There are two methods to overlay histograms in JMP, using the Distribution and Graph Builder platforms. You might want to overlay histograms to review the similarities and/or differences between the distributions of two or more variables. Overlaying the histograms allows you to compare the distributions in a more precise manner than viewing them separately. Overlaying histograms using Distribution The first method uses the Distribution platform. Below is an example using the Car Physical Data.jmp sample data table. In addition to overlaying histograms, normal distribution curves are overlayed in this example. If you do not desire distributional curves in your graph, simply disregard the related steps. The structure of Car Physical Data, which has a total of 116 rows, is as follows:     From the data table, go to Analyze > Distribution. Place two numeric, continuous columns, say Displacement and Horsepower, in the Y, Columns box and click OK. The output will look like the following (I’ve removed some of the default output sections, like Quantiles and Summary Statistics, for simplicity):     If you see the histograms side by side instead of on top of one another, click on the red triangle menu next to Distributions and select Stack to see them as they are in the above image. If the histograms appear in a vertical format, click on the red triangle menus next to each variable name and choose Display options > Horizontal Layout. Another option is, rather clicking on each individual red triangle menu, to press the Ctrl key while making the change for one variable. By doing this, the change broadcasts across all other variables. As I mentioned above, I’m going to fit a normal curve to each distribution and overlay those elements as well. To produce the normal curves, hold the Ctrl key and click (Command + click on a Mac) on the red triangle menu next to Displacement. Then, choose Continuous Fit > Normal. A Fitted Normal distribution appears in the output for both variables, as seen below.       Now, I’ll go ahead and customize the colors of the elements in each plot so we can distinguish them in the final result. I will use red for Displacement and blue for Horsepower. Right click within the Displacement histogram and choose Customize. In the item list in the window that appears, click Histogram. Change the Fill Color to red and the Transparency to 0.5 (so we can more easily observe where the histograms overlap). The Customize Graph window appears as follows:     In the case for Displacement, the normal curve is already red, so we do not need to customize that item. Click OK to close the window. Now, repeat the previous steps to change the Horsepower histogram color to blue and the transparency to 0.5. We want to change the normal curve to be blue as well, so click on the Normal line item and change the Line Color field to blue. Click OK. Our output now looks like this:     Now, I’ll copy the Displacement histogram and normal curve onto the Horsepower plot so they are overlayed. To do this, first right click within the Displacement histogram and choose Edit > Copy Frame Contents. Next, right click within the Horsepower histogram graph and choose Edit > Paste Frame Contents. You may have to adjust the axis range in view to see both complete histograms . The result is both histograms and normal curves in one graph:     With this method, there is no automatic legend, but you can use the Annotate  tool to add text and the Line  tool to add a colored line element for a manual legend. After implementing these tools, my result is something like this:     Overlaying histograms using Graph Builder The second method to overlay histograms (and distribution curves) uses the Graph Builder platform. This method requires the data to be in a stacked format so that all continuous values are in one column . To stack the data, go to the Tables menu from the original Car Physical Data table and choose Stack. Place both Displacement and Horsepower in the Stack Columns box. Click OK. The new stacked data table has a column named Data that contains all data values, and a column named Label that indicates whether that value originated from the Displacement column or the Horsepower column. From the stacked data table, go to Graph > Graph Builder. Drag Data to the X role and Label to the Overlay role. Right click within the graph and choose Points > Change to > Histogram. Now, we need to make sure the plot is scaled correctly. I’ll go back to the overlayed plot in the Distribution platform and click on the red triangle menu > Histogram Options > Density Axis. This axis gives us an idea of what the Graph Builder Y axis should be. An axis appears on the right side of the histogram, and I double-click on it to open the Axis Settings window. The maximum value in this case is 0.0117586. Now, go back to the Graph Builder output, drag the Data column to Y and double click the axis to open Y Axis Settings. Set the minimum to 0 and the maximum value to 0.0117586, to mimic the density axis from the Distribution platform. I also set the increment to 0.002, and the Dec (decimal) field in the Format section to 3. If desired, you can double click on the X axis to open its Axis Settings dialog and customize the minimum, maximum, and increment values.  The result at this point is this:   Next, I will overlay the normal curves. First, we’ll need to record the mean and standard deviation values from the fitted normal distributions applied to both Displacement and Horsepower in the Distribution platform. Recall that these values are given in the output after selecting Continuous Fit > Normal. Recall the values (outlined in red) from the Distribution output below:     With these values recorded, right click within the Graph Builder plot and select Customize. Click on the + icon to add a custom script. We’ll use the syntax below for each normal curve. The Pen Color statement defines the color of the curve while the Y Function draws a normal density curve with specified mu and sigma parameters (recorded from the Distribution output for each variable).   Pen Color( "<color>" ); Y Function( normal density(x, mu, sigma), x ); Using the syntax above and the (rounded) mu and sigma values for the fitted Normal distribution applied to Displacement and Horsepower, I enter the following text into the custom script window.   //Horsepower Pen Color( "blue" ); Y Function( Normal Density( x, 130.198, 39.8225 ), x ); //Displacement Pen Color( "red" ); Y Function( Normal Density( x, 158.31, 60.4088 ), x ); Click OK. The result is this:   Now, I’ll make a few customizations to finalize the graph to my preferences. I prefer to remove the graph label, the Y axis label, as well as the X axis label. I’ll double click in each field and use the delete key to remove the text. Also, I don’t want to show any tick labels on the Y axis. I double click on the axis to open Y Axis Settings and uncheck the Labels checkbox for major tick marks in the Axis Label Row section of the dialog. Also, I want to move the legend inside the graph. I click on the red triangle menu next to Graph Builder and choose Legend Position > Inside Right. Lastly, I’ll extend the range of the x-axis slightly for a more complete picture. I open X Axis Settings and set the minimum as 0 and the maximum as 400. Finally, I click on the Done button and am left with the following graph:       The above examples show how to overlay histograms and normal curves using two methods – the Distribution platform and the Graph Builder platform in JMP. If desired, this example can be generalized to overlay more than two histograms and normal curves, or fit other distributional curves to your data. ... View more

Often in an experiment, more than one measure is taken on the same subject or experimental unit. This means that a repeated measures analysis of the data may be necessary to make valid inferences and to draw meaningful conclusions. JMP offers multiple methods to analyze repeated measures: a multivariate repeated-measures approach, a univariate split-plot approach, and an additional capability through JMP Pro to perform such an analysis with the Mixed Model personality within the Fit Model platform. The types of analyses are compared in the following discussion. The example uses the DOGS (dogs.jmp) sample data table, which is the result of a study with repeated measures. In this example, before performing analysis on the DOGS data set, we will rename the ID variable as Subject and change the modeling type from continuous to nominal. Figure A shows selected columns from the DOGS table. This data table contains information on 16 dogs assigned to treatment groups defined by the independent variable drug, having values ‘morphine’ and ‘trimeth.’ The blood concentration of histamine is recorded before drug injection and again at one and three minutes after injection. The log of each value is taken (a common transformation to achieve more linearity in the response variable), which results in three variables, LogHist0, LogHist1, and LogHist3. Also, there is an additional Subject column, declared as Nominal as mentioned above, which will be used to account for the within-subject variability in a univariate analysis of repeated-measures data. Figure A: Arrangement of Data Table, Multivariate Approach     Figure B shows selected columns from the restructured DOGS table where the   LogHist   columns have been stacked into a single response column. Figure B:    Arrangement of Data Table, Univariate Split-Plot Approach and Mixed Model Approach      A Multivariate Approach The original DOGS table with multiple response columns is in the form needed for a multivariate analysis of variance (MANOVA) that tests the same effects − nothing needs to be changed. With this data table active, again choose Fit Model from the Analyze Menu. Specify LogHist0, LogHist1 and LogHist3 as Y variables. Change the Fitting Personality to Manova. Assign drug as the model effect and run the model.   When there are multiple Y variables, JMP automatically performs a multivariate analysis. When you first run the model, the multivariate control panel appears. To test the effect of drug over time, select ‘Repeated Measures’ as the response design from the popup menu on the control panel. In the repeated-measures dialog that appears, use the default effect name Time but check ‘Univariate Tests Also’ to obtain univariate and adjusted univariate tests. This option includes a test of sphericity (not shown here), which checks whether the unadjusted univariate F tests are appropriate. If the sphericity chi-square test is not significant, you can use the unadjusted univariate F tests. However, if the sphericity test chi-square is significant, then the criterion is rejected and the multivariate F tests or the adjusted univariate F tests should be used. JMP gives both the Greenhouse-Geisser (G-G), and the Huynh-Feldt (H-F) adjusted F tests. A Univariate Split-Plot Approach A univariate model has a single response. To analyze the data as a univariate analysis of variance (ANOVA), you must include each source of variation (between-subjects and within-subjects) as an effect in the model. The univariate analysis requires that the response measurements be in a single column. Using the Stack command in the Tables menu, you can stack the LogHist0, LogHist1, and LogHist3 columns to create a new response column, as shown in Figure B. The new response LogHist and the new classification variable Time were created by the Stack command. With the data table correctly set up, choose Fit Model from the Analyze Menu. Select LogHist as Y, and add the Effects in Model as shown in Figure C. Figure C: Univariate Repeated Measures Specification     To create the model shown above, which has a random effect for testing the between-subjects effect in the model, click the following variables and buttons: drug in the variable selection list, then Add Subject in the variable selection list, then Add drug in the variable selection list, and Subject in the Effects in Model list, then Nest Subject [drug] in the Effects in Model list, then select Random from the Effect Attributes pop-up menu giving Subject [drug]& Randomin the Effects in Model list Time in the variable selection list, then Add drug in the variable selection list and Time in the variable selection list, then Cross The between-subject effect, drug, is the whole plot effect of a split-plot design. The Subject effect is nested within drug. This term is specified as a random effect. Random effects included in the model indicate multiple sources of variation in the data. All sources of variation are taken into consideration in the REML model; therefore effect estimates and effect tests are adjusted and calculated appropriately. After running this model you can examine the significance of the model effects seen in the ‘Fixed Effect Tests’ section in the results window, which are shown below in the Comparing Results section. Mixed Model Approach In JMP Pro, the Mixed Model personality within the Fit Model platform also offers the capability to analyze repeated measures data. This method requires the response measurements to be structured in a single column as displayed in Figure B. The Mixed Model personality fits a variety of covariance structures. This is in contrast to both the MANOVA, which assumes an unstructured covariance matrix where all variances and covariances are estimated individually, and the univariate split-plot ANOVA, which assumes all errors are independent. When data is normally distributed, the latter is equivalent to assuming a compound symmetry covariance structure within a Mixed Model. With the data table active, choose Fit Model from the Analyze Menu. From the Personality drop down menu, select Mixed Model. Assign LogHist as the Y variable, add Time, drug, and drug*Time in the Fixed Effects tab, and add Subject to the Random Effects tab. Click on the Repeated Structure tab and keep the default selection, ‘Residual’, which represents the compound symmetry covariance structure. In this example, we’ll use this option to show consistent results across method. As explained in the previous paragraph, the compound symmetry structure is equivalent to the assumed covariance structure in a univariate split-plot analysis. Run the model, and the significance of the fixed effects will appear in the last section of the results window. Comparing the Results Multivariate Approach        Univariate Split Plot Approach      Mixed Model Approach (JMP Pro)     Comparing the Methods A comparison of analysis results is shown above. By examining each set of results, you can see the relationship among the multivariate and univariate effects tests, including the mixed model analysis. Important points to note are: For between-subject effects (drug), the multivariate approach gives the same results as the univariate approach when there are no missing values. If there are missing values, a univariate analysis uses all non-missing data values but the multivariate analysis excludes any subject with any missing values. If there are no missing values, the within-subjects Time variable in the univariate model is the same as the unadjusted Time effect in a multivariate model having a ‘Repeated Measures’ response design. However, these tests are appropriate only if the sphericity test criterion (mentioned previously) is met. Otherwise, the multivariate tests or the adjusted univariate tests should be used. Using the compound symmetry covariance structure within the Mixed Model personality generates the same results as the univariate split-plot analysis because of the fairly normal distribution of the data. With data containing repeated measures in time, note that the alternative covariance structure AR(1) frequently is appropriate, as it allows for correlated observations but does not overfit the model. Often in a repeated-measures study, the most important effect is the within-subject by between-subject interaction – the hypothesis of interest is whether the study treatment has an effect over time. In the univariate analysis, the drug*Time interaction appears insignificant. In this example, the more powerful multivariate approach shows the drug*Time interaction effect to have marginal significance. Summary JMP can analyze repeated measures data with a univariate split-plot model, a multivariate analysis or, with JMP Pro, a mixed model. Each type of analysis has its advantages and disadvantages: The multivariate analysis is easy and intuitive to specify in JMP. Its tests are usually more powerful.  From a computing standpoint, this method is most efficient. However, if a subject is missing a value, all information for that subject is lost to the analysis. The univariate analysis can use all the data–only a subject's missing measurement is lost to the analysis.  However, the univariate analysis can be very computationally intensive, particularly if there are many subjects. Both of the above methods assume an extreme covariance structure. The multivariate analysis assumes unstructured covariance matrix where all variances and covariances are estimated individually. The split-plot analysis assumes all errors are independent. With both of these assumptions, information in your data is used to estimate the covariance parameters. This can result in the overfitting of your model. The advantage of a mixed model is that it allows you to select a less extreme covariance structure resulting in a more powerful model. In the JMP Fitting Linear Models Guide, the Additional Examples section of the Mixed Models chapter offers more information about overfitting or underfitting a model and usage of the various covariance structures in the Mixed Model personality. In the univariate tests for within-subject effects and interactions involving these effects, the above assumptions about the covariance matrix are required for the probabilities provided by the ordinary F tests to be correct. If these assumptions are not met (if the sphericity test is rejected), then probabilities for adjusted univariate F tests (given in the multivariate report) or the multivariate F tests should be used. Because of these assumptions, the univariate approach should be considered only when the Sphericity condition is met. For more information on this test and other ideas discussed in this sample, see the JMP Fitting Linear Models book, which is found by selecting Help > Books > Fitting Linear Models (Chapter 3: Standard Least Squares Report and Options, Chapter 7: Mixed Models, and Chapter 8: Multivariate Response Models). References Cole and Grizzle, J.E. (1966), "Sixteen Dogs," Biometrics, 22:810 ... View more

The Transpose platform enables you to rotate your data set such that the columns become the new rows and the rows become the columns. This is a simple task to achieve in JMP.   As we know, JMP requires the data to be in a specific format to use each platform. If you want to see the distribution of your data using the Distribution platform, the values of interest must be in a single column and not spread out among multiple columns. If you want to do a t-test in the Fit Y by X – Oneway platform, your data table must have one column containing the two distinct group values and one column containing the data values, rather than having a column for each group containing the data measurements. Because of the way JMP uses data in each platform, sometimes it may be necessary to restructure your original data table, as data may be recorded in a format not ideal to performing your analysis with a JMP platform. Let’s discuss a case where using the Transpose platform would be necessary. Say there are patients in a clinic and a certain measurement is taken from each before and after some type of procedure or event. The data is collected in the structure below, with the measurements for each patient entered in only two rows (one for the Before measurement and one for the After), with a new column for each patient.       However, we are interested in using JMP to perform a paired t-test (because the Before and After data values are dependent on one another), which will help us determine whether the two samples (before and after) are significantly different from one another.   To do a paired t-test, we need to use the Matched Pairs platform in JMP (Analyze -> Specialized Modeling -> Matched Pairs). To run the analysis, we must have the Before measurements for each patient in one column and the After measurements in another. In other words, we need the rows Before and After to become the columns, and we need each Patient column to become a row in the new data table.   To do this, simply go to Tables -> Transpose, and place all Patient x columns in the Transpose Columns box. Place Time in the Label box. The result is:       Now, we can open the Matched Pairs platform and place the Before and After columns in the “Y, Paired Response” role. This gives a paired t-test comparing the before and after measurements for the sample of patients.   In this short video, I use a JMP sample data table to demonstrate the Transpose feature with both a simple example and another with a grouping variable. This video is part 3 of 3 in the Manipulating Data in JMP series. Part 1 showed how to use Tables>Stack, and part 2 was about using Tables>Split. Thank you for watching!   ... View more

One way to manipulate your data in JMP is to "split" a data table, or to separate the data values contained in one (or more) column(s) and place them into multiple new columns. This may be necessary when your data is in a vertical format and the analysis you want to perform or graph you want to create in JMP requires the data to be structured in a horizontal manner. In this video, I demonstrate how to use the Split dialog and walk through a few examples, displaying the capabilities JMP offers for this type of data manipulation. This video is Part 2 of 3 in the Manipulating Data in JMP series. The first video focused on Tables > Stack. The third video in this series shows how to use Tables > Transpose.   ... View more

In this short video, I demonstrate how to modify the structure of a data table in JMP using the Stack feature. This tool is useful is when your data was not collected or originally structured in a manner that aligns with the JMP platform you wish to use. This video is part 1 of 3 in the Manipulating Data in JMP series. The next two parts demonstrate the Split and Transpose capabilities in JMP.   ... View more