boxchart
Description
boxchart(
creates a notched box plot of
the response data for each factor value of the oneway aov
)anova
object
aov
. This syntax is supported only if the factor is
categorical.
boxchart(___,
specifies
options using one or more namevalue arguments in addition to any of the input argument
combinations in the previous syntaxes. For example, you can specify the box median line
color and the marker style. For a list of properties, see BoxChart Properties.Name=Value
)
returns a
graphics vector b
= boxchart(___)b
of BoxChart
objects for the
generated box plots.
Examples
Plot Data for OneWay ANOVA
Load popcorn yield data.
load popcorn.mat
The columns of the 6by3 matrix popcorn
contain popcorn yield observations in cups for three different brands.
Perform a oneway ANOVA to test the null hypothesis that the popcorn yield is not affected by the brand of popcorn.
aov = anova(popcorn,FactorNames="Brand")
aov = 1way anova, constrained (Type III) sums of squares. Y ~ 1 + Brand SumOfSquares DF MeanSquares F pValue ____________ __ ___________ ____ __________ Brand 15.75 2 7.875 18.9 7.9603e05 Error 6.25 15 0.41667 Total 22 17 Properties, Methods
The small pvalue indicates that at least one brand has a different popcorn yield that is statistically significant.
Create a box plot of the response data for each value of Brand
.
boxchart(aov) xlabel("Brand") ylabel("Popcorn Yield")
The shaded region of the first box plot does not overlap with the shaded regions of the other box plots, indicating that the difference in popcorn yield for the first brand is statistically significant.
Plot Data for TwoWay ANOVA
Load popcorn yield data.
load popcorn.mat
The columns of the 6by3 matrix popcorn
contain popcorn yield observations in cups for the brands Gourmet, National, and Generic. The first three rows of the matrix correspond to popcorn that was popped with an oil popper, and the last three rows correspond to popcorn that was popped with an air popper.
Create string arrays containing factor values for the brand and popper type by using the repmat
function.
brand = [repmat("Gourmet",6,1);repmat("National",6,1);repmat("Generic",6,1)]; poppertype = [repmat("Air",3,1);repmat("Oil",3,1);repmat("Air",3,1);... repmat("Oil",3,1);repmat("Air",3,1);repmat("Oil",3,1)]; factors = {brand,poppertype};
Perform a twoway ANOVA to test the null hypothesis that the popcorn yield is not affected by the brand of popcorn, type of popper, or the interaction between the brand and type of popper.
aov = anova(factors,popcorn(:),FactorNames=["Brand","PopperType"],... ModelSpecification="interactions")
aov = 2way anova, constrained (Type III) sums of squares. Y ~ 1 + Brand*PopperType SumOfSquares DF MeanSquares F pValue ____________ __ ___________ ____ __________ Brand 15.75 2 7.875 56.7 7.679e07 PopperType 4.5 1 4.5 32.4 0.00010037 Brand:PopperType 0.083333 2 0.041667 0.3 0.74622 Error 1.6667 12 0.13889 Total 22 17 Properties, Methods
aov
is an anova
object that contains the results of the twoway ANOVA. The small pvalues for Brand
and PopperType
indicate that both the brand and type of popper have a statistically significant effect on the popcorn yield. The large pvalue for Brand:PopperType
indicates that not enough evidence exists to reject the null hypothesis that the interaction term does not have a statistically significant effect on the popcorn yield.
Use boxchart
to plot the response data grouped by the values for Brand
and the response data grouped by PopperType
. To see the color boxchart
assigns to each popper type, add a legend.
boxchart(aov,["Brand","PopperType"]) legend
The box plots indicate that the popcorn yield is higher for popcorn popped in oil, regardless of the brand. For each type of popper, the Gourmet brand yields the most popcorn and the Generic brand yields the least. This result is consistent with the results from the twoway ANOVA.
Specify Axes for Box Plots
Load popcorn yield data.
load popcorn.mat
The columns of the 6by3 matrix popcorn
contain popcorn yield observations in cups for the brands Generic, Gourmet, and National. The first three rows of the matrix correspond to popcorn that was popped with an oil popper, and the last three rows correspond to popcorn that was popped with an air popper.
Create string arrays containing factor values for the brand and popper type using the function repmat
.
brand = [repmat("Gour.",6,1);repmat("Nat.",6,1);repmat("Gen.",6,1)]; poppertype = [repmat("Air",3,1);repmat("Oil",3,1);repmat("Air",3,1);... repmat("Oil",3,1);repmat("Air",3,1);repmat("Oil",3,1)];
Perform a twoway ANOVA to test the null hypothesis that the popcorn yield is not affected by the brand of popcorn or type of popper.
aov = anova({brand,poppertype}, popcorn(:), FactorNames=["Brand","PopperType"]);
Create a 1by2 tiled chart layout. In the first set of axes, plot the box plots for the brand. In the second set of axes, plot the box plots for the popper type.
tiledlayout(1,2) % Left axes ax1 = nexttile; boxchart(ax1,aov,"Brand") xlabel(ax1,"Brand") ylabel(ax1,"Popcorn Yield") % Right axes ax2 = nexttile; boxchart(ax2,aov,"PopperType") xlabel(ax2,"Popper Type")
The box plot median lines indicate that the brand of popcorn has a larger effect on the popcorn yield than the type of popper.
Set Box Median Line and Face Color
Load popcorn yield data.
load popcorn.mat
The columns of the 6by3 matrix popcorn
contain popcorn yield observations in cups for three different brands.
Perform a oneway ANOVA to test the null hypothesis that the popcorn yield is not affected by the brand of popcorn.
aov = anova(popcorn,FactorNames="Brand")
aov = 1way anova, constrained (Type III) sums of squares. Y ~ 1 + Brand SumOfSquares DF MeanSquares F pValue ____________ __ ___________ ____ __________ Brand 15.75 2 7.875 18.9 7.9603e05 Error 6.25 15 0.41667 Total 22 17 Properties, Methods
Plot the response data for the different values of Brand
. Plot the median line in red, the box face in gray, and the box edges in black.
boxchart(aov,BoxFaceAlpha=0.2,BoxFaceColor="k",... BoxEdgeColor="k",BoxMedianLineColor="r") xlabel("Brand") ylabel("Popcorn Yield")
The shaded region of the first box plot does not overlap with the shaded regions of the other box plots, indicating that the difference in the popcorn yield for the first brand is statistically significant.
Input Arguments
aov
— Analysis of variance results
anova
object
Analysis of variance results, specified as an anova
object.
The properties of aov
contain the factors and response data used by
boxchart
to generate the box plots.
factors
— Factors used to group response data
string vector  cell array of character vectors
Factors used to group the response data, specified as a string vector or cell array
of character vectors. The boxchart
function groups the response
data by the combinations of values for factors in factors
. The
factors
input argument must be one or two of the categorical
factor names in aov.FactorNames
.
Example: ["g1","g2"]
Data Types: string
 cell
ax
— Target axes
Axes
object
Target axes, specified as an Axes
object. If you do not specify the axes, then boxchart
uses the current axes (gca
).
NameValue Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue arguments must appear after other arguments, but the order of the
pairs does not matter.
Example: Orientation="horizontal",BoxMedianLineColor="r",WhiskerLineStyle=""
creates horizontal box plots with red median lines and dashed whiskers.
The BoxChart
properties listed here are only a subset. For a complete
list, see BoxChart Properties.
BoxFaceColor
— Box color
RGB triplet  hexadecimal color code  color name  short name
Box color, specified as an RGB triplet, hexadecimal color code, color name, or short name. The box includes the box edges and median line. To specify the color of the box edges and median line separately, you can use the BoxEdgeColor
property. To specify the color of the median line only, use the BoxMedianLineColor
property.
For a custom color, specify an RGB triplet or a hexadecimal color code.
An RGB triplet is a threeelement row vector whose elements specify the intensities of the red, green, and blue components of the color. The intensities must be in the range
[0,1]
; for example,[0.4 0.6 0.7]
.A hexadecimal color code is a character vector or a string scalar that starts with a hash symbol (
#
) followed by three or six hexadecimal digits, which can range from0
toF
. The values are not case sensitive. Thus, the color codes"#FF8800"
,"#ff8800"
,"#F80"
, and"#f80"
are equivalent.
Alternatively, you can specify some common colors by name. This table lists the named color options, the equivalent RGB triplets, and hexadecimal color codes.
Color Name  Short Name  RGB Triplet  Hexadecimal Color Code  Appearance 

"red"  "r"  [1 0 0]  "#FF0000"  
"green"  "g"  [0 1 0]  "#00FF00"  
"blue"  "b"  [0 0 1]  "#0000FF"  
"cyan"
 "c"  [0 1 1]  "#00FFFF"  
"magenta"  "m"  [1 0 1]  "#FF00FF"  
"yellow"  "y"  [1 1 0]  "#FFFF00"  
"black"  "k"  [0 0 0]  "#000000"  
"white"  "w"  [1 1 1]  "#FFFFFF"  
"none"  Not applicable  Not applicable  Not applicable  No color 
Here are the RGB triplets and hexadecimal color codes for the default colors MATLAB^{®} uses in many types of plots.
RGB Triplet  Hexadecimal Color Code  Appearance 

[0 0.4470 0.7410]  "#0072BD"  
[0.8500 0.3250 0.0980]  "#D95319"  
[0.9290 0.6940 0.1250]  "#EDB120"  
[0.4940 0.1840 0.5560]  "#7E2F8E"  
[0.4660 0.6740 0.1880]  "#77AC30"  
[0.3010 0.7450 0.9330]  "#4DBEEE"  
[0.6350 0.0780 0.1840]  "#A2142F" 
Example: BoxFaceColor="red"
Example: BoxFaceColor=[0 0.5 0.5]
Example: BoxFaceColor="#EDB120"
MarkerStyle
— Outlier style
"o"
(default)  "+"
 "*"
 "."
 "x"
 ...
Outlier style, specified as one of the options listed in this table.
Marker  Description  Resulting Marker 

"o"  Circle 

"+"  Plus sign 

"*"  Asterisk 

"."  Point 

"x"  Cross 

"_"  Horizontal line 

""  Vertical line 

"square"  Square 

"diamond"  Diamond 

"^"  Upwardpointing triangle 

"v"  Downwardpointing triangle 

">"  Rightpointing triangle 

"<"  Leftpointing triangle 

"pentagram"  Pentagram 

"hexagram"  Hexagram 

"none"  No markers  Not applicable 
Example: MarkerStyle="x"
Example: MarkerStyle="none"
JitterOutliers
— Outlier marker displacement
"off"
(default)  "on"
 true
or 1
 false
or 0
Outlier marker displacement, specified as "on"
or "off"
, or as numeric or logical 1
(true
) or 0
(false
). A value of "on"
is equivalent to true
, and "off"
is equivalent to false
. So, you can use the value of this property as a logical value. The value is stored as an on/off logical value of type matlab.lang.OnOffSwitchState
.
If you set the JitterOutliers
property to "on"
, then boxchart
randomly displaces the outlier markers along the XData
direction to help you distinguish between outliers that have similar aov.Y
values. For an example, see Visualize and Find Outliers.
Example: JitterOutliers="on"
Notch
— Median comparison display
"off"
(default)  "on"
 true
or 1
 false
or 0
Median comparison display, specified as "on"
or "off"
, or as numeric or logical 1
(true
) or 0
(false
). A value of "on"
is equivalent to true
, and "off"
is equivalent to false
. So, you can use the value of this property as a logical value. The value is stored as an on/off logical value of type matlab.lang.OnOffSwitchState
.
If you set the Notch
property to "on"
, then boxchart
creates a tapered, shaded region around each median. Box plots whose notches do not overlap have different medians at the 5% significance level. For more information, see Box Chart (Box Plot).
Notches can extend beyond the lower and upper quartiles.
Example: Notch="off"
Orientation
— Orientation of box plots
"vertical"
(default)  "horizontal"
Orientation of box plots, specified as "vertical"
or
"horizontal"
. By default, box plots have a vertical orientation,
so that the maov.Y
statistics are aligned with the
yaxis. Regardless of the orientation,
boxchart
stores the maov.Y
values in the
YData
property of the BoxChart
object.
Example: Orientation="horizontal";
Output Arguments
b
— Box plots
vector of BoxChart
objects
Box plots, returned as a vector of BoxChart
objects. If the factors
input argument contains only one categorical factor name, b
contains a single BoxChart
object. If factors
contains two categorical factor names, b
contains the same number of BoxChart
objects as the number of values for the second factor. Use b
to set properties of the box plots after creating them. For more information see BoxChart Properties.
Version History
Introduced in R2022b
See Also
Objects
Functions
Properties
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