Dependent and Independent Variables

We explain what dependent and independent variables are and the relationship between them. In addition, quantitative and qualitative variables.

1. Dependent and independent variables

Variables are symbols that represent some type of quantity or indeterminate factor, that is, that can vary, that is not fixed. It is the opposite, in that sense, to a constant . When they are mathematical symbols they are usually represented with letters (x, y), but they can also be logical or otherwise.

Among the variables , independent variables are those that can take various numerical values ​​(or arguments) and are generally represented as x . The independent variables directly affect the dependent variables (generally and ).

The difference between them has to do with the fact that one depends on the other, and therefore the relationship between the two can be used in a controlled way to study the way in which said dependence occurs. That is, they can be understood as cause ( x ) and effect ( y ), since the independent variable is in the hands of the researcher, while the other is not .

Let’s try to explain this with an example . If we know that for every hamburger we eat we should do two hours of exercise, we can express the relationship between both things in a mathematical way by saying that for every x hamburger meals, we will get 2 and hours of exercise, because x = 2y.

The independent variable is hamburgers, since we can eat the amount that we decide freely, while the dependent variable will always be the amount of hours of exercise, as they emerge from the first premise.

2. Variables of an investigation

Variables are a fundamental aspect of any investigation or experiment. The way to determine the relationship between the variables that concern us , that is, to propose the beginning of the investigation, will be known as hypotheses and consists of particular statements.

Apart from what has already been explained of the dependent and independent variables, we can talk about other possible types of variable:

• Quantitative variables . They are those that represent expressible relationships in terms of quantity, that is, quantifiable, numerable. They are classified as discrete (the set of all possible values ​​expressed in isolated points) and continuous (intervals between points or possible values ​​within a range).
• Qualitative variables . On the contrary, they represent relationships of meaning, property or quality, not numerically expressible. They are classified in turn in nominal (serve to name, has no inherent order or sequence) or ordinal (obey an ordered series, expressing degrees of the same thing).

3. Examples of variables

Next we will propose a series of statements in which the independent variables ( x ) are differentiated from the dependent ones ( y ):

• The ozone layer of the atmosphere shrinks in a certain amount (y) with each ton of toxic gases emitted monthly (x).
• Cigarette smoking (x) decreases physical endurance (y).
• It is desired to study the impact of the consumption of yerba mate (x) on the frequency of colon cancer in Uruguayan society (y).
• Experts affirm an inversely proportional relationship between the intelligence of an individual (x) and their levels of political fanaticism (y).
• Scientists suspect that a certain type of bacteria reproduces more easily (y) in the presence of some organic alkaloids (x).