The “Paired data sets” button allows you to determine if there is a statistical difference between the same set of samples tested twice. Known as a Paired t-Test, this is often used in before and after situations. In this example, we’re comparing diameters of parts before and after a grind operation.

The first step is to choose your alpha value. What’s that? Well, in traditional hypothesis testing, we begin by assuming that the characteristic we’re assessing (diameter in this example) is the same for both data sets. So in this case, our default hypothesis (H0, also known as the “null-hypothesis” or “h-naught”) is that average diameters are unchanged from the first test to the second. We won’t be willing to reject that default hypothesis unless we reach a certain confidence level that they’re different. The key question you need to answer is: **how confident do you need to be?** That’s where alpha comes in. Notice the cell in the upper left labeled “alpha”. That’s where you set your decision rule. If you want to be 95% confident that the data sets have different means before rejecting H0, then set alpha to 0.05. If you want to be even more confident (say, 99%), then set alpha to 0.01. It’s up to you! After you’ve chosen your alpha value, then simply label each data set and enter their values.

In this example, the diameters of each sample were measured both before and after the grind operation. Since each sample was measured twice (before and after), their scores have a paired relationship. As shown in the data summary boxes on the right, the mean diameter before the grind operation was 4.195 cm and 4.05 cm afterward. The “Difference Summary” section on the left shows the average difference and the Upper and Lower confidence bounds for that difference. Notice that the confidence bounds **do not include zero**, which means it is highly likely that the difference is not, in fact, zero. In other words, it is likely that the diameters before and after truly are different, as indicated by the fact that the p-value is lower than the chosen alpha value.

The p-values here are the result of a statistical calculation meant to determine how likely it is that the means of these two data sets would be this different if they truly were part of the same distribution. If the p-value ends up being lower than your chosen alpha value (i.e., your decision rule), then you can confidently reject H0 and accept the alternative hypothesis (known as H1 or “h-one”) that these two data sets most likely come from different distributions.

Copyright 2020 David Margil