What is correlation analysis?

Correlation analysis is a staple of data analytics. It’s a commonly used method to measure the relationship between two variables. It helps researchers understand the extent to which changes to the value in one variable are associated with changes to the value in the other. 

This analysis often applies to quantitative data collected through research methods such as naturalistic observation, archival data, live polls, and surveys. The goal is often to identify the relationship, trends, and patterns between two datasets and variables.  

Correlations are often misused and misunderstood, especially in the insight industry. Below is a helpful guide to help you understand the basics and mechanics of correlation analysis. 

Correlation analysis, also known as bivariate, is a statistical test primarily used to identify and explore linear relationships between two variables and then determine the strength and direction of that relationship. It’s mainly used to spot patterns within datasets. 

It’s worth noting that correlation doesn't equate to causation. In essence, one cannot infer a cause-and-effect relationship between the two types of data with correlation analysis. However, you can determine the relationship's size, degree, and direction. 

The degree of association in correlation analysis is measured by a correlation coefficient. The Pearson correlation, which is denoted by r, is the most commonly used coefficient. The correlation coefficient quantifies the degree of linear association between two variables and can take values between -1 and +1.

• No correlation: This is when the value r is zero.

• Low degree: A small correlation is when r lies below ± .29

• Moderate degree: If the value of the correlation coefficient is between ± 0.30 and ± 0.49, then there’s a medium correlation.

• High degree: When the correlation coefficient takes a value between ±0.50 and ±1, it indicates a strong correlation.

• Perfect: A perfect correlation occurs when the value of r is near ±1, indicating that as one variable increases, the other variable either increases (if positive) or decreases (if negative). 

You can also identify the direction of the linear relationship between two variables by the correlation coefficient's sign. 

Positive correlation

Scores from +0.5 to +1 indicate a robust positive correlation, meaning they both increase simultaneously.

Negative correlation

Scores from -0.5 to -1 indicate a sturdy negative correlation, meaning that as a single variable increases, the other reduces proportionally. 

No correlation

If the correlation coefficient is 0, it means there’s no correlation or relationship between the two variables being analyzed. It's worth noting that increasing the sample size can lead to more precise and accurate results.

Significance of the correlation 

Once we learn about the strength and direction of the correlation, it’s critical to evaluate whether the observed correlation is likely to have occurred by chance or whether it’s a real relationship between the two variables. Therefore, we need to test the correlation for significance. The most common method for determining the significance of a correlation coefficient is by conducting a hypothesis test. 

The hypothesis test (t-test) helps us decide whether the value of the population correlation coefficient ρ is "close to zero" or "significantly different from zero." We decide this based on the sample correlation coefficient (r) and the sample size (n). 

As with other hypothesis tests, the significance level is set first, generally at 5%. If the t-test yields a p-value below 5%, we can conclude that the correlation coefficient is significantly different from zero. Furthermore, we simply say that the correlation coefficient is "significant." Otherwise, we wouldn’t have enough evidence to conclude that there’s a true linear relationship between the two variables.

In general, the larger the correlation coefficient (r) and sample size (n), the more likely it is that the correlation is statistically significant. However, it's important to remember that a significant correlation doesn’t necessarily imply causation between the two variables. 

Below are the factors you must consider when arranging a correlation analysis:

• Performing a correlation analysis is only appropriate if there’s evidence of a linear relationship between the quantitative variables. You can use a scatter plot to assess linearity. If you can’t draw a straight line between the points, a correlation analysis isn’t recommended.

• Ensure you draw a dispersed plot since it assists in glancing and uncovering exceptions, heteroscedasticity, and non-linear relations.

• Avoid analyzing correlations when information is rehashed proportions of a similar variable from a similar individual at the equivalent or changed time focus.

• The existing sample size should be determined a priori. 

Correlation analysis is primarily used to quantify the degree to which two variables relate. By using correlation analysis, researchers evaluate the correlation coefficient that tells them to what degree one variable changes when the other changes too. It provides researchers with a linear relationship between two variables. 

Correlation analysis is used by marketers to evaluate the efficiency of a marketing campaign by monitoring and analyzing customers' reactions to various marketing tactics. As such, they can better understand and serve their customers. 

Another use of correlation analysis is among data scientists and experts tasked with data monitoring. They can use correlation analysis for root cause analysis and minimize Time To Deduction (TTD) and Time To Remediation (TTR). 

Different anomalies or two unusual events happening simultaneously or at the same rate can help identify the exact cause of an issue. As a result, users incur a lower cost of experiencing the issue if they can understand and fix it soon using correlation analysis. 

Correlation analysis has numerous business values, including identifying potential inputs for more complex analyses and testing for future changes while holding other factors constant. 

Additionally, businesses can use correlation analysis to understand the relationship between two variables. This type of analysis is easy to interpret and comprehend, as it focuses on the variance of one data row in relation to another dataset.

One of the primary business values of correlation analysis is its ability to identify hidden issues within a company. For example, if there’s a positive correlation between customers looking at reviews for a particular product and whether or not they purchase it, this could indicate a place where testing can provide more information. 

By testing whether increasing the number of people who look at positive product reviews leads to an increase in purchases, businesses can develop hypotheses to improve their products and services.

Correlation analysis can also help businesses diagnose problems with multiple regression models. For instance, if a multivariate or multiple regression model isn’t producing the expected results or if independent variables are not truly independent, correlation analysis can help discover these issues.

In digital environments, correlations can be especially helpful in fueling different hypotheses that can then be rapidly tested. This is because the testing can be low risk and not require a significant investment of time or money. 

With the abundance of data available to businesses, they must be careful in selecting the variables they’ll analyze. By doing so, they can uncover previously hidden relationships between variables and gain insights that can help them make data-driven decisions. 

As previously stated, correlation doesn't strictly imply causation, even when you identify a significant relationship by correlation analysis techniques. You can’t determine the cause by the analysis.

The significant relationship implies that there’s much more to comprehend. Additionally, it implies that there are underlying and extraneous factors that you must further explore to look for a cause. Despite the possibility of a causal relationship existing, it would be irresponsible for researchers to utilize the correlation results as proof of such existence. 

A real-life example of correlation analysis is health improvement vs. medical dose reductions. Medical researchers can use a correlation study in clinical trials to better comprehend how a newly-developed drug impacts patients. 

If a patient's health improves due to taking the drug regularly, there’s a positive correlation. Conversely, if the patient's health deteriorates or doesn't improve, there’s no correlation between the two variables (health and the drug).

Correlation shows us the direction and strength of a relationship between two variables. It’s expressed numerically by the correlation coefficient. Correlation analysis, on the other hand, is a statistical test that reveals the relationship between two variables/datasets.

Regression and correlation are the most popular methods used to examine the linear relationship between two quantitative variables. Correlation measures how strong the relationship is between a pair of variables, while regression is used to describe the relationship as an equation. 

Correlation analysis can help you to identify possible inputs for a more refined analysis. You can also use it to test for future changes while holding other things constant. The whole purpose of using correlations in research is to determine which variables are connected.