Afan chart is made of a group of dispersion fan diagrams,which may be positioned according to two categorising dimensions.Adispersion fan diagram is a circular diagram whichreports the same information about a dispersion as abox plot:namelymedian,quartiles, and two extreme values.
The elements of adispersion fan diagram[1]are:
The scale on the circular line begins at the leftwith the starting value (e. 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 observedvalues; thus it encompasses the values from the first to the third quartile.The white feathers indicate the dispersion of the middle 90% of theobserved values.
The length of the white part of the diameter corresponds with the numberof observations.
A fan chart gives a quick summary of observed values which depend from two variables. This is possible thanks of a dense representationand 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 plotsis the possibility to compare dispersion fan diagrams not only within one directionbut within two directions (horizontally and vertically).
The following example presents data from the data setMathAchievewhich is part of theR packagenlmeof José Pinheiro et al.[2]It contains mathematics achievement scores of 7185 students.The students are categorisedaccording to sex and membership of a minority ethnic group.
The graphics show the mathematics achievement scores in dependencyon the socio-economic status of the students (x axis)and on the average socio-economic status of all studentsat the same school (y axis).The four graphic panels differentiate the studentsaccording to sex and membership of a minority ethnic group.
The fan charts reveals clearly how the median valueis partially following a big main tendencywhile the values of the single subgroups (with the cells) scatter largelywhat could lead to doubts about a possible correlation.
