How to Calculate Standard Error of Correlation Coefficient in Excel

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The correlation coefficient is a commonly used statistical measure that quantifies the strength and direction of the relationship between two variables. However, the correlation coefficient alone is not sufficient to fully understand the nature of the relationship between variables. To obtain a more clarifying analysis, it is important to estimate the precision of the estimated correlation coefficient. This is where the standard error of the correlation coefficient comes into play. In this article, we will discuss what the standard error of the correlation coefficient is and how to calculate it in Excel using different methods.

Overview of Standard Error of Correlation Coefficient Excel


Introduction to Standard Error of Correlation Coefficient

Before calculating the standard error of the correlation coefficient, let’s have a transparent idea about the topic in brief.

What Is the Standard Error of Correlation Coefficient?

The standard error of the correlation coefficient measures the precision of the estimated correlation coefficient. It represents the degree of uncertainty or variability of the correlation coefficient estimate in repeated sampling. A smaller standard error indicates a more precise estimate of the true population correlation coefficient. The standard error of the correlation coefficient is particularly important when interpreting the results of a correlation analysis, as it provides additional information about the reliability and accuracy of the estimated correlation coefficient. In short, the standard error of the correlation coefficient measures how much the sample correlation coefficient is likely to differ from the true population correlation coefficient. Let’s find the standard error of the correlation coefficient in Excel, it’s quite simple.


Arithmetic Formula to Find Standard Error of Correlation Coefficient

The arithmetic formula to find the standard error of the correlation coefficient is:

SEr = sqrt((1 - r^2) / (n - 2))

where SEr is the standard error of the correlation coefficient, r is the sample correlation coefficient, and n is the sample size.

The formula is derived from the standard deviation of the sample correlation coefficient, which is a measure of the amount of variation in the estimated correlation coefficient that we would expect to see if we took repeated samples of the same size from the same population.


How to Calculate Standard Error of Correlation Coefficient in Excel: 3 Easy Methods

Without any further delay, let’s jump to the procedures to calculate the standard error of the correlation coefficient in Excel. We’ll show different options in Excel like VBA, Data Analysis, and obviously formulas for our calculations.


1. Calculate Standard Error of Correlation Coefficient from Correlation Coefficient

In the first method, we will use the CORREL function of Excel to calculate the correlation coefficient

Step 01: Find Correlation Coefficient Using CORREL Function

Before calculating the standard error of the correlation coefficient, we have to calculate the correlation coefficient first. Excel has the CORREL function, which can do the work just fine. You have to insert the two ranges of data as the arguments for the function.

  • Apply the following formula in a new cell of the Excel worksheet.

=CORREL(C5:C14,D5:D14)

In the formula,

Correlation coefficient calculation


Step 02: Use Arithmetic Formula to Calculate Starndar Error of Correlation Coefficient

Afterward, count the number of data points for calculating the standard error of the correlation coefficient. To do this, we’re using the COUNT function, which counts the number of cells in a given range.

  • Apply the following formula to determine the number of terms.

=COUNT(C5:C15)

Counting no. of terms

  • Finally, we are set to calculate the standard error of the correlation coefficient. Use the following formula in any cell. We have used it in cell F12. The SQRT function determines the square root of any number in Excel.

=SQRT((1-(F5)^2)/(F8-2))

As a result, you will see the standard error of the correlation coefficient in that cell.

Calculating standard error of correlation coefficient


2. Using Data Analysis to Determine Standard Error of Correlation Coefficient

Another way to calculate the standard error of the correlation coefficient is by using the Data Analysis ribbon. We will calculate the correlation coefficient and then calculate the standard error with a regular formula.

  • Firstly, install Data Analysis if it’s not included in your Excel. Then, go to Data Tab > Data Analysis.

Opening data analysis

  • From the Data Analysis window, select Correlation then click OK.

Correlation in data analysis

  • In the next window, select the data range to calculate the correlation coefficient in the Input Range box and select Columns from the Grouped By section. Also, choose the range for output in the Output Range section. Click OK.

Set up for correlation input output

  • You will see the correlation coefficient in the output range. Now, use that output for calculating the standard error. Just use the regular formula as given below.

=SQRT((1-(C19)^2)/(COUNT(C5:C15)-2))

Determining SE of correlation coefficient


3. Inserting VBA Macro to Calculate Standard Error of Correlation Coefficient

As we all know, almost all tasks in Excel can be done with VBA. Let’s use the opportunity to calculate the standard error of the correlation coefficient.

  • Firstly, open the VBA window by pressing Alt + F11.
  • Then, insert a new module by selecting Insert > Module.

Inserting new module in VBA

  • Afterward, insert the following code in the code window.

Code:

Sub Calculate_StdErr()
Dim R As Double
Dim n As Long
Dim StdErr As Double
'Calculate correlation coefficient
R = Application.WorksheetFunction.Correl(Range("C5:C15"), Range("D5:D15"))
'Get sample size
n = Range("C5:C15").Cells.Count
'Calculate standard error of correlation coefficient
StdErr = Sqr((1 - R ^ 2) / (n - 2))
'Output standard error to cell
Worksheets("VBA").Range("F5").Value = StdErr
End Sub

Code for calculating SE of correlation coefficient

Code Breakdown:

  • Declare variables: The variables “R” and “n” are declared as double and long data types, respectively, to store the correlation coefficient and sample size.
  • Calculate correlation coefficient: The correlation coefficient is calculated using the “Correl” function in Excel, which takes two ranges of data as input. In this example, the data is in cells C5:C15 and D5:D15.
  • Get sample size: The sample size is determined by counting the number of cells with data in the range C5:C15 using the “Count” function.
  • Calculate standard error: The standard error of the correlation coefficient is calculated using the formula Sqr((1 – R ^ 2) / (n – 2)), where “R” is the correlation coefficient and “n” is the sample size.
  • Output standard error: The calculated standard error is output to cell F5 on the “VBA” worksheet using the “Range” and “Value” properties.
  • Finally, run the code by pressing F5. instantly, you will see the standard error of the correlation coefficient in cell F5.

SE of correlation coefficient result using VBA


Frequently Asked Questions

  • What does the standard error of correlation coefficient tell us?

Ans: The standard error of the correlation coefficient gives an estimate of the precision of the sample correlation coefficient. A smaller standard error indicates a more accurate estimate of the true population correlation coefficient.

  • Why is it important to calculate the standard error of correlation coefficient?

Ans: The standard error of the correlation coefficient is an important measure of the accuracy and reliability of the sample correlation coefficient. It helps researchers to assess the significance of the correlation and to determine whether it is likely to be a chance finding or a true relationship.

  • What is the significance level used for hypothesis testing with the standard error of the correlation coefficient?

Ans: The significance level used for hypothesis testing with the standard error of the correlation coefficient is typically 0.05, which denotes a 95% confidence interval. However, this can be adjusted depending on the specific research question or context.

  • Can you calculate the standard error of the correlation coefficient for more than two variables in Excel?

Ans: No, Excel does not provide a built-in function to calculate the standard error of the correlation coefficient for more than two variables. However, it is possible to calculate this using specialized statistical software or programming languages.


Summary

  • Firstly, we described the way to calculate standard error using the Excel formula.
  • Then, we showed the use of Data Analysis to calculate the standard error.
  • We also explained how to do the task with Excel VBA.

Things to remember

  • We used cell reference in various formulas for calculating the standard error of the correlation coefficient. You have to adjust it according to your dataset.
  • Don’t forget to save the file in xlsm format before running the VBA code.

Download Practice Workbook

You can download the practice workbook from here.


Conclusion

In conclusion, the standard error of the correlation coefficient is a critical measure in statistics that helps to estimate the sampling variability in the calculated correlation coefficient. A smaller standard error indicates a more precise estimate of the population correlation coefficient. In this article, we explained how to calculate the standard error of the correlation coefficient in Excel. We hope it will be helpful to you.


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Mehedi Hasan Shimul
Mehedi Hasan Shimul

Md. Mehedi Hasan, with a BSc in Electrical & Electronic Engineering from Bangladesh University of Engineering and Technology, holds a crucial position as an Excel & VBA Content Developer at ExcelDemy. Driven by a deep passion for research and innovation, he actively immerses himself in Excel. In his role, Mehedi not only skillfully addresses complex challenges but also exhibits enthusiasm and expertise in gracefully navigating tough situations, emphasizing his steadfast commitment to consistently deliver exceptional and quality content.... Read Full Bio

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