Customizing Box Plot in varibility chart to Display Sigma-Based Intervals

[#1]

Hello everyone,

I am currently working with JMP and using box plots to visualize my data. I noticed that it is possible to configure the display of outliers or quantiles, but I would like to know if it is possible to modify the box plot settings to show intervals based on standard deviations (sigma) around the mean, instead of the usual quartiles.

For example, I would like the box to represent mean ± 3 sigma, and the whiskers to represent ± 4 sigma or ± 6 sigma, in order to better visualize statistical dispersion using this approach.

Does anyone know if this can be done directly in JMP? If yes, could you please guide me on how to set this up or if there is a specific script or option available?

Thank you in advance for your help!

[#2]

You would have to write a graphical script for such visualizations.

Some links regarding box plots:

• Statistics Knowledge Portal - Box Plot 
• Essential Graphing > Graph Builder > Element Types and Options > Box Plot 

[#3]

Thank you very much, Jarmo.

I already have many scripts completed (variabilty chart, graph builder) , and I will share an example where I need this type of box plot (standard deviation). However, the actual preference is for a quantile box plot rather than a standard deviation box plot. I have read your suggestions but haven’t seen any examples using standard deviation. Could you please advise on how to create a visualization incorporating standard deviation?

To summarize I would like Box Type = Std dev ( quantile NO, Outliers NO)

VarChart = dt << Variability Chart(
		Invisible,
		Y( Eval( Y_list ) ),
		X( Eval( X_list ) ),
		Analysis Type( "Choose best analysis (EMS REML Bayesian)" ),
		Show Range Bars( 0 ),
		Connect Cell Means( 1 ),
		Variability Summary Report( 1 ),
		Std Dev Chart( 0 ),
		Points Jittered( 1 ),
		Show Box Plots( 1 ),
		Local Data Filter(
			Add Filter( 
			columns( :Temperature, :Corner, :Revision, :XY ),
			 )
		),
		SendToReport(
			Dispatch( {}, "Mean", NumberColBox, {Set Format( "Fixed Dec", 8, 3 )} ),
			Dispatch(
				{},
				"Std Dev",
				NumberColBox,
				{Set Format( "Fixed Dec", 8, 3 )}
			),
			Dispatch(
				{},
				"Minimum",
				NumberColBox,
				{Set Format( "Fixed Dec", 8, 3 )}
			),
			Dispatch(
				{},
				"Maximum",
				NumberColBox,
				{Set Format( "Fixed Dec", 8, 3 )}
			),
			Dispatch( {},"Variability Chart",FrameBox,{Frame Size( 1400, 800 )}), // Format A4 (Hauteur, Largeur) 
			Dispatch( {}, "CV", NumberColBox, {Visibility( "Collapse" )} ),
			Dispatch( {}, "Std Err Mean", NumberColBox, {Visibility( "Collapse" )} ),
			Dispatch( {}, "Lower 95%", NumberColBox, {Visibility( "Collapse" )} ),
			Dispatch( {}, "Upper 95%", NumberColBox, {Visibility( "Collapse" )} ),
			Dispatch( {}, "Range", NumberColBox, {Visibility( "Collapse" )} ),
			Dispatch( {}, "Median", NumberColBox, {Visibility( "Collapse" )} ),
			Dispatch( {}, "Observations", NumberColBox, {Visibility( "Collapse" )} ),
			Dispatch( {}, "2", ScaleBox, {Label Row( Set Font Size( 16 ) )} )
		)
	);

[#4 · Accepted solution]

I would consider having box plot with standard deviations confusing as box plots utilize median and quantiles.  

Here is very hard-coded idea to demonstrate single rectangle with a line (no whiskers but they could be added with Line())

Names Default To Here(1);
dt = Open("$SAMPLE_DATA/Variability Data/2 Factors Crossed.jmp");
obj = dt << Variability Chart(
	Y(:Measurement),
	X(:Operator, :part#),
	Model("Crossed")
);

fb = Report(obj)[FrameBox(1)];

ms = fb << Find Seg(MarkerSeg(1));

xs = ms << Get X Values;
ys = ms << Get Y Values;

v = ys[1::3];

s = Std Dev(v);
m = Mean(v);

fb << Add Graphics Script(
	Pen Size(3);
	Pen Color("Green");
	Rect(0.35, 3*s + m, 0.75, -3*s+m);
	Pen Color("Blue");
	Line({0.35, m}, {0.75, m})
);

I don't know how much data you have, but you could consider overlaying distribution instead of using the rectangles

or violin plots

[#5]

Thank you very much, Jarmo. I will try your solutions. It would be much more convenient if a function were directly integrated into the software.

[#6]

For that JMP Community does have a JMP Wish List where you can post ideas which you hope to be implemented to JMP in some future version.

[#7]

I tried to implement your solution, but the boxplot does not stay in place. When using a loop, it shifts on the graph. How can I display all the boxplots simultaneously? Below is the For loop I created.

		// To count the number of catagories in a specific column
	Summarize (T=by(dt:Temperature));
	Summarize (C=by(dt:Corner));
	Ntemp=  N Items(T);
	NCorner=  N Items(C);
	
For( v = 0, v < Ntemp*NCorner , v++, 
	fb << Add Graphics Script(
		Pen Size(2);
		Pen Color("Red");
		Rect(0.3+v, 3*s + m, 0.7+v, -3*s+m);
		Line({0.3+v, m}, {0.7+v, m});
		// Positive
		V line(	((1+2*v)/2),	3*s + m, 	4*s + m );
		Line({	0.3+v, 			4*s + m}, {	0.7+v, 4*s + m});
		V line(	((1+2*v)/2),	4*s + m, 	6*s + m );
		Line({	0.3+v, 			6*s + m}, {	0.7+v, 6*s + m});
		// negative
		V line(	((1+2*v)/2),	-3*s + m, 	-4*s + m );
		Line(	{0.3+v, 		-4*s + m}, {0.7+v, -4*s + m});
		V line(	((1+2*v)/2),	-4*s + m, 	-6*s + m );
		Line({	0.3+v, 			-6*s + m}, {0.7+v, -6*s + m});
	);
	wait(0);
);

[#8 · Accepted solution]

You have to do the looping inside the Graphic Script (and possibly evaluate some variables inside it).

[#9]

One example (this is still missing quite a few things such as scaling Y-axis and "whiskers" and it isn't as dynamic as it could be)

Names Default To Here(1);
dt = Open("$SAMPLE_DATA/Variability Data/2 Factors Crossed.jmp");
obj = dt << Variability Chart(
	Y(:Measurement),
	X(:Operator, :part#),
	Model("Crossed")
);

dt_groups = dt << Summary(
	Group(:Operator, :part#),
	Freq("None"),
	Weight("None"),
	output table name(""),
	Private
);
group_sizes = dt_groups[0, "N Rows"];
Close(dt_groups, no save);

group_size = group_sizes[1]; // lazy assumption that all groups have same size

fb = Report(obj)[FrameBox(1)];
ms = fb << Find Seg(MarkerSeg(1));
xs = ms << Get X Values;
ys = ms << Get Y Values;


yvals = Shape(ys, N Items(group_sizes), group_size);

xv = xs[1::N Items(xs)::group_size];
stddevs = V Std(yvals`);
means = V Mean(yvals`);

Eval(EvalExpr(
	fb << Add Graphics Script(
		Pen Size(3);
		s = Expr(stddevs);
		m = Expr(means);
		x = Expr(xv);
		For(i = 1, i <= N Items(s), i++,
			Pen Color("Green");
			Rect(x[i]-0.2, 3*s[i]+m[i], x[i]+0.2, -3*s[i]+m[i]);
			Pen Color("Blue");
			Line({x[i]-0.2, m[i]}, {x[i]+0.2, m[i]});
		);
	);	
));