The Phistogram

Abstract

AbstractThis article introduces a new kind of histogram-based representation for univariate random variables, named the phistogram because of its perceptual qualities. The technique relies on shifted groupings of data, creating a color-gradient zone that evidences the uncertainty from smoothing and highlights sampling issues. In this way, the phistogram offers a deep and visually appealing perspective on the finite sample peculiarities, being capable of depicting the underlying distribution as well, thus becoming an useful complement to histograms and other statistical summaries. Although not limited to it, the present construction is derived from the equal-area histogram, a variant that differs conceptually from the traditional one. As such a distinction is not greatly emphasized in the literature, the graphical fundamentals are described in detail, and an alternative terminology is proposed to separate some concepts. Additionally, a compact notation is adopted to integrate the representation’s metadata into the graphic itself.Keywords: statistical graphicdata visualization toolperceptioncolor-gradient techniquesmoothing uncertaintyequal-area histogramDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also.