Paired t test in Excel using the QI Macros

When to Use the Paired t Test - Two Sample

In the constant quest to reduce variation and improve products, companies need to evaluate different alternatives. A t test using two paired samples compares two dependent sets of test data. It helps determine if the means (i.e., averages) are different from each other.

Consider the following example.

Weight Loss Paired t test

If a diet claims to cause more than a 10 lb weight loss over a six month period, you could design a test using several individuals before and after weights. The samples are "paired" by each individual. You might want to know if the diet truly delivers greater than a 10 lb weight loss. The null hypothesis is less than or equal to 10. The alternate hypothesis is greater than 10.

• H₀ <= 10 lbs
• H_a > 10 lbs

Since the null hypothesis stated as "less than or equal to", this is a one-sided test.

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

Then, 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 = 0.05):

And a hypothesized mean difference (in this case 10 lbs):

The QI Macros paired t test two sample macro will perform the calculations and interpret the results for you:

Interpreting the Paired t test results

Since the null hypothesis is that weight loss is less than or equal to 10, this is a one-sided test. Therefore, use the one-tail values for your analysis.

Note: The two-sided values would apply if our null hypothesis was that:
H₀: mean difference = 10 lbs.)

Since the t statistic < t critical (.182< 1.753) and p value > a ( 0.429> 0.05) , we can accept the null hypothesis that the weight loss is less than or equal to 10.

Example of t test one-sample

We could have cast this as a t test one sample. If we calculate the difference between the before and after weights, we could test whether the difference is greater than 10 lbs.

Again, since the p value of .429172 is greater than 0.05, we accept the null hypothesis that weight loss is less than or equal to 10 lbs.

The Paired t test and the t test one sample tests are just some of the tests included in the QI Macros Statistical Process Control software. Other tests include:

• t test two sample assuming equal variances
• t test two sample assuming unequal variances
• f test
• ANOVA - Analysis of Variance
• Overvew of all hypothesis tests in Excel

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