PairwiseProbabilityPlot [{{y11,…,y1n},…,{ym1,…,ymn}}]
plots a CDF of columns in the data against each other.
PairwiseProbabilityPlot
PairwiseProbabilityPlot [{{y11,…,y1n},…,{ym1,…,ymn}}]
plots a CDF of columns in the data against each other.
Details and Options
- PairwiseProbabilityPlot is also known as a P-P plot matrix.
- It plots high-dimensional data by creating a grid of individual plots of just two data columns at a time.
- The plot compares column yi={y1i,y2i,…,ymi} against column yj={y1j,y2j,…,ymj} by plotting a a probability-probability plot of yi against reference data yj in panel {i,j}.
- The plot in panel consists of points whose coordinates are , where is the probability that a value in yi is less than the k^(th)-smallest value in yj, for k=TemplateBox[{{{p, _, j}, , n}}, Ceiling].
- Probability plots can help identify the shapes of the distributions of the data column yi relative to column yj:
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yi and yj are similarly distributedthe probability that values are less than x is higher for yi than yjthe probability that values are less than x is lower for yi than yjthe probability that values are less than x is higher for yi than yj for smaller values of xthe probability that values are less than x is higher for yi than yj for larger values of x
- PairwiseProbabilityPlot [Tabular […]cspec] extracts and plots values from the tabular object using the column specification cspec.
- The following forms of column specifications cspec are allowed for plotting tabular data:
-
{coly1,…,colyn} plot the colyi against colyj in a pairwise manner
- PairwiseProbabilityPlot takes the same options as ProbabilityPlot , with the following changes and additions: [List of all options]
-
- PlotLayout can have the following settings:
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"Descending" data columns going down and to the right"Ascending" data columns going up and to the right"DescendingHalfMatrix" lower half of the descending layout"AscendingHalfMatrix" upper half of the ascending layout
- Headers specifies the labels to use for each column in the data, and will generally be displayed above each column and after each row in the final plot.
- Possible settings include:
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None leave the plot columns and rows unlabeledAutomatic automatically label columns and rowsAll always include column and row labels"Indexed" number the columns and rows 1, 2, …, n{lbl1,lbl2,…,lbln} use the given labels lbli
- HeaderAlignment determines how data column labels are aligned with regard to the plot columns and rows.
- HeaderAlignment can take the following forms:
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Center center the labels in the header positions{h,v} separate horizontal and vertical alignments within the header position{cols,rows} use col for plot columns and row for plot rows
- HeaderBackground and HeaderStyle can take the following forms:
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None use ambient stylingsty use the style sty for all headers{sty1, sty2,…,styn} use the given styles styifor successive headers{cols,rows} use col for plot columns and row for plot rows
- HeaderDisplayFunction determines how headers are displayed.
- Possible settings are:
-
Automatic automatic formattingNone use unprocessed labels
- ColorData ["DefaultPlotColors"] gives the default sequence of colors used by PlotStyle .
- The arguments to ColorFunction are yi1,yi2,…,yin. By default, the color function arguments are scaled per data column to be between 0 and 1.
- Use ColorFunctionScaling None to use unscaled values, or ColorFunctionScaling {cfsc1,cfsc2,…} to selectively scale column values.
- Possible settings for PlotHighlighting include:
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Automatic automatically highlight positions in the panelsNone disable interactive highlighting
- Highlight options with settings specific to PairwiseProbabilityPlot
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AspectRatio 1 ratio of height to width for each panelHeaders Automatic labels to use for each data column yiImageMargins 0. the margins to leave around the graphicPreserveImageOptions Automatic whether to preserve image options when displaying new versions of the same graphicWorkingPrecision MachinePrecision the precision used in internal computations for symbolic distributions
List of all options
Examples
open all close allBasic Examples (3)
Create an array of probability plots from data with labeled columns:
Compare all columns in a dataset:
Provide header names for the data:
Scope (3)
Data (2)
Plot datasets:
Plot arrays of values:
Tabular Data (1)
Get tabular data:
Create a pairwise array of probability plots:
Use a different theme for the plot:
Options (47)
AspectRatio (2)
By default, PairwiseProbabilityPlot uses an equal height-to-width ratio:
Use a fixed height-to-width ratio:
Axes (3)
AxesStyle (3)
Change the style for the axes:
Specify the style of each axis:
Use different styles for the ticks and the axes:
Background (2)
By default, PairwiseProbabilityPlot has a white background:
Set a background color:
ColorFunction (3)
Color by scaled and coordinates:
Color with a named color scheme:
ColorFunction has higher priority than PlotStyle for coloring:
Frame (2)
On PairwiseProbabilityPlot , a frame is drawn on each subplot by default:
Draw a frame on the left and bottom edges of the panels:
FrameStyle (2)
Specify the style of the frame:
Specify the style for each frame edge:
GridLines (2)
By default, PairwiseProbabilityPlot does not draw gridlines:
Draw a background grid:
HeaderBackground (2)
By default, PairwiseProbabilityPlot uses a white header background:
Set a header background color:
Headers (3)
By default, PairwiseProbabilityPlot does not label headers:
Number the columns for unlabeled data:
Provide header names for the columns:
ImageSize (6)
Use named sizes such as Tiny , Small , Medium , and Large :
Specify the width of the plot:
Specify the height of the plot:
Allow the width and height to be up to a certain size:
Specify the width and height for a graphic, padding with space if necessary:
Setting AspectRatio Full will fill the available space:
Use maximum sizes for the width and height:
Use ImageSize Full to fill the available space in an object:
Joined (2)
Data is not joined by default:
Join the points:
PlotLayout (3)
Switch the orientation of the diagonal elements:
Show plots below the diagonal:
Only show plots above the diagonal:
PlotLabel (1)
Add an overall label to the plot:
PlotMarkers (3)
Use open markers:
Change the size of the default plot markers:
Use explicit graphics for plot markers:
PlotStyle (1)
Style the data using PlotStyle :
PlotTheme (2)
Use a theme to customize the plot:
Change the color scheme:
ReferenceLineStyle (4)
ReferenceLineStyle by default uses a Dotted form of PlotStyle :
Draw a dotted red reference line:
Draw a solid red reference line:
Use None to turn off the reference line:
Spacings (1)
Change the space between the plots:
Related Guides
Text
Wolfram Research (2024), PairwiseProbabilityPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/PairwiseProbabilityPlot.html (updated 2025).
CMS
Wolfram Language. 2024. "PairwiseProbabilityPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/PairwiseProbabilityPlot.html.
APA
Wolfram Language. (2024). PairwiseProbabilityPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PairwiseProbabilityPlot.html
BibTeX
@misc{reference.wolfram_2025_pairwiseprobabilityplot, author="Wolfram Research", title="{PairwiseProbabilityPlot}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/PairwiseProbabilityPlot.html}", note=[Accessed: 17-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_pairwiseprobabilityplot, organization={Wolfram Research}, title={PairwiseProbabilityPlot}, year={2025}, url={https://reference.wolfram.com/language/ref/PairwiseProbabilityPlot.html}, note=[Accessed: 17-November-2025]}