When diving into statistics, understanding the concepts of variance, covariance, and correlation can seem like navigating a complex maze. However, these tools are essential for making sense of data and drawing meaningful insights.
Whether you’re assessing market trends or evaluating research findings, understanding these measurements is crucial. Grasping how variance, covariance, and correlation work can help you gain a clearer picture of your data. This knowledge will empower you to make informed decisions.
In this blog, we will break down these key statistical concepts in a straightforward and accessible manner. Our goal is to help you understand and apply them effectively.
What is Variance?
In statistics, variance refers to the spread of a data set. This measurement identifies how far each number in the data set is from the mean.
This is particularly useful in market research for calculating the likelihood of future events. A variance of zero indicates all values in a data set are identical, while any positive variance shows some degree of spread.
The larger the variance, the more spread in the data set. A large variance means that the numbers in a set are far from the mean and each other. A small variance means that the numbers are closer together in value.
How to Calculate Variance
To calculate variance, first find the differences between each number in the data set and the mean. Next, square these differences. Finally, divide the sum of the squared differences by the number of values in the set.
The formula for variance is as follows:
In this formula, X represents an individual data point. The symbol u stands for the mean of the data points. Finally, N indicates the total number of data points.
Note that while calculating a sample variance in order to estimate a population variance, the denominator of the variance equation becomes N – 1. This removes bias from the estimation, as it prohibits the researcher from underestimating the population variance.
Advantages of Variance
One of the primary advantages of variance is that it treats all deviations from the mean of the data set in the same way, regardless of direction.
This prevents the squared deviations from summing to zero, which would otherwise suggest no variability in the data set.
Disadvantage of Variance
One of the most commonly discussed disadvantages of variance is that it gives added weight to numbers that are far from the mean, or outliers. Squaring these deviations can sometimes skew the interpretation of the data.
What is Covariance?
Covariance provides insight into how two variables are related to one another.
More precisely, covariance refers to the measure of how two random variables in a data set will change together.
A positive covariance means the variables at hand are positively related. Meaning they move in the same direction.
A negative covariance means the variables are inversely related, or that they move in opposite directions.
How to Calculate Covariance
The formula for covariance is as follows:
In this formula, X represents the independent variable, Y represents the dependent variable, N represents the number of data points in the sample, x-bar represents the mean of the X, and y-bar represents the mean of the dependent variable Y.
Covariance vs Correlation Are They The Same?
Simply put, no.
Both covariance and correlation show whether variables are positively or inversely related, but they are not the same.
This is because correlation also informs the degree to which the variables move together.
Researchers use covariance to measure variables with different units of measurement. By leveraging covariance, researchers are able to determine whether units are increasing or decreasing. However, they are unable to solidify the degree to which the variables are moving together. This is due to the fact that covariance does not use one standardized unit of measurement.
Correlation, on the other hand, standardizes the measure of interdependence between two variables. Therefore, it informs researchers as to how closely the two variables move together.
Correlation Coefficient
We use the term “correlation coefficient” to refer to the resulting correlation measurement. It will always maintain a value between one and negative one.
When the correlation coefficient is one, the variables under examination have a perfect positive correlation. When one moves, so does the other in the same direction, proportionally.
If the correlation coefficient is less than one, but still greater than zero, it indicates a less than perfect positive correlation. The closer the correlation coefficient gets to one, the stronger the correlation between the two variables.
When the correlation coefficient is zero, it means that there is no identifiable relationship between the variables. If one variable moves, it’s impossible to make predictions about the movement of the other variable.
A correlation coefficient of negative one indicates that the variables are perfectly negatively or inversely correlated. If one variable increases, the other will decrease at the same proportion. The variables will move in opposite directions from each other.
If the correlation coefficient is greater than negative one, it indicates that there is an imperfect negative correlation. As the correlation approaches negative one, the correlation grows.
Now that you have a basic understanding of variance, covariance, and correlation, you’ll be able to avoid the common confusion that researchers experience all too often.
