# Correlation analysis between metrics: what you need and how to carry it out

Have you ever wondered if there is a causal relationship between two variables just because they are correlated? Or perhaps you are trying to figure out if there is a correlation between two features in your dataset? If so, keep reading to learn about the best approach to tackle these questions.

This article will delve into the world of correlation analysis and how it can assist your organization in making data-driven decisions. We will explore the concepts of positive and negative correlation and how you can apply these analytical tools to identify patterns and trends in your data.

Table of Content

## What is correlation analysis?

A correlation analysis is a statistical technique used to determine whether a relationship exists between two or more variables. In other words, it helps to understand if one variable moves as a function of another, if they are related in some way.

The correlation between two variables is determined by a numerical value called the correlation coefficient, which can range from -1 to 1. When the coefficient is close to 1, it indicates a strong positive correlation between the variables. Conversely, when it is close to -1, it indicates a strong negative correlation. If the coefficient is near 0, it suggests that there is little to no correlation between the two variables.

## When is it necessary to perform a correlation analysis?

From a business perspective, this technique can be very useful in answering questions such as:

• What is the relationship between two usage characteristics of our product? For example, is there a correlation between the amount of time users spend in a certain section of your application and their conversion rate?
• Are they dependent or independent? Do they increase and decrease together (positive correlation)? This refers to whether the two variables move in the same direction. For example, as website traffic increases, does the number of purchases made also increase?
• Does one increase when the other decreases and vice versa (negative correlation)? Or are they not correlated at all? This refers to whether the two variables move in opposite directions. For example, as the price of your product increases, does the quantity sold decrease?
• Does a change in price affect subscription creation? This involves evaluating whether there is a correlation between the price of your product and the number of subscriptions created.
• Does an increase in comments influence reshares? Here, you would evaluate whether there is a correlation between the number of comments on a post and the number of times it is shared.

Correlation analysis is one of the most common ways to understand the relationship between two or more variables. However, it is important to note that there are other analytical techniques that can also be useful for answering similar questions, such as hypothesis testing, decision trees, network analysis, matrices, or classification. Nevertheless, correlation analysis is one of the most common ways to understand the relationship between two or more variables.

Next, we will demonstrate how to perform correlation analysis using Python Pandas and how to read a resulting heatmap from a correlation analysis.

## Correlation Analysis in Python Pandas

Creating a correlation plot in Python Pandas is a straightforward process.

To begin, ensure that your data only contains numerical and boolean variables in the columns (other data types will be ignored by the function). You don’t need to be concerned about missing values since the function will automatically exclude them.

Once your data is properly formatted, you can easily generate a correlation plot by running a few simple commands:

DataFrame.corr() or DataFrame.corr(method =’pearson’)

This will only work for data in DataFrame format. You can also run Series.corr() to calculate the correlation between 2 series.

DataFrame.corr() returns a table of correlations between the variables in the data set. Here is an example output:

We can observe that both score and num_comments are highly positively correlated with a correlation value of 0.63. There is some positive correlation of 0.2 between total awards received and score (0.2) and num_comments (0.1).

## How to create and interpret heat maps

To improve the visual representation of the correlation analysis, we can display the correlation table using a heatmap. This will provide a clear visual representation of the strength and direction of the correlations between the variables.

To create it we can use the following code:

When executed, it returns a correlation graph:

Each square shows how each pair of variables is related. If the number is close to zero, that means there is no relationship between them. But if the number is closer to 1 or -1, it means that there is a strong relationship between them.

To interpret this graph in one pass we must look at the colors, the darker the square, the stronger the relationship between the two variables. The diagonal squares are all 1 because the same variables are being compared and are therefore perfectly related. It is important to note that the graph is symmetrical and diagonal because we are comparing the same variables on both sides.

Another example of this type of graph is intended to show whether there is a relationship between variables such as having children, parents, siblings, expensive tickets (fare) or a specific age, all compared to the survival of passengers on the Titanic (yes, it is a sad but effective example). In this case, the graph shows that there are not very strong relationships between the different variables, but it helps us to know which variables are important in predicting passenger survival.

We observe that the strongest correlation, which is 0.4, is present between parents/children and siblings. Based on this, we can conclude that the variables are not significantly correlated. However, this correlation analysis can help us identify appropriate variables to use as inputs for developing a machine learning model that predicts the probability of passenger survival.

## Correlation imply causation?

It is important to note that correlation does not imply causality. Although a strong and significant correlation suggests a possible causal relationship, it is not a conclusive proof. Correlation may be the result of coincidence or there may be an unknown third variable that influences both variables. Therefore, it is necessary to evaluate other factors before concluding a causal relationship.

• Strength: a relationship is more likely to be causal if the correlation coefficient is large and statistically significant. This is directly related to the output data from the correlation table.
• Consistency: a relationship is more likely to be causal if it can be reproduced.
• Temporality: a relationship is more likely to be causal if the effect always occurs after the cause.
• Gradient: a relationship is more likely to be causal if greater exposure to the alleged cause produces a greater effect. This is related to positive or negative correlation. As mentioned earlier, negative correlation occurs when one variable decreases as the other increases.
• Experiment: a relationship is more likely to be causal if it can be experimentally verified. You can perform hypothesis tests to demonstrate this.
• Analogy: a relationship is more likely to be causal if there are proven relationships between similar causes and effects.

## Conclusion

In this article we have explained the usefulness of correlation analysis in identifying patterns and trends in large data sets. In addition, we showed you how to perform correlation analysis in Python Pandas and how to interpret different heat maps and correlation tables. We also explore case studies of using correlation analysis and discuss the importance of keeping in mind that correlation does not imply causation.

By understanding correlation analysis and its effective application, companies can make data-driven decisions more reliably and improve the effectiveness of their business strategies.