑‑‑> B  

     We use some special names for the roles each of these variables play in this relationship. A is called the independent variable, and B is called the dependent variable. One way to think about and remember this is to say that the dependent variable depends on the independent variable in the relationship. Look at the arrow diagram and say this a couple of times.   

     Many examples of this simple yet most important relationship exist. Let's look at one that is of political significance in the South and in South Carolina in particular. It is one that has great implications for social and medical policy in the region. It involves the question of infant mortality (measured by deaths per 1000 births before the age of 1 year). The South has long had the highest rates of infant mortality in the nation, and South Carolina has about the highest of any state. Why? To answer that question we must look for causal variables. One that medical science has well established as a causal factor is birth weight. The relationship can be described as follows: the lower the birth weight, the more likely an infant is to die. In arrow diagram form: 

              Birth Weight ‑‑‑‑‑‑‑‑‑‑‑> Infant Mortality 

     Let's make the picture a little more complicated and add a third variable that also has a causal relationship with the other two. Suppose the arrow diagram looks as follows: 

                     A ‑‑‑‑‑‑‑‑‑> B ‑‑‑‑‑‑‑‑‑> C    

     Now we have two causal relationships, one between A and B, and a second one between B and C. In a sense, there is also a third one between A and C, but it is mediated by variable B. In this case, variable B is called an intervening variable. In order to specify the role that each variable plays, we must talk about the role it plays in relation to some other variable(s). For example, A is an independent variable with respect to B, and B is an independent variable with respect to C, but with respect to A and C both, B is an intervening variable. Got it?

     Let's apply this terminology to our infant mortality example and expand it a bit. So low birth weight causes high infant mortality‑‑so what? If we think about what causes low birth weight, we begin to see the public policy implications. One of the principal causes of low birth weight is poor nutrition, and one of the principal causes of poor nutrition is poverty. I've added two intervening variables and now you see the southern connection. Here's what we have in arrow diagram form. 

                poverty ‑‑> poor nutrition ‑‑> birth weight ‑‑> infant mortality

 

     A good exercise at this point would be for you to describe the roles that each of these variables play with respect to the other variables. Try it!

     Although we may say a relationship is causal, in reality what usually happens in the complex world of human behavior is much weaker than that.  The independent variable usually does not cause a change in the dependent variable, but merely makes some change more likely to happen. We might say that many of our causal relationships are really about variables that  make something more likely to happen, but are neither necessary nor sufficient in making it happen. For example, low education contributes to poverty by making poverty more likely. But low education is neither necessary nor sufficient in creating poverty. And, until we get to a certain level of really low poverty, poverty only contributes to poor nutrition 

       2. Conditioning 

     Now we will start making things a little more complicated.  Sometimes a third variable weakens or strengthens a relationship.  Then we say that a variable plays a conditioning role in the relationship, or to put it another way, the relationship only exists (or is more likely to exist) under certain conditions.  

     To use our example about infant mortality, we might say that knowledge about good nutrition will not by itself cause a person to have good nutrition. Nutritional knowledge is more likely to lead to good nutrition under the condition of financial means. So financial means conditions the relationship between nutritional knowledge and the actual practice of good nutrition. Knowing the conditioning variables is politically important, because if we want to do something about infant mortality, for example, we might want to create programs and/or policies that create the right conditions for decreasing infant mortality or increasing good nutritional practices, which we know helps reduce infant mortality.  

     In path diagram form, we have a relationship between A and B that is affected, or conditioned, by the value of a third variable C. So in terms of our example, A is nutritional knowledge and B is the practice of nutrition, and C, the conditioning variable, is financial means. You must  have the money to buy and consume the things you know are good for you. And just in case you did not know this, it turns out that better food generally costs more, so knowledge by itself is not really enough!  

                                         A --------------------------------à B

                                                           /\

                                                            |

                                                            |

                                                            |

                                                           C   

       3. Reciprocal 

     An easy way to think about a reciprocal relationship is to think of it as a two directional causal relationship. Each variable simultaneously plays the role of both independent and dependent variable. Each reinforces the other. Unlike a simple causal relationship, no clear indication tells us which variable changes first in time. Either variable could change first, or the changes may be so close in time that telling which came first is impossible to tell. A reciprocal relationship is shown in an arrow diagram as follows. 

                                    A <‑‑‑‑‑‑‑‑> B

 

     Although making the example of infant mortality illustrate this kind of relationship is a bit more difficult, we can make it fit if we stretch things a bit. Low concern over nutrition tends to reduce nutrition. However, we might also make an equally strong argument that poor nutrition leads one to be less concerned about good nutrition. To the extent that poor general health causes low motivation in all areas of life, poor nutrition may cause low nutritional motivation. Which comes first? Logically, either could happen first.    

       4. Symmetrical 

     This is a rather simple situation where one variable simultaneously causes changes in two other variables. Or you might say that we have one independent variable and two dependent variables. The arrow diagram is as follows.

  The significance of this simple relationship is in our next type of relationship, or to be more precise, "non-relationship." 

       5. Spurious  

     This is an apparent, yet false causal relationship that is the result of some unknown third variable having a symmetrical relationship with the first two variables. Therefore, a spurious relationship is an untrue relationship. This could be diagramed in an arrow diagram as shown below. 

     This poses a great problem for researchers. Every causal relationship is potentially spurious. We never know for sure until we have tested all possible third variables. The process of doing this is called controlling for third variables. The fact that we can never control for all third variables along with the fact that we may someday find some third variable that renders what we thought to be a causal relationship to be spurious are additional reasons why scientific explanations are open and always subject to change. 

     For example, medical researchers noticed that people with very low levels of cholesterol have higher death rates. They wondered what was going on, because low cholesterol is supposed to be good.            

                        low cholesterol --------------> high death rate 

     As good researchers, they looked at things that could cause this relationship to be spurious. Pretty quickly they found some good candidates for that third variable: smoking and alcohol. High levels of alcohol consumption and heavy smoking depress the appetite and cause cholesterol to be low. Simultaneously, these activities contribute to higher death rates.

       6. Controlling for a Third Variable 

     When we are trying to see if a relationship is spurious, we control for whatever third variables we think might be related to both the independent and dependent variables. We do this by reexamining the relationship for each value of the control variable. Using the example above about cholesterol and death rates, we would control for smoking by looking at the relationship for smokers and then look again for non-smokers. If the relationship is spurious, then the relationship between cholesterol and  death rate would disappear when looking at each group alone.  

     It turns out that this is the very same test for seeing if a third variable intervenes between an independent and dependent variable. When you control for the possible intervening variable, the relationship disappears.  

     Let's look back at our example of infant mortality. Here is where it gets complicated and highly controversial. Researchers have long noted a relationship between race and infant mortality. Black mothers are more likely to have underweight infants than are white mothers. Most observers regarded this apparent relationship between race and birth weight as spurious. The third variable was assumed to be poverty. Here is what that relationship would look like in path diagram form. This looks like the arrow diagram for the spurious relationship, but because the arrow between race and poverty is in the other direction, it is really the diagram for an intervening relationship.

      Theoretically, direction of the arrow makes a logical difference (poverty would be an intervening variable rather than a variable that makes the original relationship possible spurious), but  direction makes no statistical difference. How can you tell if the relationship is intervening or possible spurious? How can you tell the direction of the arrow? The answer is theory! Having poverty affect the race of a person makes no sense.

     Back to the question of controlling. The point is that if we would control for poverty, the relationship between race and birthweight, and in turn, mortality, should disappear. This is because the effects of race work through poverty and would have no direct effect itself. At least that is what we thought.