To properly identify the key differences between dependent and independent variables, we need to first understand what variables are. Although the meaning may slightly vary depending on how and in which field it is being used, it points to the same thing—especially in the field of mathematical modelling, statistical modelling and experimental sciences.
Generally, a variable is a character, number, or quantity that can take different values over time. Variables are classified into 2 main types, namely; dependent and independent variables.
This classification is made based on the variable's ability to change without depending on another variable.
Dependent variables are variables whose changes depend solely on another variable—usually the independent variable. That is, the value of the dependent variable will only change if the independent variable changes.
The direction of this change is usually determined by a function which represents the relationship between the dependent and independent variable. In mathematical sciences, it is represented as a function of the independent variable (e.g. y = f(x) = 3x+2, where y is the dependent variable, x is the independent variable and f(x) is the function of the independent variable).
Also known as the predicted variable, we can say that the dependent variable measures the effect of the independent variable on the test unit(s).
Independent variables are variables whose variations do not depend on another variable. They are controlled inputs, whose variation depends on the researcher or individual working with the variables.
Also known as the predictor variable, it is the determinant of the value of the dependent variable. It is usually used to test the rate of change of the dependent variable as it changes under a non-variable condition.
For example, the time taken to move a car from a particular point A to a point B to a varying speed. In this case, the non-variable is the distance covered, the independent variable is the speed while the dependent variable is the time which changes with respect to the change in the speed of the vehicle.
A dependent variable is a variable whose variations depend on another variable—usually the independent variable. An Independent variable is a variable whose variations do not depend on another variable but the researcher experimenting.
Although the variations of these two variables depend on something else in the real sense, the difference is what they depend on. A dependent variable depends on an independent variable, while an independent variable depends on external manipulation.
For example, when measuring how the speed of a car will affect the time it will take to reach a certain place, the time taken (dependent variable) depends on the speed (independent variable). The speed, on the other hand, depends on the driver.
Dependent variables are often referred to as the predicted variable, while the independent variables are the predictors or regressors. They are alternatively called these names because of their role in research experiments.
Independent variables are the variables that determine how dependent variables vary, i.e. they predict dependent variables. Dependent variables, on the other hand, are the variables being predicted by the independent variables.
For example, when predicting the cups of water required to fill a big drum, the predicted variable is the number of cups of water, while the predictor is the size of the cup. If the size of the cup is big, it will take fewer cups and if it is small, it will take more cups to fill the drum.
An example of a dependent variable is a student's class of degree, which depends on the student's CGPA and the school's grade or rating scale. Factors like age, marital status, salary, etc. that influences an individual's cost of living are examples of an independent variable.
These examples are not general, as it may take another position depending on the situation they are being used. For example, the class of degree which is a dependent variable above will become an independent variable if it is being used to determine whether a student qualifies for a scholarship or not.
Similarly, an individual's salary may become a dependent variable, which depends on the years of experience.
In a scientific experiment, the dependent variable is directly used to inform the conclusion of the experiment, while the independent variable is used to determine the values of the dependent variable. The independent variable only indirectly influences the conclusion of the experiment.
For example, when investigating the cause of the increased failure rate in students, they study things like the number of hours spent reading per day by a student. The independent variable is the number of hours spent reading by a student and the dependent variable is the student's grade.
The student's grade is what determines whether the student passed or not. Therefore, directly informing our conclusion on the effect of long hours of reading on students' grades.
Dependent variables cannot be manipulated by the researcher or any other external factor, and as such is not liable to any form of bias. It is neither people to the researcher's bias nor the respondents' bias.
Independent variables are easily obtainable and do not require complex mathematical procedures and observations like dependent variables. This is because it can be easily manipulated by the researcher or collected from respondents through some data collection techniques.
In some cases, the independent variables are natural factors that cannot be manipulated by the researcher, which are also easily obtainable. This results in less time taken to obtain independent variables.
Dependent variables are obtained from longitudinal research or solving complex mathematical equations. This is a very expensive and time-consuming process for the researcher.
Independent variables are prone to researcher and respondents' bias, therefore affecting the results of the research. This can only be completely avoidable if the independent variables are naturally occurring and are not manipulated by the researcher.
For example, when investigating the effect of sunlight on pigmentation, researchers control the exposure of sunlight on each sample of the experiment.
In mathematical and statistical computations, dependent variables are obtained from a predefined formula, while independent variables are usually obtained from respondents or through the manipulation of the researcher.
To obtain the dependent variable, mathematicians need to first define a function showing the relationship between the dependent and independent variables. A formula will then be formulated to solve the function, whose solution is the dependent variable.
In most cases, the relationship between the variables is obtained by studying a small sample of a larger population. An example is a quadratic formula used in solving quadratic equations.
Dependent variables are usually positioned vertically on the graph while independent variables are positioned horizontally. The horizontal axis in the graph is alternatively called the x-axis while the vertical axis is called the y-axis.
The graphs are plotted by tracing each value of the dependent variable horizontally and each value of the independent variable vertically to the point where they both intersect. The points are marked for each variable, and the aggregation of these points is what makes the graph.
These points can be joined together using a straight line, curve or rectangular bars depending on the data visualization techniques chosen by the researcher.
In a research experiment, the dependent variables are usually the effect, while the independent variables are the cause. Also, the relationship between the dependent and independent variables can be said to be a cause and effect relationship.
Let us consider research into the relationship between the nutrients taken by a child and its effect on growth. In this case, the dependent variable is child growth, while the independent variable is the nutrients taken by the child.
The nutrient taken by the child is what will cause the child to grow, making it the cause and child growth the effect.
The values of the dependent variables are strictly obtained through formula, observations, or scientific experiments. Independent values, on the other hand, can be subjected to manipulation by the researcher or respondent's bias.
This is not the case with dependent variables that do not give room for external manipulation. In some cases, the dependent values are obtained through an automated procedure, with little to no involvement from the researcher.
This, however, has some setbacks like a computer error, high cost of maintenance, and lack of proper monitoring
The dependent variable depends on the independent variables, while the independent variable depends on external factors like the researcher, respondents, or natural factors. These factors are what determine the values of the variables.
Dependent variables may also be said to indirectly depend on external factors because of their dependency on independent variables. For instance, if the values of an independent variable being manipulated by the researcher due to personal bias, it will also affect the values of the dependent variable.
This may.also lead to incorrect conclusions since the authenticity of the data has been made questionable by the researcher.
Dependent and independent variables are both variables and therefore have similar characteristics. They can both be used in similar fields of research, mathematics, and statistics. Some of the similarities between dependent and independent variables are highlighted below:
Both dependent and independent variables vary in value as time goes on. They do not have a constant value. This is clear from the fact that they are both types of variables, and variation is one of the general characteristics of a variable. The relationship between these variations may, however, be direct or indirect.
These two variables are used alongside each other, and a change in the independent variable will translate to a change in the dependent variable. That is, they are similar in the sense that they change at the same time.
These changes may, however, occur in the opposite direction to each other.
Dependent variables and independent variables can both take multiple variables. For example, when dealing with a 3-dimensional problem in mathematics, we can have the function:
f(X) =Y, where X=(x1, x2, x3) and Y=(y1, y2, y3).
It is, however, important to note that the multi-variation of these variables do not necessarily have to be of the same dimension. Consider the example function below:
f(X) =y, where X=(x1, x2, x3).
In this case, y is 1-dimensional, while X is 3-dimensional.
Since dependent and independent variables are used alongside each other, it is clear that they can jointly be used to solve a research problem. For example, when investigating the amount of force needed to push a truck, the dependent variable (the distance moved by truck after pushing) and the independent variable (the force needed to push the truck) are both used in this investigation.
As stated earlier, dependent and independent variables have similar uses, which is due to their common identity as a variable. We have highlighted some of these uses below:
Dependent and independent variables are relevant in all fields of mathematics and statistics, and are used to solve complex problems. When dealing with a particular problem, researchers break down the problem into mathematical terms so that it can be easily solved using mathematical techniques.
This can be seen in the case of ordinary differential equations that are used to derive a formula for the rate of change of price, in a market, and also predict future changes.
A similar thing can be seen in statistics, where analysts plot dependent variables against independent variables and use the result to analyze trends and inform decisions.
When behavioural psychologists study human behaviour, they identify particular traits in an individual, then investigate the reason why the trait is being exhibited. This is sometimes done using the brute force approach, where the psychologist will identify particular causes, take them away, then study whether there will be a change in behavioural patterns.
For example, there is a consensus that a person's behaviour depends on the kind of environment (independent variable) he or she is being brought up in. That is why a larger percentage of the people that deal in hard drugs are from the slums.
This conclusion should, however, be made carefully, as it leads to many cases of wrong profiling.
When studying the effect of sunlight on plant pigmentation, biologists take sunlight as the independent variable and plant pigmentation as the dependent variable. The subject of research, in this case, is the plant.
Usually, different samples of the same plant will be exposed to different levels of sunlight over a particular period. The levels of pigmentation, the amount of sunlight exposure, and the duration of the study will be recorded.
All this will be done provided that all other factors that may affect the plant pigmentation, like water and time of observation are equal.
Dependent and Independent variables are used to carry out laboratory experiments in chemistry, and recorded to be used for further research in other fields. Let us consider the study of the amount of heat required to melt gold, which is an element from the periodic table.
Chemists subject gold to a very high temperature until they were able to arrive at the melting point of gold. The dependent variable, in this case, is the state of the gold which changes from solid to liquid, while the independent variable is the temperature.
Today, this information is used by jewellery manufacturers to melt gold and remake them into attractive jewellery. Some even go as far as using it for interior decoration, as there is no limitation on what can be made from hold.
These variables are generally used for research purposes, and no research can be carried out without using dependent and independent variables. This is the reason why dependent and independent variables can be found in every field.
Even during our daily life as an individual, there is always a reason for what we do, and even having no reason is a reason itself. It is a predefined element of nature.
Therefore, whether directly or indirectly, researchers make use of dependent and independent variables.
Variables are generally important for both personal uses by individuals and scientific experiments by researchers. They are one of those things that we use in our daily activities either consciously or unconsciously.
However, a lack of proper understanding will lead to it being misused and may have negative effects. Therefore, to make proper use of variables and inform better decisions, one may need to know what variables are, how, and when you use them.
Variables are divided into dependent and independent types, and understanding the similarities and differences between these 2 variables are the key to their proper use.
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