Two Sample t-Test Assuming Unequal Variances

Use a t-Test to determine if means (i.e., averages) are the same or different

Prerequisite: Before using the t-test, use an F-test to determine if the variances are equal or unequal.
If they are not equal go to: Two-Sample t-Test assuming equal variances.
(The QI Macros Stat Wizard will do this for you automatically.)

Video Example: Analyze Data Sets with a Two Sample t-Test

Example of a Two Sample t-Test Assuming Unequal Variances

In this example, we want to compare two types of structural steel and want to know if the strengths (in 1000 lbs/sq. in.) are the same or different. Next we conduct some tests and enter the data into Excel:

f test data

Warning: While you can run a t-Test using Excel's Data Analysis Toolpak, if you don't enter the two columns in the correct order, Excel will give you incorrect results. The QI Macros have eliminated this problem.

How to Perform a t-Test Assuming Unequal Variances using QI Macros for Excel

See how....

  1. Select the data with the mouse and click on the QI Macros Menu, Statistical Tools and then t-Test two sample assuming unequal variances:
  2. two sample t test unequal variances
  3. The QI Macros will prompt for a significance level (default is .05):

    two sample t test significance level
  4. Next the QI Macros will prompt for the hypothesized difference in the means (default is 0):
  5. hypothesized difference in means for t test in QI Macros

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The QI Macros will perform the calculations and interpret the results for you:

t test calculation in the QI Macros

What's Unique About t-Test Calculations in the QI Macros? 

When you run the t-test, the QI Macros will compare the p-value (0.197) to the significance level (0.05) and interpret the results for you. Cannot Reject the Null Hypothesis because p > 0.05" and that the "Means are the same".

Here is Some Guidance to Interpret the t-Test Results Yourself:

See how....

  • The null hypothesis H0 is that the mean difference (x1-x2) = 0
  • or in other words the means are the same

  • The alternative hypothesis Ha is that the mean difference <> 0

    or in other words the means are not the same, they are different

If
Then
test statistic > critical value 
(i.e. t> tcrit)
Reject the null hypothesis
test statistic < critical value 
(i.e. t< tcrit)
Cannot Reject the null hypothesis
p value < a Reject the null hypothesis
p value > a Cannot Reject the null hypothesis

Since the null hypothesis is that the mean difference (x1-x2) = 0, this is a two-sided test. Therefore, use the two-tail values for your analysis.

Since the t statistic < t critical (1.355 < 2.145) and p value > a ( 0.197 > 0.05) , we cannot reject the null hypothesis - the means are the same.

The two recipes produce steel with the same mean tensile strength at a 95% confidence level.

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Hypothesis Testing Quick Reference Card

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