# Relationships Between Variables

In dealing with relationships between variables in research, we observe a variety of dimensions in these relationships.

## Positive and Negative Relationship

Two or more variables may have a positive, negative, or no relationship. In the case of two variables, a positive relationship is one in which both variables vary in the same direction.

However, they are said to have a negative relationship when they vary in opposite directions.

When a change in the other variable does not accompany the change or movement of one variable, we say that the variables in question are unrelated.

For example, if an increase in his wage rate accompanies one’s job experience, the relationship between job experience and the wage rate is positive.

If an increase in an individual’s education level decreases his desire for additional children, the relationship is negative or inverse.

If the level of education does not have any bearing on the desire, we say that the variables’ desire for additional children and ‘education’ are unrelated.

### Strength of Relationship

Once it has been established that two variables are related, we want to ascertain how strongly they are related.

A common statistic to measure the strength of a relationship is the so-called **correlation coefficient **symbolized by *r. r* is a unit-free measure, lying between -1 and +1 inclusive, with zero signifying no linear relationship.

As far as the prediction of one variable from the knowledge of the other variable is concerned, a value of r= +1 means a 100% accuracy in predicting a positive relationship between the two variables, and a value of r = -1 means a 100% accuracy in predicting a negative relationship between the two variables.

## Symmetrical Relationship

So far, we have discussed only symmetrical relationships in which a change in the other variable accompanies a change in either variable.

This relationship does not indicate which variable is the independent variable and which variable is the dependent variable.

In other words, you can label either of the variables as the independent variable.

Such a relationship is a symmetrical** relationship. **In an **asymmetrical relationship, **a change in variable *X* (say) is accompanied by a change in variable *Y,* but not vice versa.

The amount of rainfall, for example, will increase productivity, but productivity will not affect the rainfall. This is an asymmetrical relationship.

Similarly, the relationship between smoking and lung cancer would be asymmetrical because smoking could cause cancer, but lung cancer could not cause smoking.

## Causal Relationship

Indicating a relationship between two variables does not automatically ensure that changes in one variable cause changes in another.

It is, however, very difficult to establish the existence of causality between variables. While no one can ever be certain that variable *A* causes variable *B*, one can gather some evidence that increases our belief that *A* leads to *B.*

In an attempt to do so, we seek the following evidence:

- Is there a relationship between
*A*and*B?*When such evidence exists, it indicates a possible causal link between the variables. - Is the relationship asymmetrical so that a change in
*A*results in*B*but not vice-versa? In other words, does*A*occur before*B?*If we find that*B*occurs before*A,*we can have little confidence that*A*causes. - Does a change in A result in a change in B regardless of the actions of other factors? Or, is it possible to eliminate other possible causes of
*B?*Can one determine that C,*D,*and*E*(say) do not co-vary with*B*in a way that suggests possible causal connections?

## Linear and Non-linear Relationship

A linear relationship is a straight-line relationship between two variables, where the variables vary at the same rate regardless of whether the values are low, high, or intermediate.

This is in contrast with the non-linear (or curvilinear) relationships, where the rate at which one variable changes in value may differ for different values of the second variable.

Whether a variable is linearly related to the other variable or not can simply be ascertained by plotting the K values against *X* values.

If the values, when plotted, appear to lie on a straight line, the existence of a linear relationship between *X* and *Y* is suggested.

Height and weight almost always have an approximately linear relationship, while age and fertility rates have a non-linear relationship.