Hi, my name is Carly Metcalfe and I'm a PhD student of Dr. Montgomery's at Arizona State University, and I'm going to be working through some of the class examples using the different softwares that have been discussed in this course. So I'm going to start off talking about the very first example used in Module two, the Portland cement data, and I'm going to walk through how we would perform a two-sample t-test using JMP. So if you remember this example is there's an engineer, and they're studying a new formulation of Portland cement mortar, and they're adding this polymer latex emulsion during the mixing and it results in this much shorter cure time. But before they go change everything to this new mixture, they want to make sure that this new formulation doesn't have an adverse effect on the tension bond strength. So they perform this experiment where there are 10 samples from the original formulation, and then another 10 samples from the modified formulation. This is what the data looked like, the Dr. Montgomery presented, it's also in the text. So we have the two groups, the modified mortar group and the unmodified mortar group. So in JMP, I'm going to talk about how we enter and organize this data, we're going to create a JMP data table. I'm going to show you how to plot the data and then perform the two-sample t-test, I'm also going to show you how we can make a normal probability plot to assess the assumptions of the two-sample t-test. So let's get started. So this is my JMP platform, we have some menus here at the top and some shortcuts. The first thing we're going to do is create a new data table. So they're many things in JMP, there are more than one way to do it so just because I show you one way doesn't mean there isn't another option on how to do it. So we're going to use New Data Table, this button right here, to create a new data table, or we can also go to File, New, Data Table. We start off with just one column, JMP always wants to start off with at least one column, we can easily create a new column. So if we were to type this data in as it was shown in the text in our table, we could say this column is going to be called Modified, modified formulation and we could simply start entering the data. So the first observation was 16.85, and the second observation was 16.4 and so on. We can also create a new column, I can just double-click into this column or we could have right-clicked and inserted a new column, or you can use this column feature in the main options that says Cols, New Column. So lots of ways to make a new column. We can simply call this the Unmodified version and start typing the data in to these cells. So the first observation was 16.2 and so on. I've already entered all these data into another data table, so I'm going to open that up for us now. So here's all of our data in two columns, the modified mortar and the unmodified mortar, and you'll see right here that JMP shows us that these are both continuous variables. Also I can double-click on this column and get some column information including the column name, the data type that says that it's numeric. This is how the data was presented to us, but if we want to perform a two-sample t-test, we actually want all of the data in one column, all of our response data, all of this bond strength measurement data, and then another column we want a factor whether it's the modified or the unmodified formulation. So what we're going to do is we're going to stack these two columns. So I'm going to go to Tables, and from this menu I'm going to select Stack, and then I'm going to select both of these columns and enter them over here to the Stack Columns box and say, OK. Now we have a new data table that has all of my strength data in one column, and then my factor data, my treatment, my categorical variable in another column, and so we'll see to that JMP now gives this a character data type as opposed to a response data which is the numeric. One other thing you can do, it's not necessary, you could go to Tables and sort this data. So maybe I wanted to sort it by the groups. So click Sort, I'll enter a label into the By and say OK, and now I have all of the modified formulation first, and then the unmodified formulation second, and I might want to change these to Formulation and I can also change this to Strength. You could change the sizing of your columns as you see fit. So the next thing we're going to do is try and plot this data. My go to plot in JMP is to go to Graph, Graph Builder. It's very interactive, you can drag and drop as you see fit, it's very forgiving too, so if you don't like what you did you can very easily undo it, and it's meant to be very interactive for you to discover the best way to display your data. So what I'm going to do is take our strength data, our response, and drag it over to the y-axis, and then I'm going to take our formulation column, our treatment, and drag that over to the x. Now I have the dot diagram that Dr. Montgomery showed you in the textbook. This is just vertical as opposed to the horizontal plot that is shown in textbook. So you can see this strength data and we can see the difference between the modified mortar and the unmodified mortar strength information. You might want to change this plot to a box plot. So above the top of the graph builder are different options for plots. When I click Box Plot it gives me two box plots. So maybe I really like that and I'm done, I can click this Done button and I have my plot all ready to go. So now if I want to run the two-sample t-test, I'm going to go to Analyze and we're going to go to Fit Y by X. In Fit Y by X, I'm going to enter my strength data in as the response and I'm going to enter the formulation data in as our x factor. I'll click OK and there again we get that dot plot, so that's really nice. Remember for this two-sample t-test for this data set we noticed that the variances were very similar. So we are going to use that pooled estimate of variance and we're going to use a pooled t-test. When I go to run my analysis, and in JMP you'll notice the red triangles are always key, if you're trying to figure out how to do something checkout the red triangle. So we're going to go to this red triangle and we find that the second option here is this Means/Anova/Pooled t. That's what we want for this test, so we're going to select that and a series of tables populate for us and we're going to specifically be looking for this Pooled t Test. A reminder that JMP uses the unmodified formulation minus the modified formulation, the textbook goes modified minus unmodified. So our t-test statistic or as JMP calls it the t Ratio is 2.186876 and the text, it's negative two because of this swapping of the order of the formulations. Our average difference here is that 0.278. We also have a 95 percent confidence interval for the difference and our degrees of freedom which are n minus 2 or 20 minus 2 18, and then we have our p-value. So this test was a two-sample or a two-tailed test, our alternate hypothesis was that mu one does not equal mu two, we're going to use this p-value right here, this 0.0422. If there have been a one-tailed test then we would use this 0.211. So that's how we can get all these nice results in the Pooled t Test from JMP. There's also a table down here that gives us the means from each group, their standard errors and 95 percent confidence intervals for the individual means. The last thing I'm going to show you is how we can check our assumptions by making a normal probability plot. So I'm going to go to my red triangle again, of course, and I'm going to come down to Normal Quantile Plot, and we're going to plot the quantile by actual. So now I have this plot, it makes a normal quantile plot for both the modified group and unmodified group. We can see that our data forms a pretty straight line so we feel comfortable with our normal assumption, and we also notice that the slopes of these two lines are parallel which confirms our assumption of using equal variance. If you'll notice too in the output for the pooled t-test, JMP highlights that we're assuming equal variance with this test. When you're done and you're all set with your analysis, you can always minimize things that you maybe aren't ready to share or that we're not critical to your analysis and you can save this script by going to the red triangle and going down to the bottom to Save Script and you can save the script to your data table. Now, when you save this data table, the next time you open it, you can simply run this script and your previous analysis will come up. Another option might be for you to save a plot and copy and paste a plot into a presentation or a portion of the output into a presentation. So one nice way we can do that is if we hover over the top of this output, we can go to the Selection tool as opposed to the Arrow tool and if I click on the Selection tool, I can highlight parts of the output that I might want to copy and paste and then I can simply copy this and paste it into Word or PowerPoint or how ever you want to share this information. Just remember that when you're done with the selection tool, you should go back up to this menu and switch back to the arrow. Thanks for watching this tutorial on the two-sample t-test.
