t test Two Sample Assuming Equal Variances in Excel

When to use a t Test - Two Sample Assuming Equal 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 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

If you're producing rubber made with two different recipes, you might want to know if the tensile strengths are the same or different (Juran's QC Handbook 4th pg 23.74):

Define the null and alternate Hypothesis

• The null hypothesis H₀ is that the mean difference (1-x2) = 0

or in other words the means are the same

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

  or in other words the means are not the same

Conduct the Test

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

Conduct an F test to determine if variances are equal

Since the two recipes aren't "paired" or dependent 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 calculate the results:

Interpreting the F test results

Since F < Fcrit (3.05567 < 6.38823) and p value > a ( .15241 > 0.05, we can accept the null hypothesis that the variances are equal. Now we can run the t test assuming equal variances.

Run t test Assuming Equal Variances

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

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

The t test two sample assuming equal variances macro will calculate the results:

Interpreting the t test two sample results

Since the null hypothesis is that the mean difference (1-x2) = 0, this is a two-sided test. Therefore, use the two-tail values for your analysis.

Since the t statistic < t critical (.23727< 2.30601) and p value > a ( .81841> 0.05) , we can accept the null hypothesis that the means are the same.

Therefore we can say that the two recipes produce rubber with the same mean tensile strength at a 95% confidence level.

Excel Note:
Notice that both the F and t test results reversed the order of the recipes. For some unknown reason Excel requires the recipes with the largest variance and mean to be first to ensure correct calculations. The QI Macros reorganizes your data to ensure Excel performs the calculations correctly.

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

• t test one sample
• f test
• chi square
• ANOVA - Analysis of Variance
• Overvew of all hypothesis tests in Excel

Download the FREE 30-day Evaluation copy of the QI Macros Excel SPC Software for Six Sigma