Excel Confidence Interval for Difference in Means (2 Examples)

This article illustrates how to calculate the Confidence Interval in excel for a difference in Means. Various statistical functions and tools in Excel allow us to perform numerous statistical operations saving time and labor. You can calculate confidence interval using the statistical functions or the Data Analysis tool in excel. The following picture shows a sample result obtained from such operations. Follow the article to learn how itโ€™s done.

confidence interval for difference in means in Excel


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What Is Confidence Interval?

Confidence Interval (CI) is a statistical term referring to a range of values that include a population with an assumed confidence level. It is often used to analyze the statistical significance of a certain estimation. It depends on the sample size, sample variance, and confidence level. Statisticians normally use a 95% confidence level to calculate the confidence interval. People often misunderstand or misinterpret it saying that 95% of the sample values lie within the confidence interval though it may not be the case.


2 Ways to Calculate Confidence Interval in Excel for Difference in Means

Assume you are the manager of a bookstore with an online extension. You are wondering if the average daily sales through the website of the store are any different than the in-store sales. So you have collected the sales data for 3 weeks both from the in-store and online sales.

dataset to calculate confidence interval

Now you want to calculate the confidence interval based on this dataset to come to a conclusion. Follow the methods below to be able to do that in Excel.


1. Calculate Confidence Interval for Difference in Means Using Formulas

Follow the steps below to calculate the Confidence Interval for Difference in Means Using formulas in Excel.

๐Ÿ“Œ Steps:

  • First, enter the following formula in cell F4 to calculate the Mean of In-Store sales. Then, calculate the Mean of Online sales in a similar way. Next, subtract the two Means to get the Mean Difference.
=AVERAGE(B5:B25)

calculate means and their difference

  • After that, apply the formula in cell F7 to get the Standard Deviation for In-Store sales. Then calculate that for Online sales similarly.
=STDEV.S(B5:B25)

calculate standard deviation of each sample

  • Next, input the sample sizes and Significance Level.

enter sample sizes and significance level

  • After that, apply the following formula in cell F13 to calculate the Pooled Variance.
=((F9-1)*F7^2+(F10-1)*F8^2)/(F9+F10-2)

calculate the pooled variance

  • Then, enter the following formula in cell F14 to calculate the t-Value.
=T.INV.2T(F12,F9+F10-2)

calculate the t-value

  • Next, apply the following formula in cell F15 to get the Margin of Error.
=F14*SQRT(F13/F9+F13/F10)

calculate the margin of error

  • Finally, subtract the Margin of Error from the Mean Difference to get the Confidence Interval Lower Bound. And add them to get the Upper Bound.

calculate the confidence interval for the difference in means

  • The results suggest that there is a possibility that the Mean of daily In-Store sales will be $14.26 to $271.58 higher than Online sales.

Read More: How to Calculate Confidence Interval for Population Mean in Excel


2. Calculate Confidence Interval for Difference in Means Using Data Analysis Tool

Follow the steps below to calculate the Confidence Interval for Difference in Means Using the Data Analysis tool in Excel.

๐Ÿ“Œ Steps:

  • First, select Data >> Data Analysis. You need to enable the Analysis Toolpak add-in to access it from there.

open Data Analysis tool

  • Then, choose t-Test: Two-Sample Assuming Equal Variances and click OK.

perform a t-test for two samples assuming equal variances

  • Next, select the sample ranges as the Variable 1 Range and Variable 2 Range respectively. Then check the Labels checkbox and keep the Alpha value to 0.05. Now, enter the output range and click OK.

enter the parameters for the t-test

  • After that, you will get the following result.

result of the t-test

  • Then calculate the Mean Difference by subtracting the two Means. You have the t-Value from the analysis. Now apply the following formula in cell F21 to calculate the Standard Error.
=SQRT(F8/F9+G8/G9)

calculate mean difference and standard error

  • Then multiply the t-Value with the Standard Error to get the Margin of Error.

canculate the margin of error for confidence interval

  • Finally, you can calculate the Confidence Interval by adding and subtracting the Margin of Error to and from the Mean Difference as earlier.

calculate confidence interval for the mean difference

Read More: How to Calculate Z-Score with 95 Confidence Interval in Excel


Things to Remember

  • You can enable the Data Analysis tool from File >> Options >> Add-ins >> Go if it is not enabled already.
  • You can use a different confidence level or assume unequal sample variances if required.

Conclusion

Now you know how to calculate the Confidence Interval for Difference in Means in Excel. Hope this helped. Do you have any further queries or suggestions? Please let us know in the comment section below. You can also visit our ExcelDemy blog to explore more about excel. Stay with us and keep learning.


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Md. Shamim Reza

Md. Shamim Reza

Hello there! This is Md. Shamim Reza. Working as an Excel & VBA Content Developer at ExcelDemy. We try to find simple & easy solutions to the problems that Excel users face every day. Our goal is to gather knowledge, find innovative solutions through them and make those solutions available for everybody. Stay with us & keep learning.

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