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.
f data sets are independent of each other use the f test to determine if the variances are equal or unequal and then choose one of the following:
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.)
t test Two Sample Assuming Equal Variances Video
t test Two Sample Assuming Equal Variances Example
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.
To conduct an f test using the QI Macros for Excel, follow these steps:
- Select the data with the mouse and click on the QI Macros Menu, Statistical Tools and then select the F test:
- The QI Macros will prompt for a significance level (default = 0.05):
- The QI Macros will perform the f test 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 (0.152) to the significance level (0.05) and interprets the result for you. "Cannot Reject the Null Hypothesis because p>0.05" and that the "Variances are the same." Based on the f test results we now know which t test to run.
To conduct an t test using the QI Macros for Excel, follow these steps:
- 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 is .05):
- Next the QI Macros will prompt for the hypothesized difference in the means (default is 0):
- The QI Macros will perform the calculations and interpret the results for you:
When you run the two sample t-test, the QI Macros will compare the p-value (0.818) to the significance level (0.05) and indicate you "Cannot Reject the Null Hypothesis because p>0.05" and that the "Means are the same."
Interpreting t test two sample calculations yourself
If you want to evaluate the results manually, here is some guidance:
|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 in this example is that the mean difference (1-x2) = 0, this is a two-sided test. Therefore, use the two-tail values for our analysis.
Since the t statistic < t critical (-.237 < 2.306) and p value > a ( .818> 0.05) , we cannot reject 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.
If you use Excel's Data Analysis toolpak, Excel requires the recipe 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.
- t test one sample
- Paired two sample t test
- Two-Sample t test assuming unequal variances
- Statistics Wizard analyzes your data and selects the right statistical tests for you