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Dot Plots



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Dot Plots Leland Wilkinson SPSS Inc 233 South Wacker Chicago IL 60606 Department of Statistics Northwestern University Evanston IL 60201 email leland spss com KEY WORDS dotplot histogram kernel density estimation graphics Abstract Dot plots represent individual observations in a batch of data with symbols usually circular dots They have been used for more than a hundred years to depict distributions in detail Handdrawn examples show their authors efforts to arrange symbols so that they are as near as possible to their proper locations on a scale without overlapping enough to obscure each other Recent computer programs that attempt to reproduce these historical plots have unfortunately resorted to simple histogram binning instead of using methods that follow the rules for the hand drawn examples This paper introduces an algorithm that more accurately represents the dot plots cited in the literature To be published in The American Statistician 1999 53 3 276 281 1 1 Introduction Dot plots have a long history Jevons 1884 used dot plots to graph the weight of British Sovereign coins by year Dot plots have appeared in statistical texts such as Tippett 1944 Tukey 1977 Box Hunter and Hunter 1978 and Mosteller and Hoaglin 1991 as well as in various scientific sources e g Uman 1969 They have been widely used in the medical literature e g Krieg Beck and Bongiovanni 1988 Chastre et al 1988 The dot plot discussed in this paper displays individual observations on a continuous scale using a dot or other symbol Its distinguishing feature is the use of local displacement in a direction orthogonal to the scale in order to prevent dots from overlapping This displacement is either symmetric which produces a string of dots resembling a belt of beads or asymmetric which produces a stack of dots resembling a density Figure 1 shows examples of these two types of dot plots the symmetric dot plot and the asymmetric dot plot or dot density The data are from Allison and Cicchetti 1976



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