correlation hypothesis testing excel

Statistics Made Easy

How to Perform a Correlation Test in Excel (Step-by-Step)

One way to quantify the relationship between two variables is to use the Pearson correlation coefficient which is a measure of the linear association between two variables.

It always takes on a value between -1 and 1 where:

• -1 indicates a perfectly negative linear correlation between two variables
• 0 indicates no linear correlation between two variables
• 1 indicates a perfectly positive linear correlation between two variables

To determine if a correlation coefficient is statistically significant you can perform a correlation test, which involves calculating a t-score and a corresponding p-value.

The formula to calculate the t-score is:

t = r√ (n-2) / (1-r 2 )

• r: Correlation coefficient
• n: The sample size

The p-value is calculated as the corresponding two-sided p-value for the t-distribution with n-2 degrees of freedom.

The following step-by-step example shows how to perform a correlation test in Excel.

Step 1: Enter the Data

First, let’s enter some data values for two variables in Excel:

Step 2: Calculate the Correlation Coefficient

Next, we can use the CORREL() function to calculate the correlation coefficient between the two variables:

The correlation coefficient between the two variables turns out to be 0.803702 .

This is a highly positive correlation coefficient, but to determine if it’s statistically significant we need to calculate the corresponding t-score and p-value.

Step 3: Calculate the Test Statistic and P-Value

Next, we can use the following formulas to calculate the test statistic and the corresponding p-value:

The test statistic turns out to be 4.27124 and the corresponding p-value is  0.001634 .

Since this p-value is less than .05, we have sufficient evidence to say that the correlation between the two variables is statistically significant. 

Additional Resources

How to Create a Correlation Matrix in Excel How to Calculate Spearman Rank Correlation in Excel How to Calculate Rolling Correlation in Excel

Published by Zach

Leave a reply cancel reply.

Your email address will not be published. Required fields are marked *

Excel Tutorial: How To Test Correlation In Excel

Introduction.

Understanding the relationship between variables is a crucial aspect of data analysis. Testing correlation allows us to determine the strength and direction of the relationship between two or more variables, providing valuable insights into patterns and trends within the data. In this Excel tutorial , we will explore the step-by-step process of testing correlation in Excel, empowering you to make informed decisions based on your data.

Key Takeaways

• Understanding correlation is essential for data analysis and provides valuable insights into relationships between variables.
• Excel can be used to test correlation, and this tutorial will guide you through the step-by-step process.
• Interpreting correlation coefficients and understanding their significance is crucial for making informed decisions based on data.
• Statistical significance in correlation testing can be calculated using Excel, adding credibility to the results.
• Avoid common mistakes in correlation testing in Excel by following the provided tips for accurate results.

Understanding Correlation

Correlation is a statistical measure that describes the extent to which two or more variables change together. It is a crucial tool in data analysis as it helps in identifying relationships between variables, making it easier to interpret and make decisions based on the data.

Correlation measures the strength and direction of the relationship between two variables. It ranges from -1 to 1, where a value of 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation. In data analysis, correlation helps in understanding the patterns and making predictions based on the data.

Positive correlation occurs when the variables move in the same direction, i.e., as one variable increases, the other also increases. Negative correlation, on the other hand, happens when the variables move in opposite directions, i.e., as one variable increases, the other decreases. Finally, no correlation means that there is no evident relationship between the variables.

Using Excel for Correlation Testing

Correlation testing is a powerful tool for analyzing the relationship between two variables. In Excel, you can easily perform correlation testing using the CORREL function. In this tutorial, we will discuss the steps for preparing data in Excel for correlation testing and explain how to use the CORREL function to calculate correlation.

A. Preparing Data in Excel for Correlation Testing

• Organize your data: Before conducting correlation testing, it's important to organize your data properly in an Excel spreadsheet. Each variable should be in a separate column, and each row should represent a unique observation.
• Clean the data: Ensure that your data is free from any errors, missing values, or outliers that could affect the accuracy of the correlation test.
• Label your data: It's essential to label your variables and provide a clear indication of which variables you are testing for correlation.

B. Using the CORREL function in Excel to Calculate Correlation

The CORREL function in Excel allows you to quickly calculate the correlation between two sets of data. Follow these steps to use the CORREL function:

• Select a blank cell: Start by selecting a blank cell where you want to display the correlation coefficient.
• Enter the CORREL function: Type =CORREL( into the selected cell.
• Select the data range: Select the range of cells containing the first set of data for correlation testing.
• Add a comma: After selecting the first data range, add a comma to separate the two data ranges.
• Select the second data range: Select the range of cells containing the second set of data for correlation testing.
• Close the function: Close the function by adding a closing parenthesis ) and press Enter.

Once you have completed these steps, Excel will calculate the correlation coefficient between the two sets of data and display the result in the selected cell.

Interpreting Correlation Results

When analyzing data in Excel, it's important to understand how to interpret correlation results in order to make informed decisions based on the data.

Understanding the range of correlation coefficients

Correlation coefficients typically range from -1 to 1. A coefficient of 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.

Assessing the strength of the correlation

Correlation coefficients closer to 1 or -1 indicate a stronger relationship between the variables, while coefficients closer to 0 suggest a weaker relationship.

Considering the direction of the correlation

A positive correlation coefficient indicates that the variables move in the same direction, while a negative coefficient indicates they move in opposite directions.

Identifying patterns and trends

Correlation results can help identify patterns and trends in the data, allowing for better understanding of how variables are related to each other.

Informing predictive modeling

Understanding the correlation between variables can be crucial in predictive modeling, as it helps in determining which variables are most influential in predicting outcomes.

Guiding decision-making processes

Correlation results provide valuable insights for making data-driven decisions, as they can indicate where resources should be allocated or which strategies are most effective based on the relationships between variables.

Testing for Statistical Significance

When testing for correlation in Excel, it is important to determine whether the relationship between two variables is statistically significant. This helps in understanding whether the observed correlation is a true reflection of the relationship between the variables or just a result of random chance.

Statistical significance in correlation testing refers to the likelihood that the observed correlation between two variables is not due to random chance. It helps in determining the strength and reliability of the relationship between the variables. In other words, if a correlation is found to be statistically significant, it suggests that the relationship between the variables is more likely to be true and not just a coincidence.

B. Demonstrate how to calculate the p-value for correlation in Excel

In Excel, the p-value for correlation can be calculated using the =T.DIST.2T() function, also known as the two-tailed t-distribution function. The p-value indicates the probability of observing the correlation coefficient (r) by chance, assuming that there is no true correlation between the variables. A lower p-value suggests a stronger evidence against the null hypothesis of no correlation.

• First, select a cell where you want the p-value to be displayed.
• Next, enter the formula =T.DIST.2T(ABS(r), n-2).
• Here, r represents the correlation coefficient and n represents the sample size.
• Press Enter to calculate the p-value.

By comparing the calculated p-value to a predetermined significance level (e.g., 0.05), you can determine whether the correlation is statistically significant. If the p-value is less than the significance level, you can reject the null hypothesis and conclude that the correlation is statistically significant.

Common Mistakes to Avoid

When testing correlation in Excel, there are several common mistakes that can lead to inaccurate results. It's important to be aware of these mistakes and take steps to avoid them in order to ensure the reliability of your data analysis.

Incorrect data format:

Not checking for outliers:, using the wrong correlation function:, ignoring the sample size:, double-check data format:, address outliers:, choose the right correlation function:, consider sample size:.

In summary, this blog post covered the steps to test correlation in Excel, including how to calculate the correlation coefficient and create a scatter plot to visualize the relationship between variables. By using the =CORREL function and the chart tools in Excel, you can easily analyze the strength and direction of the relationship between your data sets.

We encourage readers to apply the Excel tutorial for testing correlation in their own data analysis. By understanding the correlation between variables, you can make informed decisions and gain valuable insights in various fields such as business, finance, science, and more.

Immediate Download

MAC & PC Compatible

Free Email Support

Related aticles

The Benefits of Excel Dashboards for Data Analysts

Unlock the Power of Real-Time Data Visualization with Excel Dashboards

Unlocking the Potential of Excel's Data Dashboard

Unleashing the Benefits of a Dashboard with Maximum Impact in Excel

Exploring Data Easily and Securely: Essential Features for Excel Dashboards

Unlock the Benefits of Real-Time Dashboard Updates in Excel

Unleashing the Power of Excel Dashboards

Understanding the Benefits and Challenges of Excel Dashboard Design and Development

Leverage Your Data with Excel Dashboards

Crafting the Perfect Dashboard for Excel

An Introduction to Excel Dashboards

How to Create an Effective Excel Dashboard

• Choosing a selection results in a full page refresh.

• school Campus Bookshelves
• menu_book Bookshelves
• perm_media Learning Objects
• login Login
• how_to_reg Request Instructor Account
• hub Instructor Commons
• Download Page (PDF)
• Download Full Book (PDF)
• Periodic Table
• Physics Constants
• Scientific Calculator
• Reference & Cite
• Tools expand_more
• Readability

selected template will load here

This action is not available.

12.1.2: Hypothesis Test for a Correlation

• Last updated
• Save as PDF
• Page ID 34784

• Rachel Webb
• Portland State University

One should perform a hypothesis test to determine if there is a statistically significant correlation between the independent and the dependent variables. The population correlation coefficient \(\rho\) (this is the Greek letter rho, which sounds like “row” and is not a \(p\)) is the correlation among all possible pairs of data values \((x, y)\) taken from a population.

We will only be using the two-tailed test for a population correlation coefficient \(\rho\). The hypotheses are:

\(H_{0}: \rho = 0\) \(H_{1}: \rho \neq 0\)

The null-hypothesis of a two-tailed test states that there is no correlation (there is not a linear relation) between \(x\) and \(y\). The alternative-hypothesis states that there is a significant correlation (there is a linear relation) between \(x\) and \(y\).

The t-test is a statistical test for the correlation coefficient. It can be used when \(x\) and \(y\) are linearly related, the variables are random variables, and when the population of the variable \(y\) is normally distributed.

The formula for the t-test statistic is \(t = r \sqrt{\left( \dfrac{n-2}{1-r^{2}} \right)}\).

Use the t-distribution with degrees of freedom equal to \(df = n - 2\).

Note the \(df = n - 2\) since we have two variables, \(x\) and \(y\).

Test to see if the correlation for hours studied on the exam and grade on the exam is statistically significant. Use \(\alpha\) = 0.05.

Correlation is Not Causation

Just because two variables are significantly correlated does not imply a cause and effect relationship. There are several relationships that are possible. It could be that \(x\) causes \(y\) to change. You can actually swap \(x\) and \(y\) in the fields and get the same \(r\) value and \(y\) could be causing \(x\) to change. There could be other variables that are affecting the two variables of interest. For instance, you can usually show a high correlation between ice cream sales and home burglaries. Selling more ice cream does not “cause” burglars to rob homes. More home burglaries do not cause more ice cream sales. We would probably notice that the temperature outside may be causing both ice cream sales to increase and more people to leave their windows open. This third variable is called a lurking variable and causes both \(x\) and \(y\) to change, making it look like the relationship is just between \(x\) and \(y\).

There are also highly correlated variables that seemingly have nothing to do with one another. These seemingly unrelated variables are called spurious correlations.

The following website has some examples of spurious correlations (a slight caution that the author has some gloomy examples): http://www.tylervigen.com/spurious-correlations . Figure 12-7 is one of their examples:

If we were to take out each pair of measurements by year from the time-series plot in Figure 12-7, we would get the following data.

Using Excel to find a scatterplot and compute a correlation coefficient, we get the scatterplot shown in Figure 12-8 and a correlation of \(r = 0.9586\).

With \(r = 0.9586\), there is strong correlation between the number of engineering doctorate degrees earned and mozzarella cheese consumption over time, but earning your doctorate degree does not cause one to go eat more cheese. Nor does eating more cheese cause people to earn a doctorate degree. Most likely these items are both increasing over time and therefore show a spurious correlation to one another.

When two variables are correlated, it does not imply that one variable causes the other variable to change.

“Correlation is causation” is an incorrect assumption that because something correlates, there is a causal relationship. Causality is the area of statistics that is most commonly misused, and misinterpreted, by people. Media, advertising, politicians and lobby groups often leap upon a perceived correlation and use it to “prove” their own agenda. They fail to understand that, just because results show a correlation, there is no proof of an underlying causality. Many people assume that because a poll, or a statistic, contains many numbers, it must be scientific, and therefore correct. The human brain is built to try and subconsciously establish links between many pieces of information at once. The brain often tries to construct patterns from randomness, and may jump to conclusions, and assume that a cause and effect relationship exists. Relationships may be accidental or due to other unmeasured variables. Overcoming this tendency to jump to a cause and effect relationship is part of academic training for students and in most fields, from statistics to the arts.

When looking at correlations, start with a scatterplot to see if there is a linear relationship prior to finding a correlation coefficient. If there is a linear relationship in the scatterplot, then we can find the correlation coefficient to tell the strength and direction of the relationship. Clusters of dots forming a linear uphill pattern from left to right will have a positive correlation. The closer the dots in the scatterplot are to a straight line, the closer \(r\) will be to \(1\). If the cluster of dots in the scatterplots go downhill from left to right in linear pattern, then there is a negative relationship. The closer those dots in the scatterplot are to a straight line going downhill, the closer \(r\) will be to \(-1\). Use a t-test to see if the correlation is statistically significant. As sample sizes get larger, smaller values of \(r\) become statistically significant. Be careful with outliers, which can heavily influence correlations. Most importantly, correlation is not causation. When \(x\) and \(y\) are significantly correlated, this does not mean that \(x\) causes \(y\) to change.

Advisory boards aren’t only for executives. Join the LogRocket Content Advisory Board today →

• Product Management
• Solve User-Reported Issues
• Find Issues Faster
• Optimize Conversion and Adoption

Correlation analysis: How to calculate in Excel (with examples)

A skilled PM should be versed in various quantitative analysis methods to make better product decisions.

One of the most common ways to analyze products and look for new insights is to conduct a correlation analysis.

In this guide, we’ll define what correlation analysis is, demonstrate how to conduct such an analysis, and list common mistakes to avoid.

What is correlation analysis?

Correlation analysis is a statistical method that helps us identify relationships between two variables.

In other words, a correlation analysis helps us determine whether changing variable A (for example, time in an app) can influence variable B (for example, users’ spending).

Correlation analysis vs. odds ratio analysis

There are two ways to identify relationships between variables:

• Odds ratio analysis
• Correlation analysis

The main difference between these tools is what type of outcome they can assess:

We use odds ratio analysis to identify how variables impact an outcome that’s discrete. Discrete outcomes can be answered in a yes-or-no manner. An example could be 30-day retention. Did a user retain after 30 days: yes or no?

If your output variable is continuous — that is, it cannot be answered in a yes-or-no fashion (for example, users’ spending) — correlation analysis is your best bet.

Correlation analysis formula

Correlation analysis is an advanced statistical topic. Calculating the correlation coefficient mathematically is a daunting task.

The correlation coefficient formula is:

r = n ∑ X Y − ∑ X ∑ Y ( n ∑ X 2 − ( ∑ X ) 2 ) ⋅ ( n ∑ Y 2 − ( ∑ Y ) 2 )

Luckily, you don’t have to master advanced mathematics to perform a correlation analysis. An Excel spreadsheet is more than enough.

All you need to do is to use the =correl function:

A result is a number between -1 and 1:

• If your result is close to -1, there’s a strong negative correlation
• If your result is close to 1, there’s a strong positive correlation
• If your result is close to 0, there’s no correlation between your variables

Correlation analysis example (Excel)

Now, let’s demonstrate correlation analysis with a practical example.

Let’s say you manage an in-app customer support chat and you are interested in whether resolving issues faster leads to higher customer satisfaction. If that conjecture is true, you might use this insight to inform your roadmap and prioritize reducing the customer support contact time to drive satisfaction.

Over 200k developers and product managers use LogRocket to create better digital experiences

There are three steps to testing that hypothesis:

• Calculate the correlation
• Measure correlation reliability
• Check for confounding variables

1. Calculate the correlation

For starters, all you need are two columns of data.

Let’s start with the input variable, which is the time spent talking to customer support in the chat. In our case, since the interactions tend to be quick, let’s measure it in seconds.

The output variable is satisfaction. Let’s use a monthly 1–10 NPS survey sent to users:

After collecting this data, we just need to use the =correl() function. First, highlight the satisfaction (output variable we want to affect) and then the time spent talking to customer support (the input variable we want to improve).

Correlation coefficient (r) = -0.77

The correlation of -0.77 suggests a negative correlation. The longer people talk to customer support (higher input variable), the lower the overall satisfaction (lower output variable).

Although this seems to support our initial hypothesis, we shouldn’t stop here. We still need to stress-test our findings.

2. Measure correlation reliability

The next step should be to measure how reliable the actual correlation is.

To do that, we use R-squared calculation ( r 2 ). r 2 represents the amount of variation between variables that can be explained by the correlation coefficient.

To put the statistical nitty-gritty aside and simplify a bit, r 2 tells us how trustworthy our correlation results are. When we square our correlation coefficient, we’ll get a number between 0 and 1:

Here, 0 means our correlation results are weak and probably not trustworthy, and 1 means it’s a perfect correlation.

Back to our example, if we square our -0.77, we’ll get:

r 2 = -0.77 2 = 0.59

That means our correlation is relatively reliable but far from perfect. Let’s keep that in mind when drawing conclusions and planning the subsequent bets.

3. Check for confounding variables

Now, let’s avoid the most common correlation analysis mistake: confusing correlation for causation.

The fact that two variables are correlated doesn’t necessarily mean that one variable directly influences the other. There might be another variable we don’t consider that impacts both input and output variables:

Let’s look at an example. There’s a strong correlation between the amount of ice cream consumed and the number of drownings. The more ice cream people consume, the more they drown.

But does that mean those drownings are caused by eating ice cream? Should we ban ice cream?

Of course not. The fact is, there’s another variable that influences both ice cream consumption and drowning rates: the temperature.

On the one hand, the higher the temperature, the more ice cream people consume. On the other hand, increased temperature encourages more people to swim in the ocean, which, in turn, leads to a higher number of drownings:

Although ice cream consumption and the number of drownings are correlated, there are at least two more variables that cause the correlation. So, even if we decided to ban eating ice creams altogether, the number of drownings wouldn’t decrease — even though these variables are strongly correlated.

In our customer support example, a hidden confounding variable might also exist.

For example, it could be the severity of the issue. The higher the severity, the lower the satisfaction and the more time customer support needs to resolve the issue. Reducing the time spent with customer support wouldn’t necessarily mean higher satisfaction if the severity of the problems is still high:

You can identify causation by running a series of experiments.

First, hypothesize other variables that could impact your analysis and run a correlation analysis on them. Then, run small experiments on these variables to notice which one actually moves the needle.

You can also benefit from qualitative research, such as customer interviews, to better understand the context and formulate more robust hypotheses.

At the end of the day, correlation is just an insight into what to focus on, and it’s rarely enough to draw strong conclusions.

Correlation is a powerful and relatively simple analysis tool. It helps you determine whether changes in one variable predict changes in another variable.

Although correlation analysis is an advanced statistical topic, in reality, all you need is Excel or Google Sheets and a simple =correl() formula.

However, remember to also check correlation strength and search for confounding variables.

Correlation doesn’t necessarily mean causation. If you are looking for truly valuable insights, you need to dig deeper, consider multiple variables and run a set of experiments to spot which variables actually cause other variables to move.

After all, although eating ice cream and drowning are correlated, it doesn’t mean banning ice cream would save people’s lives.

Featured image source: IconScout

LogRocket generates product insights that lead to meaningful action

Get your teams on the same page — try LogRocket today.

Share this:

• Click to share on Twitter (Opens in new window)
• Click to share on Reddit (Opens in new window)
• Click to share on LinkedIn (Opens in new window)
• Click to share on Facebook (Opens in new window)
• #product analytics
• #tools and resources

Stop guessing about your digital experience with LogRocket

Recent posts:.

Leader Spotlight: Growing the omnichannel market, with Christine Kuei

Christine Kuei, Director of Product Management at Forever 21, shares her experience growing and optimizing omnichannel experiences.

Decoding marketing jargon: A glossary of terms

The world of product marketing is always evolving. Even for experts, it can be hard to keep up with the latest concepts, terms, and jargon.

Leader Spotlight: Bettering learning velocity, with Jonas O. Klink

Jonas talks about his team’s initiatives to “better the learning velocity” — taking an initial idea through hypothesis-driven development to build customer-centric, scalable solutions.

Leader Spotlight: Energizing your leadership style, with Navya Rehani Gupta

Navya Rehani Gupta talks about her three main pointers for mastering the art of zooming in and zooming out.

Leave a Reply Cancel reply

Correlation tests

• Cohen’s Kappa in Excel tutorial
• Pearson correlation coefficient in Excel
• Run Chi-square and Fisher’s exact tests in Excel
• RV coefficient test in Excel tutorial
• Biserial correlations tutorial in Excel
• Spearman correlation coefficient in Excel tutorial

Expert Software for Better Insights, Research, and Outcomes