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 compares two samples of test data. It helps determine if the means (i.e., averages) are the same or different from each other. The QI Macros offers several two sample t tests.
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.)
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 (x1-x2) = 0
- The alternative hypothesis Ha is that the mean difference <> 0
or in other words the means are not the same
or in other words the means are 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:
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 (0.152) to the significance level (0.05) and tells you to "Accept the Null Hypothesis because p>0.05" and that the "Variances are the same."
Interpreting the F test results
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 (.33 < 6.39) and p value > a ( .152> 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 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 (0.818) 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 two sample 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 (1-x2) = 0, this is a two-sided test. Therefore, use the two-tail values for your analysis.
Since the t statistic < t critical (-.237 < 2.306) and p value > a ( .818> 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:
If you use Excel's Data Analysis toolpak, Excel requires the recipes with the largest variance and mean to be first to ensure correct calculations. The QI Macros does not have this requirement in order to perform the calculations correctly.
