Standard rose diagrams are a favorite method of depicting orientations because of their ease of comprehension, but they are known to have two serious problems. First, arbitrary decisions about class width and starting position can dramatically alter the resulting diagram, although the degree of variation has been underappreciated. Second, when rose diagrams are correctly scaled to the square root of the class frequency, they can be awkward to evaluate. Possible solutions that deserve consideration include (1) representing 1° classes with rays of dots ("dot diagrams", allowing linear scaling), and (2) overcoming arbitrariness by combining all possible rose diagrams for a dataset into one diagram ("summed datasets"). Solution #1 can work by plotting either one dot per datum ("corona dot diagrams") or one dot for each value above or below the mean membership ("mean-deviation dot diagrams"). Both plot types can show either raw or summed data. Drawing one-degree class-width diagrams and summing (combining) all possible rose diagrams offers the only non-arbitrary versions of orientation diagrams, but summing diagrams smoothes the data slightly, thereby additionally weighting clusters of similar but not identical data points. My recommendation is to publish a dot plot of the raw data, and another of the summed results. Mean-deviation diagrams and factor-averaged summed datasets work together particularly well.

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