help for strip

Strip plots: oneway dot plots

strip
varlist
[if exp]
[in range]

[
,
vertical
{
stack
|
quantile
trscale(trans)
}
height(#)
{
centre
|
center
}

width(#)
{
floor
|
ceiling
}

separate(varname) variablelabels

addplot(plot)
graph_options ]

strip
varname
[if exp]
[in range]

[
,
vertical
{
stack
|
quantile
}
height(#)
{
centre
|
center
}

width(#)
{
floor
|
ceiling
}

over(groupvar)
separate(varname)

addplot(plot)
graph_options
]

Description

strip plots data as a series of marks against a single magnitude
axis. By default this axis is horizontal. With the option vertical
it is vertical. Optionally, data points may be stacked or cumulated
into histogram- or dotplot-like or distribution or quantile
function displays.

The default results of strip are fairly trivial, as if you had
called up a scatter plot of a variable of interest and a variable
created as some constant. The power of the command lies in its options.
To that end, run the examples: the code for the examples is included
in a do-file alongside this help file and the ado file.

Options

General appearance

vertical specifies that the magnitude axis should be vertical.

stack specifies that data points with identical values are to be
stacked, as in dotplot, except that by default there is no binning
of data.

quantile specifies that data points are to be plotted with
respect to an implicit cumulative probability scale.
By default displays resemble cumulative distribution plots; otherwise with
vertical displays resemble quantile plots. Note that with
quantile specifying connect(L) [sic] to join points within groups
may be helpful.

Given quantile, the further option trscale() specifies use
of a transformed scale for cumulative probability. The argument
trans is Stata syntax specifying the transformation. For example,
trscale(invnormal(@)) specifies a normal quantile scale. Here
@, which must be specified, is a placeholder for the name of the
temporary variable holding cumulative probability. Otherwise, the syntax
must mention one or more Stata functions and may mention pertinent
operators or numeric constants. Note that calculations are separate for
each variable and group plotted and that for graphical purposes, each
transformed set is transformed back to the interval [0, 1].

stack and quantile may not be combined.

height(#) controls the amount of graph space taken up
by stacked data points under the stack or quantile options
above. The default is 0.8. This option will not by itself change the
appearance of a plot for a single variable. Note that the height may
need to be much smaller or much larger than 1 with over(), given
that the latter takes values literally. For example, if your classes are
0(45)360, 36 might be a suitable height.

centre or center centres or centers markers for each
variable or group on a hidden line.

Binning

width(#) specifies that values are to be rounded in
classes of specified width. Classes are defined by default by
round(varname,width). See also the
floor and ceiling options just below.

floor or ceiling in conjunction with width() specifies
rounding by width * floor(varname/width) or
width * ceil(varname/width) respectively. Only one
may be specified. (These options are included to give some users the
minute control they may desire, but if either option produces a marked
difference in your plot, you may be rounding too much.)

Grouping

over(groupvar) specifies that values of varname
are to be shown separately by groups defined by groupvar. This
option may only be specified with a single variable. If stack is
also specified, then note that distinct values of any numeric
groupvar are assumed to differ by at least 1. Tuning height()
or the prior use of egen, group() label will fix any problems. See
help on egen if desired.

Note that by() is also available as an alternative or complement
to over(). See the examples for detail on how over() and
by() could be used to show data subdivided by a cross-combination
of categories.

separate() specifies that data points be shown separately
according to the distinct classes of the variable specified. Commonly,
but not necessarily, this option will be specified together with
stack or quantile.

Other details

variablelabels specifies that multiple variables be
labelled by their variable labels. The default is to use variable names.

addplot(plot) provides a way to add other
plots to the generated graph; see help addplot_option.

graph_options are options of scatter, including by(),
on which see by_option.

jitter() is among those options, but (personal opinion) jittering
is only rarely as helpful as stacking or cumulating as a way to show
identical or close values clearly.

Remarks

Meta-remarks

The very large list of references here has just grown over several years
from a much shorter set of more usual length. A rationale for its
length, beyond the amusement of the program author, might include:
providing overwhelming evidence of how long and how widely these plots
have been invented, or re-invented; documenting explicitly the variety
of plot forms (and the variety of plot names) in more detail than in
other sources; maximising the scope for people to find congenial
references in literature accessible to them; challenging people to
suggest other earlier and/or excellent examples. Equally, there is here
neither intent nor claim to produce a comprehensive list.

The need for and utility of the plots produced by this command may vary with
the number of variables shown (1 or more);
the number of groups shown (1 or more);
and the number of observations in each group for each variable.
However, such dependence is in my view weaker than is often stated. At
one extreme, with a few variables or groups and small samples, you
should have space to show all data points directly. At another extreme,
many data points often blur into each other, but that doesn't make strip
plots useless, if only because marked outliers, gaps, spikes and so
forth are likely to be evident when they are present. With large
samples, cumulative or quantile versions of strip plots are likely to be
especially helpful.

There is not a sharp distinction in the literature or in software
implementations between dot plots and strip plots. Commonly,
but with many exceptions, a dot plot is drawn as a pointillist analogue
of a histogram. Sometimes, dot plot is used as the name when data points
are plotted in a line, or at most a narrow strip, against a magnitude
axis. Strip plot implementations, as here, usually allow stacking
options, so that dot plots may be drawn as one choice.

Early history

Such plots under these and yet other names go back at least as far as
Langren (1644): see Tufte (1997, p.15) and in much more detail Friendly
et al. (2010) and Friendly and Wainer (2021).

Galton (1869, pp.27-28; 1892, pp.27-28) gave a schematic dot
diagram showing how the heights of a million men might be plotted. G.H.
Darwin (1873) invoked the same idea: "If one were to draw a vertical
line on a wall, and were to measure the heights of several thousand men
of the same race against this line, recording the height of each by
driving in a pin, the pins would be densely clustered about a certain
height, and the density of their distribution would diminish above and
below." (I owe the Darwin reference to Pritchard (2018). It is not
included in, or even cited within, the 5 volumes of (Sir George)
Darwin's Scientific Papers.)

Jevons (1884), Wallace (1889), Bateson and Brindley (1892), Bateson
(1894), Brunt (1917, 1931), Gause (1930), Shewhart (1931, 1939), Pearson
(1931, 1938), Pearson and Chandra Sekhar (1936), Shaw (1936), Brinton
(1939), Tippett (1943) and Zipf (1949) are other early sources. Pearson
(1939) shows evidence of private use by Student [W.S. Gosset]. C.B.
Williams often used such diagrams in his papers (e.g. 1940, 1944) and
books (1964, 1970).

In his now famous paper introducing the Iris data to statistical
science, Fisher (1936) gave a histogram in which each value is
represented by a rectangle of constant area, hence using essentially the
same principle. The same idea was used by Karsten (1923, p.348), McCall
(1939, p.488), Svendsen (1940), on which see Murphy (1997, p.341), Dixon
and Massey (1951, 1957, 1969, 1983), Eddy (1979), Murphy (1985, p.61)
and Wilks (2006, 2011, 2019, p.34 in all editions).

General discussions

Sasieni and Royston (1996) and Wilkinson (1999a) give general
discussions: see Sasieni and Royston (1994) for the first Stata
implementation.

Dot diagram can mean scatter plot!

Fisher (1925 and later editions) used dot diagram in the sense of
scatter plot, as did Draper and Smith (1966). Similarly the term
dot plot is sometimes used that way (Yau 2011, 202, 2024; Desbarats 2023a).

Examples and variations of dot and strip plots

Wilks (1948), Hald (1952) and Box et al. (1978) used the term
dot frequency diagram or dot diagram, as did Rowntree (1981),
Berry and Lindgren (1990, 1996), Bajpai et al. (1992), Harris
(1999), Armitage et al. (2002), Blæsild and Granfeldt (2003),
Bartholomew (2016), Naghettini (2016) and Bianconi (2024). Monkhouse
and Wilkinson (1952) used the term dispersion diagram, as did
McGrew and Monroe (1993, 2000) and Morrocco and Ballantyne (2008); the
term is also used for box plot-like displays (e.g. Hogg 1948; Ottaway
1973). Miller (1953, 1964) used the terms dispersion graph and
dispersion diagram. Truran (1975), Silk (1979), White (1984) and
Slocum et al. (2010) used the term dispersion graph for
stacked dotplots. Pearson (1956) gives several examples. Dickinson
(1963) used the term dispersal graph. Tukey (1974) used the term
dot pattern. Tukey (1977, p.50) showed a dot plot for an example
in which a box plot works poorly. See also examples in Tukey (1970a,
1970b) and Mosteller and Tukey (1977, p.456). Harris (1999) used the
term dot array chart. Kendall (1971), Kleiner and Graedel (1980),
Chambers et al. (1983), Becker and Chambers (1984), Becker
et al. (1988), Fox (1990), Thompson (1992), Cleveland (1994), Lee and Tu
(1997), Wilkinson (1999b, 2005), Reimann et al. (2008) and
Rousselet et al. (2017) used the term one-dimensional plot or
one-dimensional scatter plot. Härdle (1991) used the term
needle plot. Wennberg and Cooper (1996) used the term
distribution graph. Jacoby (1997) used the term
univariate scatter plot, as did Edwards (2000), Weissgerber et al. (2015),
Kirk (2016), Filzmoser et al. (2018) and Humphreys and Ruxton
(2022). Jacoby also used the term unidimensional scatter plot.
Gerbing (2020) used the term one-variable scatterplot. Harris
(1999) used one-axis and one-dimensional terms such as
one-axis data distribution, percentile, point and scatter graphs and
one-dimensional data distribution graphs. Woloshin (2000) used the term
turnip graphs, attributing it to J.E. Wennberg. Ryan et al.
(1985) discuss their Minitab implementation using the term dotplot.
Note also later editions such as Ryan et al. (2013). Krieg
et al. (1988), Velleman (1989), Staudte and Sheather (1990), Hoaglin
et al. (1991), Gonick and Smith (1993), Swan and Sandilands (1995),
Wilkinson (1992, 1999b, 2005) Wild and Seber (2000), Utts and Heckard
(2002), Dodge (2008), Burt et al. (2009), Ryan (2009), Wilcox
(2009), Doane and Seward (2011), Janert (2011), Peacock and Peacock
(2011), Cook et al. (2016), Rousselet et al. (2017); Albert
(2018), Weissgerber et al. (2019), Wilks (2019), De Veaux
et al. (2021), Diez et al. (2022), Correll (2023) and Unwin (2024)
are among many others also using the term dot plot or
dotplot. Yandell (2007), Thas (2010), Janert (2011), Sleeper
(2018, 2020), Wexler (2021) and Desbarats (2023b) used the terms
jittered plots or jitter plot or jittered strip plot for
jittered versions. Cumming (2012) used dotplot for unstacked and
dot histogram for stacked plots. The latter term also appears in
Wright and London (2009), Koponen and Hildén (2019), Schwabish
(2021), Butler (2022) and Wilkinson (2023). McGrew et al. (2014)
and Lembo and McGrew (2024) used individual value plot and
individual point distribution. Atkinson (1985), Stuetzle (1987),
Madansky (1988), Thiébaux (1994), Draper and Smith (1998) and Goos
and Meintrup (2015, 2016) used histogram. Wexler et al.
(2017) and Sleeper (2020) used unit histogram. Bradstreet (2012),
Rice and Lumley (2016) and Cairo (2019) used dot chart. Cleveland
(1985) used the term point graph, as did Harris (1999) and Slocum
et al. (2010). Computing Resource Center (1985) and Hamilton
(1992) used the terms oneway plot and oneway scatterplot.
Pagano and Gauvreau (1993) used the term one-way scatter plot.
Feinstein (2002, pp.67, 167) used the term one-way graph. The term
line plot appears in Hill and Dixon (1982), Cooper and Weekes
(1983), Benjamini (1988), Klemelä (2009), Christensen et al.
(2011) and Schuenemeyer and Drew (2011), that of line chart appears
in Robertson (1988), and that of linear plot appears in Hay (1996).
The term strip plot (or strip chart) (e.g. Millard 1998,
2013; Millard and Neerchal 2001; Dalgaard 2002; Venables and Ripley
2002; Maindonald and Braun 2003; Robbins 2005; Faraway 2005, 2014;
Sarkar 2008; Sawitzki 2009; Thas 2010; Harris and Jarvis 2011; Few 2009,
2012, 2015, 2020; Cairo 2013, 2016; Camões 2016; Friendly and Meyer
2016; Harris 2016; Hilfiger 2016; Rousselet et al. 2016, 2017;
Carlson 2017; Spiegelhalter 2019; Afifi et al. 2020; Schwabish
2021, 2023; Wexler 2021; Humphreys and Ruxton 2022; Correll 2023;
Desbarats 2023b; Bianconi 2024) appears traceable to work by J.W. and
P.A. Tukey (1990). The term dot strip plot appears in Smith
(2022). The term blob chart appears in Adams (1992). The term
dit plot appears in Ellison (1993, 2001) and Wilkinson et al.
(1996). The terms number line, number-line plot and
number axis appear in Helsel and Hirsch (1992), McGrew and Monroe
(1993, 2000), Monmonier (1991, 1993), Dent (1996), Harris (1999) and
Wolfram (2017). The term bar-dot graph appears in Wilkinson
et al. (1996) for a dot plot superimposed on bars showing means. People
in neuroscience often plot event times for multiple trials as
raster plots: Brillinger and Villa (1997) is a token reference from the
statistical literature. See Kass et al. (2014) for more. The term
stripe graph appears in Harris (1999). The term stripes plot
or stripe plot appears in Wilkinson (1994, 2023), Leisch (2010) and
Everitt and Skrondal (2010). Doane and Tracy (2000) combined dotplots,
a beam to indicate data range and a fulcrum to indicate mean as centre
of gravity, as one kind of beam and fulcrum display. The term
data distribution graph appears in Robbins (2005). The term
column scatter graph or plot for vertical strip plots appears in
Motulsky (1995, 2010, 2014, 2018) and in Girgis and Mohanty (2012). The
term barcode plot or bar code plot or barcode chart
appears in Keen (2010, 2018), Thas (2010), Kirk (2012) and Smith (2022).
The term circle plot appears in McDaniel and McDaniel (2012a,
2012b). The term Wilkinson dot plot appears in Chang (2013, 2019),
Koponen and Hildén (2019), Sleeper (2020), Schwabish (2021) and
Wexler (2021). The term swarm or beeswarm plot appears in
Eklund (2013), Martinez et al. (2017), Andrews (2019), Holmes and
Huber (2019), Koponen and Hildén (2019), Field (2021), Schwabish
(2021), Smith (2022), Bianconi (2024), Doggett and Way (2024), Yau
(2024) and Kirk (2025). The term instance chart appears in Kirk
(2016). The term wheat plot appears in Few (2017) and Schwabish
(2021). The term SinaPlot appears in Sidiropoulos et al.
(2018) for a hybrid of violin plot and strip chart. The term
raincloud plot appears in Allen et al. (2019) and Schwabish
(2021) for a hybrid of strip chart, box plot and violin plot and in
Schwabish (2023) for a hybrid of strip chart and box plot with whiskers
to 10% and 90% points. Correll (2023) documents and discusses numerous
variants appearing under that name. The term spread-plot appears
in Vail and Wilkinson (2020). The term SuperPlots was used by Lord
et al. (2020) for displays showing two kinds of replication.
Stacked dot and strip plots appear to qualify as one kind of
gatherplot (Park et al. 2023).

Wigglesworth (1954), Moroney (1956), Wallis and Roberts (1956, p.178),
Clement and Robertson (1961), Youden (1962), Gregory (1963), Haggett
(1965, 1972), Draper and Smith (1966), Cole and King (1968), Cormack
(1971), Koch and Link (1971), Moore (1971), Williamson (1972), Davis
(1973, 1986, 2002), Agterberg (1974), Hammond and McCullagh (1974),
Tufte (1974, 2020), Lehmann (1975, 1998), Lewis (1977), Wright (1977),
Barnett and Lewis (1978), Johnston (1978), Mardia et al. (1979),
Murphy (1979, 1982), Smith (1979), Brown and Hu (1980), Bertin (1981,
1983), Green (1981), Wetherill (1981, 1982), Dobson (1983 and later),
Bentley and Kernighan (1984), Light and Pillemer (1984), Mosteller and
Wallace (1984), Bentley (1985, 1988), Aitchison (1986), Clark and
Hosking (1986), Colinvaux (1986, 1993), Ibrekk and Morgan (1987), Jones
and Moon (1987), Chatfield (1988), Flury and Riedwyl (1988), Siegel
(1988), Sprent (1988), Hald (1990), Morgan and Henrion (1990),
Hutchinson (1993), Baxter (1994), Kent and Coker (1994), Daly
et al. (1995), Guttorp (1995), Henry (1995), Jongman et al. (1995),
Berry (1996), Cliff (1996). McNeil (1996), Siegel and Morgan (1996),
Behrens (1997), Flury (1997), Yandell (1997), Cobb (1998), Griffiths
et al. (1998), Bland (2000), Nolan and Speed (2000), Manly (2001),
Spence (2001, 2007, 2014), Dupont (2002), Field (2003, 2010, 2016), Good
and Hardin (2003), Mead, Curnow and Hasted (2003), Barnett (2004),
Heiberger and Holland (2004, 2015), van Belle et al. (2004),
Wasserman (2004), Robbins (2005), Hammer and Harper (2006, 2024),
Maronna et al. (2006, 2019), Young et al. (2006), Agresti and
Franklin (2007), Cook and Swayne (2007), Morgenthaler (2007), Freeman
et al. (2008), Urbanek (2008), Warton (2008, 2022), Yamamoto
et al. (2008), Schneider (2009), Theus and Urbanek (2009), Wainer (2009,
2016), Whitlock and Schluter (2009, 2015, 2020), Andersen and Skovgaard
(2010), Keen (2010, 2018), Zar (2010), Drummond and Vowler (2011), Kent
(2012), Sokal and Rohlf (2012), Wills (2012), Greenacre and Primicerio
(2013), Ramsey and Schafer (2013), Yau (2013, 2024), Amaratunga
et al. (2014), Hector (2015, 2021), Berinato (2016; who also uses the term
in another sense: p.30), Goos and Meintrup (2016), Greenacre (2016),
Irizarry and Love (2017), Wolfe and Schneider (2017), Agresti (2018),
Kriebel and Murray (2018), Pearson (2018), Standage (2018, 2019, 2020),
Greenacre (2019), Grant (2019), Healy (2019), Koponen and Hildén
(2019), Selvin (2019), Irizarry (2020, 2025), Mudelsee (2020) Vanderplas
et al. (2020), DelSole and Tippett (2022), Alexander (2023),
Kabacoff (2024), Yu and Barter (2024) and Kirk (2025) are some other
references with examples of strip plots.

The Federal Reserve publishes predictions of interest rates using dot
plots. See for illustration and discussion (e.g.) the Economist (2015).

Compare stem-and-leaf plots

Siegel (1988) gives an especially lucid discussion of stem-and-leaf
plots presented to maximise their resemblance to both histograms and
strip plots (in the present sense). His first edition is preferable on
this point to the second edition, Siegel and Morgan (1996). Other lucid
explanations were given by Berry (1996) and Berry and Lindgren (1996).

Rugs

Strip plot-like displays on the margins of other graphs (e.g.
histograms, density plots, scatter plots) are now often known as
rugs or rug plots, although their use predates this term. See
(e.g.) Brunt (1917, 1931), Wallis and Roberts (1956, p.178), Boneva
et al. (1971), Binford (1972), Box and Tiao (1973), Davis (1973,
1986, 2002), Daniel (1976), Lewis (1977), Brier and Fienberg (1980),
Brown and Hu (1980), Tukey and Tukey (1981), Chambers et al.
(1983), Tufte (1983, 2006, 2020), Bentley and Kernighan (1984), Murphy
(1985, p.61), Aitchison (1986), Hastie and Tibshirani (1986), Rousseeuw
and Leroy (1987), Fox (1990), Berry and Lindgren (1990, 1996), Hastie
and Tibshirani (1990) (who do use the term), Härdle (1990, 1991),
Hastie (1992), Clark and Pregibon (1992), Scott (1992, 2015), Cleveland
(1993), Pitman (1993), Jongman et al. (1995), Wand and Jones
(1995), Wilks (1995, 2006, 2011, 2019), Fan and Gijbels (1996), Gasser
(1996), Ripley (1996), Simonoff (1996, 2003), Bowman and Azzalini
(1997), Flury (1997), Reiss and Thomas (1997, 2001, 2007), Millard
(1998), Gershenfeld (1999), Harris (1999) (who uses the term
border plot), Johnson and Albert (1999), Friendly (2000), Schimek (2000), Utts
and Heckard (2002), Baxter (2003), Good and Hardin (2003), Barnett
(2004), Jewell (2004), Wasserman (2004, 2006), Aitkin et al. (2005,
2009), Gelman and Hill (2007), Bolker (2008), Bowman (2008), Friendly
(2008), Härdle et al. (2008), Minnotte et al. (2008),
Sarkar (2008), Hastie et al. (2009), Sawitzki (2009), Sheather
(2009), Barnett and Dobson (2010), Everitt and Skrondal (2010), Keen
(2010, 2018), Maindonald and Braun (2010), Christensen et al.
(2011), Everitt et al. (2011), Gower et al. (2011), Harris and
Jarvis (2011), Matthiopoulos (2011), Schuenemeyer and Drew (2011),
Feigelson and Babu (2012), Lee (2012), Legendre and Legendre (2012),
Weigel (2012), Chang (2013, 2019), Fahrmeir et al. (2013),
Greenacre and Primicerio (2013), James et al. (2013), Faraway
(2014), Perpiñán Lamigueiro (2014, 2018), Harrell (2015),
Heiberger and Holland (2015), Efron and Hastie (2016), Friendly and
Meyer (2016), Harris (2016), Carlson (2017), Martinez et al.
(2017), Wood (2017), Albert (2018), Field (2018), Bouveyron et al.
(2019), Koponen and Hildén (2019), Racine (2019), Irizarry (2020,
2025), Gerbing (2020), Friendly and Wainer (2021), Setlur and Cogley
(2022), Shen and North (2023), Wimberly (2023), Kabacoff (2024),
Maindonald et al. (2024) and Yu and Barter (2024). See Cox (2025)
for a miniature review of adding rugs in Stata. Tufte (1983, p.135)
uses the term differently, for a series of plots linked together using
their marginal distributions.

Hybrid dot-box plots

Hybrid dot-box or box-dot plots were used by Crowe (1933, 1936, 1971)
(on whose work see Johnston 2019), Matthews (1936), Hogg (1948),
Monkhouse and Wilkinson (1952), Farmer (1956), Gregory (1963), Hammond
and McCullagh (1974), Lewis (1975), Matthews (1981), Wilkinson (1992,
1994, 1999b, 2005, 2023), Ellison (1993, 2001), McGrew and Monroe
(1993, 2000), Wilkinson et al. (1996) (who also call them dox
plots), Curry (1999), Harris (1999), Wild and Seber (2000), Quinn and
Keough (2002, 2024), Young et al. (2006), Hendry and Nielsen
(2007), Morrocco and Ballantyne (2008), Motulsky (2010, 2014, 2018),
Christensen et al. (2011), Krause and O'Connell (2012), Chang
(2013, 2019), Davino et al. (2014), McGrew et al. (2014), Goos
and Meintrup (2015), Friendly and Meyer (2016), Gierlinski (2016),
Greenacre (2017), Irizarry and Love (2017), Wexler et al. (2017),
Chiou and Bergey (2018), Keen (2018), Kriebel and Murray (2018), Sleeper
(2018) (whose explanation is singularly confused), Holmes and Huber
(2019), Weissgerber et al. (2019), Irizarry (2020, 2025), Gerbing
(2020), Wexler (2021), Diez et al. (2022), Alexander (2023),
Bianconi (2024), Kabacoff (2024), Maindonald et al. (2024), Unwin
(2024), Yu and Barter (2024) and Desbarats (2025). See also Miller
(1953, 1964).

Boxplots

Boxplots in widely current forms are best known through the work of
Tukey (1970a, 1970b, 1972, 1977). Various mutations were suggested or
documented by McGill et al. (1978), Frigge et al. (1989),
Potter (2006) (ranging from elementary confusions to some original
suggestions), Keen (2010, 2018) and Martinez et al. (2011).
Drawing whiskers to particular percentiles, rather than to data points
within so many IQR of the quartiles, was emphasised by Cleveland (1985),
but anticipated by Matthews (1936) and Grove (1956) who plotted the
interoctile range, meaning between the first and seventh octiles, as
well as the range and interquartile range. Dury (1963), Johnson (1975),
Cressie (1991), Pagano and Gauvreau (1993), Harris (1999), Feinstein
(2002), Utts and Heckard (2002), Blæsild and Granfeldt (2003), Good
and Hardin (2003), Myatt (2007), Lane and Sándor (2009), Myatt and
Johnson (2009, 2011), Draghici (2012), Davino et al. (2014), Chang
(2013, 2019), McGrew et al. (2014), Goos and Meintrup (2015, 2016),
Wickham and Grolemund (2017), Agresti (2018), Afifi et al. (2020)
and Lembo and McGrew (2024) showed means as well as minimum, quartiles,
median and maximum. Schmid (1954) showed summary graphs with median,
quartiles and 5 and 95% points. Schmid and Schmid (1979) used 10% and
90% points instead. Bentley (1985, 1988), Davis (2002), Spence (2007,
2014), Few (2009), Motulsky (2010, 2014, 2018), Gierlinski (2016) and
Smith (2022) plotted whiskers to 5 and 95% points. Crowe (1971,
pp.70-71) plotted median, quartiles and 10% and 90% points on the margins of
histograms. Moore and McCabe (1989, suggestion on p.35), Morgan and
Henrion (1990, pp.221, 241), Helsel and Hirsch (1992, p.26) Dent (1996,
p.3), Fauth and Resetarits (1999), Spence (2001, p.36), Gotelli and
Ellison (2004, 2013, pp.72, 110, 213, 416), Wilks (2011, p.280; 2019,
p.365) and Schwabish (2021, p.198; 2023, p.313) plotted whiskers to 10%
and 90% points, as was also mentioned by Ramsey and Schafer (2013,
p.19). See also Feinstein (2002, p.308). Harris (1999) showed examples
of both 5 and 95% and 10 and 90% points. Altman (1991, pp.34, 63),
Feinstein (2002, p.301) and Greenacre (2016) plotted whiskers to 2.5%
and 97.5% points. Reimann et al. (2008, pp.46-47) plotted
whiskers to 5% and 95% and 2% and 98% points. Humphreys and Ruxton
(2022, p.80) mention use elsewhere of 2% and 98% and 9% and 91% points.

Quartile or midgap plots

A variant design was called a quartile plot by Tufte (1983, p.124f;
2001, p.124f; 1990a, p.62; 1990b, p.131f) and Wright and London (2009)
and a midgap plot by Seheult (1986) and Stock and Behrens (1991).
It consists of a point symbol for the median, no visible box, and
whiskers between each quartile and the extreme beyond. See also
Wilkinson et al. (1996, p.742), Tufte (2020, p.100) and Quinn and
Keough (2024, p.348).

Quantile-box plots and their kin

Parzen (1979a, 1979b, 1982, 1997) hybridised box and quantile plots as
quantile-box plots. See also (e.g.) Shera (1991), Militký and
Meloun (1993), Meloun and Militký (1994), Nair et al. (2013),
Evans and Cox (2017) and Cox (2020). Shelly (1996), Guevara and
Avilé (2007), Feigelson and Babu (2012, p.208) and Holmes and Huber (2019,
p.129) plotted quantile plots and box plots side by side. Note,
however, that the quantile box plot of Keen (2010, 2018) is just a box
plot with whiskers extending to the extremes. In contrast, the quantile
box plots of JMP are evidently box plots with marks at 0.5%, 2.5%, 10%,
90%, 97.5%, 99.5%: see Sall et al. (2014, pp.143-4).

Here are some notes on variants of quantile-box plots. (A) The
box-percentile plot of Esty and Banfield (2003) plots the same
information differently, plotting data as continuous lines and producing
a symmetric display in which the vertical axis shows quantiles and the
horizontal axis shows not plotting position p, but both
min(p, 1 - p) and its mirror image
-min(p, 1 - p) . Minor detail: in their paper plotting positions are
misdescribed as "percentiles". See also Martinez et al. (2011,
2017), which perpetuates that confusion.

The idea of plotting min(p, 1 - p) (or its percent
equivalent) appears independently in (B) "mountain plots" (Krouwer
1992; Monti 1995; Krouwer and Monti 1995; Goldstein 1996) and in (C)
plots of the "flipped empirical distribution function" (Huh 1995). See
also Xue and Titterington (2011) for a detailed analysis of folding a
distribution function at any quantile. From literature seen by me, it
seems that none of these threads -- quantile-box plots or the later
variants (A) (B) (C) -- cites each other. Note that the mountain plot
of Urbanek (2008) is a different idea.

Precursors of box plots

Ideas similar to box plots go back much further. Cox (2009) gives
various references. Bibby (1986, pp.56, 59) gave even earlier references
to their use by A.L. Bowley in his lectures about 1897 and to his
recommendation (Bowley, 1910, p.62; 1952, p.73) to use minimum and
maximum and 10, 25, 50, 75 and 90% points as a basis for graphical
summary. Range-bar plots as in Spear (1952, 1969) are often cited, but
see also the earlier work of Haemer (1948) and the slightly later work
of Schmid (1954).

Deviations from means

Plots showing values as deviations from means were given by Shewhart
(1931), Pearson (1956), Davis (2002, p.81), Grafen and Hails (2002,
pp.4-7), McKillup (2005, 2012), Klemelä (2009), Whitlock and
Schluter (2009, pp.396, 519; 2015, p.464 and cf.p.609; 2020, p.468),
McKillup and Dyar (2010), Welham et al. (2015) and Hector (2015,
2021). A related plot, which seems especially popular in clinical
oncology, is the waterfall plot (or waterfall chart). Common examples
show variations in change in tumour dimensions during clinical trials.
See (e.g.) Gilder (2012). Note, however, that waterfall plots or charts
also refer to at least two quite different plots in business and in the
analysis of spectra. See (e.g.) Desbarats (2023a) and Kabacoff (2024).

Quantile plots

Quantile plots were discussed by Cox (1999, 2005), including historical
comments. Further examples long in use for environmental applications
are hypsometric curves (Clarke 1966) and flow duration curves (Searcy
1959).

Cleveland dot charts

Dot charts (also sometimes called dot plots) in the sense of Cleveland
(1984, 1994) and Cleveland and McGill (1984), as implemented in
graph dot, are quite distinct. Various authors (e.g. Lang and Secic
2006, Zuur et al. 2007, Sarkar 2008, Mitchell 2010, Chang
2013/2019, Kirk 2016, Healy 2019, Afifi et al. 2020, Gerbing 2020,
Wexler 2021, Kabacoff 2024) call these Cleveland dot charts or dot
plots. For an early variant see Snedecor (1937) and also later
editions. Examples continued to Snedecor and Cochran (1967). See also
(e.g.) Bentley and Kernighan (1984, 1986), Becker et al. (1988),
Bentley (1988), Helsel and Hirsch (1992), Singer and Feinstein (1993),
Henry (1995), Dent (1996). Jacoby (1997, 2006), Sinacore (1997), Millard
(1998), Wilkinson (1999b, 2005), Harrell (2001, 2015), Millard and
Neerchal (2001), Feinstein (2002), Heiberger and Holland (2004, 2015),
Morgenthaler (2007), Cox (2008, 2024), Few (2009, 2012, 2015, 2020),
Myatt and Johnson (2009), Wainer (2009, 2014, 2016), Wickham (2009,
2016), Carr and Pickle (2010), Everitt and Skrondal (2010), Keen (2010,
2018), Martinez et al. (2011, 2017), Robinson and Hamann (2011),
Feigelson and Babu (2012), Krause and O'Connell (2012), Cairo (2013),
Yau (2013, 2024), Berinato (2016), Cook et al. (2016), Harris
(2016), Hilfiger (2016), Carlson (2017), Hoffmann (2017), Kubina
et al. (2017), Rahlf (2017, 2019), Wexler et al. (2017), Wickham and
Grolemund (2017), Albert (2018) Kriebel and Murray (2018), Standage
(2018, 2019, 2020), Nolan and Stoudt (2021), Schwabish (2021), Smith
(2022), Alexander (2023), Wickham et al. (2023) and Yu and Barter
(2024).

Other Stata references

See also Cox (2004) for a general discussion of graphing distributions
in Stata; Cox (2007) for an implementation of stem-and-leaf plots that
bears some resemblance to what is possible with stripplot; and Cox
(2009, 2013) on how to draw box plots using twoway.

Examples

. // (Stata's auto data)

. sysuse auto, clear

. strip mpg, name(STRIP1, replace)

. strip mpg, aspect(0.05) name(STRIP2, replace)

. strip mpg, over(rep78) name(STRIP3, replace)

. strip mpg, over(rep78) by(foreign, note("")) name(STRIP4, replace)

. strip mpg, over(rep78) vertical yla(, ang(h)) name(STRIP5, replace)

. strip mpg, over(rep78) vertical stack yla(, ang(h)) name(STRIP6, replace)

. strip mpg, over(rep78) vertical stack yla(, ang(h)) height(0.4) name(STRIP7, replace)

. gen pipe = "|"

. strip mpg, ms(none) mlabpos(0) mlabel(pipe) mlabsize(*2) stack name(STRIP8, replace)

. label var price "Price (USD)"

. strip price, over(rep78) xla(3000(3000)15000) ms(none) mla(pipe) mlabpos(0) name(STRIP9, replace)

. strip price, over(rep78) xla(3000(3000)15000) width(200) stack height(0.4) name(STRIP10, replace)

. // (5 here is empirical: adjust for your variable)

. gen price1 = price - 5

. gen price2 = price + 5

. strip price, over(rep78) xla(3000(3000)15000) ms(none) addplot(rbar price1 price2 rep78, horizontal barw(0.2) bcolor(gs6)) name(STRIP11, replace)

. gen digit = mod(mpg, 10)

. strip mpg, stack vertical mla(digit) mlabpos(0) ms(i) over(foreign) height(0.2) yla(, ang(h)) xla(, ang(-0.001) tlength(*2) tlcolor(none)) subtitle(stem-and-leaf plot) name(STRIP12, replace)

. strip mpg, stack vertical mla(digit) mlabpos(0) ms(i) by(foreign, note("") subtitle(stem-and-leaf plot)) yla(, ang(h)) name(STRIP13, replace)

. strip mpg, over(rep78) separate(foreign) stack name(STRIP14, replace)

. strip mpg, by(rep78) separate(foreign) stack name(STRIP15, replace)

. // (fulcrums to mark means as centres of gravity)

. gen rep78_1 = rep78 - 0.1

. egen mean = mean(mpg), by(foreign rep78)

. strip mpg, over(rep78) by(foreign, compact note("")) yla(, glp(solid)) addplot(scatter rep78_1 mean, ms(T)) stack name(STRIP16, replace)

. egen mean_2 = mean(mpg), by(rep78)

. gen rep78_L = rep78 - 0.1

. gen rep78_U = rep78 - 0.02

. strip mpg, over(rep78) stack addplot(pcarrow rep78_L mean_2 rep78_U mean_2, msize(medlarge) barbsize(medlarge)) yla(, grid glp(solid)) name(STRIP17, replace)

. clonevar rep78_2 = rep78

. replace rep78_2 = cond(foreign, rep78 + 0.15, rep78 - 0.15)

. strip mpg, over(rep78_2) separate(foreign) yla(1/5) jitter(1 1) name(STRIP18, replace)

. logit foreign mpg

. predict pre

. strip mpg, over(foreign) stack ms(sh) height(0.15) subtitle(logit model) addplot(mspline pre mpg, bands(20)) name(STRIP19, replace)

. // (reference lines where by() would seem natural)

. // (labmask (Cox 2008) would be another solution for label fix)

. egen group = group(foreign rep78)

. replace group = cond(group <= 5, group, group + 1)

. label def group 7 "3" 8 "4" 9 "5", modify

. lab val group group

. strip mpg, over(group) vertical quantile centre mcolor(blue) xmla(3 "Domestic" 8 "Foreign", tlength(*7) tlc(none) labsize(medium)) yla(, ang(h)) xtitle("") xli(6, lc(gs12) lw(vthin)) name(STRIP20, replace)

. sysuse auto, clear

. egen median = median(mpg), by(foreign)

. egen loq = pctile(mpg), by(foreign) p(25)

. egen upq = pctile(mpg) , by(foreign) p(75)

. egen mean = mean(mpg), by(foreign)

. egen min = min(mpg)

. egen n = count(mpg), by(foreign)

. gen shown = "n = " + string(n)

. gen foreign2 = foreign + 0.15

. gen foreign3 = foreign - 0.15

. gen showmean = string(mean, "%2.1f")

. local box scatter median loq upq foreign2, ms(none ..) mla(median loq upq) mlabc(blue ..) mlabsize(*1.2 ..)

. local mean scatter mean foreign3, ms(none) mla(showmean) mlabc(orange) mlabsize(*1.2) mlabpos(9)

. local min scatter min foreign, ms(none) mla(shown) mlabc(black) mlabsize(*1.2) mlabpos(6)

. strip mpg, over(foreign) centre quantile vertical height(0.4) addplot(`box' || `mean' || `min') xsc(r(. 1.2)) yla(, ang(h)) xla(, noticks) name(STRIP21, replace) note("mean on left, median and quartiles on right")

. // (Stata's blood pressure data)

. sysuse bplong, clear

. egen group = group(age sex), label

. strip bp*, over(when) by(group, compact col(1) note("") subtitle(Systolic blood pressure (mm Hg))) ysc(reverse) subtitle(, pos(9) ring(1) nobexpand bcolor(none) placement(e)) ytitle("") xtitle("") xsc(alt) name(STRIP22, replace)

. // (Stata's US city temperature data)

. sysuse citytemp, clear

. label var tempjan "Mean January temperature ({&degree}F)"

. strip tempjan, over(region) subtitle(quantile plots) quantile vertical yla(14 32 50 68 86, ang(h)) xla(, noticks) centre name(STRIP23, replace)

. gen id = _n

. reshape long temp, i(id) j(month) string

. replace month = cond(month == "jan", "January", "July")

. label var temp "Mean temperature ({&degree}F)"

. strip temp, over(region) by(month, note("") subtitle(quantile plots)) quantile vertical yla(14 32 50 68 86, ang(h)) centre name(STRIP24, replace)

. strip temp, over(region) by(month, note("") subtitle(normal quantile plots)) quantile trscale(invnormal(@)) centre vertical yla(14 32 50 68 86, ang(h)) name(STRIP25, replace)

. egen mean = mean(temp), by(region month)

. gen regionL = region - 0.4

. gen regionR = region + 0.4

. strip temp, over(region) by(month, note("") subtitle(normal quantile plots with means)) quantile trscale(invnormal(@)) centre vertical yla(14 32 50 68 86, ang(h))

addplot(rspike regionL regionR mean, horizontal) name(STRIP26, replace)

The following examples use datasets from Whitlock and Schluter (2020)
and require (1) internet access to download the data; (2) previous
installation of pctilesets; (3) Stata 18 up to allow use of
stc2 (but just change the local macro otherwise).

. import delimited using https://whitlockschluter3e.zoology.ubc.ca/Data/chapter02/chap02e3bHumanHemoglobinElevation.csv, clear

. label var hemoglobin "Hemoglobin concentration (g dl-1)"

. egen mean = mean(hemoglobin), by(population)

. egen n = count(hemoglobin), by(population)

. gen shown = "{it:n} = " + strofreal(n)

. gen where = 9

. encode population, gen(x)

. gen xL = x - 0.4

. gen xR = x + 0.4

. strip hemoglobin, over(population) vertical quantile centre trscale(invnormal(@)) xla(, tlength(0)) xtitle("") addplot(scatter where x, ms(none) mla(shown) mlabpos(0) mlabsize(medium)

|| rspike xL xR mean, horizontal lc(black)) subtitle(normal quantile plots with added means) name(STRIP27, replace)

. import delimited using https://whitlockschluter3e.zoology.ubc.ca/Data/chapter12/chap12q17StalkieEyespan.csv, clear

. gen diet = food + " diet"

. label var eyespan "Eye span (mm)"

. save eyespan, replace

. pctilesets eyespan, over(diet) pctile(25 50 75) min max saving(eyespan_pctiles, replace)

. clonevar origgvar=diet

. merge m:1 origgvar using eyespan_pctiles

. gen xbox = cond(food == "Corn", 0.9, 1.9)

. local color stc2

. strip eyespan , over(diet) quantile vertical height(0.25) xla(, tlcolor(none)) addplot(rbar p25 p75 xbox, barwidth(0.16) lcolor(`color') fcolor(none) || scatter p50 xbox, ms(Dh) mcolor(`color') msize(medium)

|| rspike p75 max xbox, lcolor(`color') || rspike p25 min xbox, lcolor(`color')) aspect(1.2) yla(1 1.2 1.4 1.6 1.8 2 2.2) xtitle("") name(STRIP28, replace)

. import delimited using https://whitlockschluter3e.zoology.ubc.ca/Data/chapter13/chap13e1MarineReserve.csv, clear

. label var biomassratio "Biomass rato"

. means biomassratio

. scalar gmean = r(mean_g)

. su biomassratio

. strip biomassratio, vertical quantile ysc(log) yli(`=gmean', lp(solid)) aspect(1) text(`=gmean + 0.1' 1.1 "geometric mean") yla(`r(min)' 1/4 `r(max)') name(STRIP29, replace)

. import delimited using https://whitlockschluter3e.zoology.ubc.ca/Data/chapter15/chap15q09HippocampalVolumeRatio.csv, clear

. encode group, gen(GROUP)

. label define GROUP 1 "febrile" 2 "non-febrile" 3 none, modify

. label var GROUP "Childhood seizures"

. label var hippovolumeratio "Hippocampal volume ratio (%)"

. egen median = median(hippovolumeratio), by(group)

. gen GROUPL = GROUP - 0.4

. gen GROUPR = GROUP + 0.4

. su hippovolumeratio

. gen where = r(min) - 5

. egen count = count(hippovolumeratio), by(GROUP)

. gen shown = "n = " + strofreal(count)

. strip hippovolumeratio , over(GROUP) vertical quantile center xla(, tlc(none)) ms(O ..)

addplot(rspike GROUPL GROUPR median, horizontal || scatter where GROUP, ms(none) mla(shown) mlabsize(medium) mlabpos(0) mlabcolor(black))

yla(47 50(10)100) note(horizontal lines show medians, pos(11)) name(STRIP30, replace)

Acknowledgments

Philip Ender helpfully identified a bug.
William Dupont offered encouragement.
Kit Baum nudged me into implementing separate().
Maarten Buis made a useful suggestion about this help.
Ronán Conroy suggested adding whiskers. He also found two bugs.
Marc Kaulisch asked a question which led to more emphasis on the use of
by() and the blood pressure example.
David Airey found another bug.
Oliver Jones asked a question which led to an example of the use
of twoway rbar to mimic pipe or barcode symbols.
Fredrik Norström found yet another bug.
Marcello Pagano verified the 1966 Draper and Smith reference.
Dionyssios Mintzopoulos and Judith Abrams underlined the value of reference lines like those in dotplot, but drawn as such.
Vince Wiggins and David Airey gave helpful and encouraging
suggestions on a related program.
Frank Harrell also made encouraging remarks.
Alona Armstrong provided the 2015 Weissgerber et al. reference.
James Sanders, William Lisowski, Eric Booth and Chinh Nguyen helped to
identify and solve a problem with box line widths that were
sometimes much too small to be visible.
David Airey found yet another bug. Nitish Upadhyaya tickled and Eddy
Simms located a further bug. Antony Unwin provided the gatherplot reference.
Richard Goldstein supplied the 2018 Chiou and Bergey reference.
Pete Taylor tickled a bug if the variables specified in by() and separate() were the same variable.

Author

Nicholas J. Cox, Durham University, U.K.

n.j.cox@durham.ac.uk

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Also see

On-line: help for dotplot, histogram,
distplot (if installed), qplot (if installed),
cisets (if installed),
pctilesets (if installed),
quantilesets (if installed)