# 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.

### Weight Loss Paired t-Test Example

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.

### To conduct a Paired t-Test in the QI Macros for Excel, follow these steps:

1. Input your data into Excel, then click and drag over it to select it

2. Next click on the QI Macros Menu, Statistical Tools and select t-Test: paired two sample for means

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

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

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The QI Macros paired t-Test macro will perform the calculations and interpret the results for you:

### What's Cool about QI Macros Paired t-Test?

When you run the Paired t-Test, the QI Macros will compare the p-value (0.429) to the significance level (0.05) and indicate that you "Cannot Reject the Null Hypothesis because p>0.05" and that the "Means are the same."

The QI Macros results are also interactive and let you change the significance level and Hypothesized Difference in Means and see what impact those changes have on your results. See areas outlined in red in the results image above.

### Interpreting the Paired t-Test Results Manually

The null hypothesis is less than or equal to 10. The alternate hypothesis is greater than 10.

• H0 <= 10 lbs
• Ha > 10 lbs

Since the null hypothesis stated as "less than or equal to", this is a one-sided test. If you want to evaluate the results manually:

 If Then t-Test statistic > critical value  (i.e. t> tcrit) Reject the null hypothesis t-Test statistic < critical value  (i.e. t< tcrit) Cannot Reject the null hypothesis t-Test p value < a Reject the null hypothesis t-Test p value > a Cannot Reject the null hypothesis

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 cannot reject the null hypothesis that the weight loss is less than or equal to 10.

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