Hello, the last example from module two that I'll demonstrate using JMP is the hardness testing example, in which we use a paired t-test to analyze this data. If you remember, there was a hardness testing machine and it presses a rod with a pointed tip into a metal specimen with some known force. And then the output from this test is to measure the depth of the depression caused by the tip. There were two different tips available, however, we had these different metal specimens and they were cut from different bar stocks and they could have had some different variability between them. So we wanted to use a paired t-test to analyze this, to reduce that block variability. So, 10 specimens were used and each specimen was tested using both tips. So there's the data for all 10 specimens and the depth of compression from tip 1 and the depth of compression of depression from tip 2. So I'm going to show you how to enter this data into JMP from a text file and also how to copy and paste it on. And then I'll show you how to demonstrate how to use a paired t-test in JMP, and there's actually two different ways that we can do that. So if I go to JMP, I have this hardness testing in a text file. We can read this in if I go to file open and I can open as a text file, just like we opened an Excel file, okay, and create that data table. But there's also a nice way if you have a small data set and you just kind of want to do the quick and dirty method, you can always select all this data and copy it. And then create a new data table. And then simply go to Edit, and paste with columns names. So if you don't want to read something in or you don't have something saved, you can just copy and paste the old-fashioned way, okay. So the first thing you'll see is that, we have all of the tip 1 information in one column and all of the tip 2 information and another column. And for this paired t-test, I actually don't want to stack this data because I want to know the difference for each specimen. So what I'm going to do is I'm going to create a new column, just double-clicking it over here, we'll do that. And if I go to the column info, I'm going to call this the difference column. And I'm even going to write that we did tip 1, and we're going to subtract tip 2 from that, okay. And then I'm going to come down here to Column Properties and I'm going to come up to the Formula option. And I'm going to go to Edit Formula and we're going to create a formula that is the difference between tip 1 and tip 2. So I'm going to select tip 1 and then I'm going to subtract tip 2. And if I click OK and OK, we now have a new column with all of the information of the differences between tip 1 and tip 2, okay. So now in are paired t-test, this is the mu sub D that we can perform a hypothesis test on. And so, now if I go to Analyze, instead of doing Fit Y by X, I'm going to go to Distribution and I'm going to select this difference into the Y box and click OK. And now, I'm going to look at the distribution of those differences. JMP gives us some default options here, but I'm actually going to go to our red triangle, of course and come down to test mean. The null hypothesis for the paired t-test is that mu sub D equals 0 and for this example, our alternative hypothesis was that mu sub D does not equal 0. So in this specified hypothesized mean, we're going to keep that as a 0, okay. Since we don't know the population standard deviation, we're using estimates. We're going to leave this box blank and that will give us our t-test as opposed to the z-test. So I'm going to click OK, and there is our t-test for the differences between the two groups. We see that the average difference was -0.1 and that our test statistic was -0.2641 and that there was not a significant difference between the two tips. So that's one way we can do this by making a new column and performing a one-sample t-test on that column. Another option is to go to Analyze and come down to Specialized Modeling and go down to the bottom of that list is a Matched Pairs option. A paired t-test is also sometimes called matched pairs. So in this platform, we'll take tip 1 and tip 2, if you want to highlight them both and enter them into this wide pair response. When I click OK, I get a plot of all of the differences, and you may want to resize this. As I said before, JMP is very interactive. You can change the axes as you want. You can stretch and shrink things as you see fit. So this is a plot of all those differences and then as we see down here at the bottom of the output again, we get the mean difference this time, JMP is doing tip 2 minus tip 1. So the difference is 0.1 instead of the -0.1, and our t-test statistic is now positive 0.26 instead of the -0.26. Okay, so that is and we also again get our p-value for the two-tailed test or p-value for a one-tailed test. So that's two ways that we can demonstrate the paired t-test using JMP. Thanks for watching.
