View source for Fan chart (statistics)

{{Short description|Data visualization with quartiles}}
thumb|400px|A dispersion fan diagram (left) in comparison with a box plot

A '''fan chart''' is made of a group of dispersion fan diagrams,
which may be positioned according to two categorising dimensions.
A ''dispersion fan diagram'' is a circular diagram which
reports the same information about a dispersion as a [[Box plot|box plot]]:
namely [[Median|median]], [[Quartile|quartile]]s, and two extreme values.

== Elements ==

The elements of a '''dispersion fan diagram'''<ref name="fischer">{{Cite book
 | first1 = Wolfram | last1 = Fischer
 | title = Neue Grafiken zur Datenvisualisierung. Band 1.     Speichengrafiken, Streuungsfächerkarten, Differenz-, Sequenz-     und Wechseldiagramme
 |trans-title=New Graphics For Data Visualisation. Volume 1. Spoke Plots, Fan Charts, Difference, Sequence and Change Diagrams
 | publisher = ZIM
 | place = Wolfertswil
 | year = 2010
 | url = http://www.fischer-zim.ch/studien/Neue-Grafiken-I-1003-Info.htm
 | isbn = 978-3-905764-06-2
}}</ref>
are:
# a ''circular line'' as scale
# a ''diameter'' which indicates the median
# a ''fan'' (a segment of a circle) which indicates the quartiles
# two ''feathers'' which indicate the extreme values.

The scale on the circular line begins at the left
with the starting value (e.&nbsp;g. with zero).
The following values are applicated clockwise.
The white tail of diameter indicates the median.
The dark fan indicates the dispersion of the middle half of the observed
values; thus it encompasses the values from the first to the third quartile.
The white feathers indicate the dispersion of the middle 90% of the
observed values.

The length of the white part of the diameter corresponds with the number
of observations.

== Application ==

A fan chart gives a quick summary of observed values which depend from two variables. This is possible thanks of a dense representation
and a constant size which does not depend on the size of the single dispersion fan diagrams.

An essential advantage compared to a sequence of box plots
is the possibility to compare dispersion fan diagrams not only within one direction
but within two directions (horizontally and vertically).

== Example ==

The following example presents data from the data set ''MathAchieve''
which is part of the R package
[https://cran.r-project.org/web/packages/nlme/ ''nlme'']
of José Pinheiro et al.<ref name="nmle">{{Cite web
     | first1 = José | last1 = Pinheiro
     | first2 = Douglas | last2 = Bates
     | title = nlme: Linear and Nonlinear Mixed Effects Models
     | year = 2013 |orig-year=1999
     | publisher = CRAN (The Comprehensive R Archive Network)
     | url = https://cran.r-project.org/web/packages/nlme/
    |display-authors=0}}</ref>
It contains mathematics achievement scores of 7185 students.
The students are categorised
according to sex and membership of a minority ethnic group.

[[File:fanchart-mathachieve-0912-en.gif|center|600px|7185 mathematics achievement scores: Results according to sex and membership of a minority ethical group]]

The graphics show the mathematics achievement scores in dependency
on the socio-economic status of the students (x axis)
and on the average socio-economic status of all students
at the same school (y axis).
The four graphic panels differentiate the students
according to sex and membership of a minority ethnic group.

The fan charts reveals clearly how the median value
is partially following a big main tendency
while the values of the single subgroups (with the cells) scatter largely
what could lead to doubts about a possible correlation.

== See also ==

* [[Box plot]]

== References ==
{{reflist}}

== External links ==
* Fischer, Wolfram (2012): [http://www.statoo.ch/sst12/presentations/Fischer.pdf ''Streuungsfächerkarten und pseudogeografische Anordnungen.'' Mit Beispielen zum verfügbaren Einkommen und zu Krankenkassenprämien in der Schweiz]. Swiss Days of Official Statistics, Vaduz LI, 2012.
* Fischer, Wolfram (2010): [http://www.fischer-zim.ch/graphics-pdf/Fanchart-MathUS-1005.pdf ''Visualising Twofold Dependencies by Fan Charts'']. ZIM.

{{Statistics|descriptive}}

[[Category:Statistical charts and diagrams]]

{{Sourceattribution|Fan chart (statistics)}}