Generating Multiple Probability Plots on One Graph with Statit Custom QC

Abstract: This article demonstrates how to generate probability plots for more than one variable on the same graph using Statit Custom QC. It will be necessary to use Statit commands rather than the Probability Plot Dialog Box.

Products: Statit e-QC, Statit e-Server, Statit Custom QC

Probability plots are usually used show whether the data approximates a normal distribution, which can be an important assumption in many statistical analyses. The Probability Plot dialog box in Statit can be used to generate plot for a single variable. You can find the Probability Plot dialog box in Statit products by choosing: Graphics -> Distribution Plots

It is also possible to customize a probability plot graph to include more than one plot, however, it is necessary to use Statit commands in the operation. If you are new to Statit commands, please do continue reading. I have tried to show the "natural" language behind the Statit commands.

Generating the First Plot Using Statit Command Language

This example shows the steps to getting two variables onto the same probability plot. I began by opening an example data file that Statit Software ships with Statit using the command:

This commands gets the file "qc.wrk" and begins a new workspace by clearing any data that may already have been entered.

Then, I decided to omit for all variables cases 19, 54,58 and 99. These cases have extreme values that only confuse this probability plot example, but in real life you probably don't want to omit information with out good cause. I used the command:

After I got the data into good shape for this example, I used the command:

to graph a probability plot of the variable Pressure. I decided on no normality test, no reference line, and no x-axis name. I set the x-axis minimum and x-axis maximum values at 75 and 150, respectively. I decided to not draw the graph until later.

Because I am going to put more than one plot on the graph, I thought it was a good idea to build a legend. So, I used the command:

to be sure the plot elements in the xy1 space were red in color and the legend was labeled "Pressure".

Calculating Z-scores of Cumulative Probability Values for the Second Plot

Now I needed some help. So I asked a local statistician about probability plots. She told me that a probability plot is a plot of the cumulative probabilities of the observation values for each case. Not only that, but, for normally distributed observations a plot of the z-scores of the cumulative probabilities results in a more or less straight line. And that is what Statit generates. So, I knew that I needed to calculate cumulative probabilities for the second variable and then calculate z-scores for the cumulative probabilities in order to get a second plot on the graph.

Seemed like a lot of work to me, but I did it anyway. The formula for cumulative probability is R/n+1, where R is the ordinal number which indicates each cases relative position in the ordered set of all cases, and, n+1 is the total number of cases plus one.

The command:

is used to calculate a new variable called rWidth by ranking Width.

I also calculated the cumulative probabilities as the new variable rt2 by dividing rWidth by the number of cases in (rWidth) plus 1 (n+1). The command looks like:

The z-score is also called the inverse of the standard normal distribution. So the command:

directly calculates the z-scores of rt2 and saves them in the new variable z2.

Drawing the Second Plot and Creating the Graph

Once I got the statistics out of the way, all I had to do was to tell Statit to get another plot on the graph, add a legend and draw everything. This took three commands. First, the command:

plotted Width along the x-axis and the z-scores in z2 on the y-axis. The color and legend subcommands are the same as before. With the command:

The legend was displayed as a column with the right center anchor point at the grahp space location 980 749.

Finally, I used the command draw to draw all of the elements, the separate plots and legend, all at once.

And the plot ...

Gathering All of the Commands in One Spot

These are all of the commands I used in the order I used them to generate two probability plots on the same graph.

If you have Statit Custom QC and aren't familiar with Statit macros, all they are is a "gathering of the commands." Copy these commands into a the Macro Editor (File->Macros->Editor) and click apply. Or copy them into a plain text (ASCII) editor like Notepad, save the file on your desktop as 2ProbPlots.stc and use the lightening bolt icon to run the combined commands as a macro.

A Few Warnings

I cheated on this plot be making sure the first gprob command generated a x-axis wide enough to accommodate both Width and Pressure data. If you aren't careful, a second plot will be generated but you will never see it because it ends up outside the space defined in the graph range.

Second, good programming protocol would normally have me cleaning up all of the intermediate variables I calculated. I left them in the dataspace so that the curious among you could look at the intermediate results.

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