# PairwiseQuantilePlot

PairwiseQuantilePlot[{{y11,,y1n},,{ym1,,ymn}}]

creates an array of quantile plots by plotting the quantiles of the columns against each other.

# Details and Options

• PairwiseQuantilePlot is also known as Q-Q 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 quantile-quantile plot of yi against yj in panel {i,j}.
• The plot in panel consists of points whose coordinates are , where is the -smallest value in yj and is the -smallest value in yi.
• If the data in column yi has the same shape as column yj, the quantile plot will show a linear relation, even if there is a difference in location or scale:
•  yi is narrower than yj yi is wider than yj yi is shifted relative to yj
• Skewed data, with more data in one tail than the other, shows slight curvature from the diagonal:
•  yi is skewed right relative to yj yi is skewed left relative to yj yi is skewed and shifted relative to yj
• Heavy tails, indicating that yi has larger magnitude values than yj in the extremes, are indicated by plots that curve away from the diagonal at the ends:
•  yi has heavier tails than yj yi has a heavier right tail than yj yi has a heavier left tail than yj
• If the data has multiple modes or peaks in the density, there will be corresponding vertical transitions in the quantile plot where a range of quantiles have effectively the same value:
•  yi is bimodal yi is multimodal yi is unformly distributed
• PairwiseQuantilePlot takes the same options as QuantilePlot, with the following changes and additions: [List of all options]
•  AspectRatio 1 ratio of height to width for each panel Background None background to use for each plot Frame Automatic whether to draw frames around each panel FrameTicks Automatic whether to label frame edges with ticks and labels GridLines Automatic whether to include gridlines in panels GridLinesStyle Automatic style for gridlines HeaderAlignment Center horizontal and vertical alignments of headers HeaderBackground Automatic background colors to use for headers HeaderDisplayFunction Automatic function to use to format headers Headers Automatic labels to use for each data column yi HeaderStyle None styles to use for headers PerformanceGoal \$PerformanceGoal aspects of performance to try to optimize PlotHighlighting Automatic highlighting effect for points PlotLayout Automatic how to arrange the panels PlotLegends Automatic legends for data PlotMarkers None markers to use to indicate each point PlotStyle Automatic graphics directives to determine styles of points PlotTheme \$PlotTheme overall theme for the plot Spacings Automatic horizontal and vertical spacings
• PlotLayout can have the following settings:
•  "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:
•  None leave the plot columns and rows unlabeled Automatic automatically label columns and rows All 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:
•  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:
•  None use ambient styling sty use the style sty for all headers {sty1,sty2,…,styn} use the given styles styi for 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 formatting None use unprocessed labels
• 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 to use unscaled values, or ColorFunctionScaling{cfsc1,cfsc2,} to selectively scale column values.
• Possible settings for PlotHighlighting include:
•  Automatic automatically highlight positions in the panels None disable interactive highlighting

# Examples

open allclose all

## Basic Examples(3)

Create an array of Q-Q plots from data with labeled columns:

Compare all columns in a dataset:

Provide header names for the data:

## Scope(2)

### Data(2)

Plot datasets:

Plot arrays of values:

## Options(27)

### AspectRatio(2)

By default, PairwiseQuantilePlot uses an equal height-to-width ratio:

Use a fixed height-to-width ratio:

### Axes(3)

By default, Frame is used instead of Axes:

Use to turn on axes:

Turn each axis on independently for all the subplots:

### Background(2)

By default, PairwiseQuantilePlot has a white background:

Set a background color:

### Frame(2)

By default, each panel plot is drawn with a frame:

Draw frames on the left and bottom edges of the panels:

### FrameStyle(1)

Specify the style of the frame:

### GridLines(2)

By default, PairwiseQuantilePlot does not draw gridlines:

Draw a background grid:

By default, PairwiseQuantilePlot does not label columns:

Number the columns for unlabeled data:

Provide header names for the columns:

By default, PairwiseQuantilePlot uses a white header background:

Set a header background color:

### 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 will fill the available space:

Use maximum sizes for the width and height:

Use to fill the available space in an object:

### PlotLabel(1)

Add an overall label to the plot:

### PlotLayout(1)

Switch the orientation of the diagonal elements:

### PlotStyle(1)

Style the data using PlotStyle:

### Spacings(1)

Change the space between the plots:

Wolfram Research (2024), PairwiseQuantilePlot, Wolfram Language function, https://reference.wolfram.com/language/ref/PairwiseQuantilePlot.html.

#### Text

Wolfram Research (2024), PairwiseQuantilePlot, Wolfram Language function, https://reference.wolfram.com/language/ref/PairwiseQuantilePlot.html.

#### CMS

Wolfram Language. 2024. "PairwiseQuantilePlot." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PairwiseQuantilePlot.html.

#### APA

Wolfram Language. (2024). PairwiseQuantilePlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PairwiseQuantilePlot.html

#### BibTeX

@misc{reference.wolfram_2024_pairwisequantileplot, author="Wolfram Research", title="{PairwiseQuantilePlot}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/PairwiseQuantilePlot.html}", note=[Accessed: 15-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_pairwisequantileplot, organization={Wolfram Research}, title={PairwiseQuantilePlot}, year={2024}, url={https://reference.wolfram.com/language/ref/PairwiseQuantilePlot.html}, note=[Accessed: 15-September-2024 ]}