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t test - Two Sample Unequal Variances

When to Use the t Test - Two Sample Assuming Unequal Variances

In the constant quest to reduce variation and improve products, companies need to evaluate different alternatives. A t test using two samples compares two independent sets of test data. It helps determine if the means (i.e., averages) are the same or different from each other. Excel offers several two sample t tests:

If data sets are independent of each other:

• Two-Sample t test assuming equal variances
• Two-Sample t test assuming unequal variances

If data sets are dependent on each other: when natural pairs of observations exist (e.g., using the same operator on a machine while comparing two different modes of operation.)

• Paired Two-Sample t test for Means

Consider the following example.

t test two sample assuming unequal variances

If you want to compare two types of structural steel, you might want to know if the strengths (in 1000 lbs/sq. in.) are the same or different:

• 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

Now, conduct a test and enter the data into Excel:

Conduct an F test to determine if the variances are equal

Since the two machines aren't "paired" in any way, the first step is to determine if the variances are equal to determine which t test to use. So, select the data with the mouse and click on the QI Macros Menu to select the F test:

The QI Macros will prompt for a significance level (default = 0.05):

The f test macro will perform the calculations and interpret the results for you:

What's cool about QI Macros f-Test? When you run the f-Test, you don't have to think. Unlike other statistical software, the QI Macros is the only SPC software that compares the p-value (0.034) to the significance level (0.05) and tells you to "Reject the Null Hypothesis because p<0.05" and that the "Variances are Different ".

Interpreting the F test results to determine if variances are equal or unequal

If you want to verify the results manually:

If	Then
test statistic > critical value  (i.e. F > F crit)	Reject the null hypothesis
test statistic < critical value  (i.e. F < F crit)	Accept the null hypothesis
p value < a	Reject the null hypothesis
p value > a	Accept the null hypothesis

Since F > Fcrit (.27> 3.18) and p value < a ( .034< 0.05, we can reject the null hypothesis that the variances are equal. Now we can run the t test assuming unequal variances.

t test Assuming Unequal Variances

Now, select the data with the mouse and click on the QI Macros Menu to select the two sample t test assuming unequal variances:

The QI Macros will prompt for a significance level (default = 0.95) and hypothesized difference in means (0):
 

The t test two sample for unequal variances macro will perform the calculations and interpret the results for you:

What's cool about QI Macros t-Test? When you run the t-Test, the QI Macros will compare the p-value (0.197) to the significance level (0.05) and tells you to "Accept the Null Hypothesis because p>0.05" and that the "Means are the same".

Interpreting the t test assuming unequal variances results

If you want to evaluate the results manually:

If	Then
test statistic > critical value  (i.e. t> tcrit)	Reject the null hypothesis
test statistic < critical value  (i.e. t< tcrit)	Accept the null hypothesis
p value < a	Reject the null hypothesis
p value > a	Accept 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 can accept the null hypothesis that the means are the same.

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

Analyze Data Sets witha Two Sample t Test

 

The t test - two sample assuming unequal variances test is just one of the tests included in the QI Macros Statistical Process Control software. Other tests include:

• t test one sample
• test of proportion
• f test
• ANOVA - Analysis of Variance
• Overview of all hypothesis tests in Excel

 

Purchase QI Macros SPC Software for Excel through our secure shopping cart or try a free, QI Macros 30-day trial!