Are there any guidelines regarding the choice of the markers in a graph?

Question

There exist some guidelines on which colors should be used in the figures to ensure that they can be read by as many people as possible, such as color blind people (example (mirror)).

Are there any guidelines regarding the choice of the markers in a graph?

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Example of markers (mirror):

Code in python to generate the plot (in case the link gets broken):

#!/usr/bin/env python

import matplotlib.pyplot as pyplot

mark_dict = {
".":"point",
",":"pixel",
"o":"circle",
"v":"triangle_down",
"^":"triangle_up",
"<":"triangle_left",
">":"triangle_right",
"1":"tri_down",
"2":"tri_up",
"3":"tri_left",
"4":"tri_right",
"8":"octagon",
"s":"square",
"p":"pentagon",
"*":"star",
"h":"hexagon1",
"H":"hexagon2",
"+":"plus",
"D":"diamond",
"d":"thin_diamond",
"|":"vline",
"_":"hline"
}

def line_plot():

    x_list = [1, 10, 30, 70]
    y_list = [10, 20, 30, 40]

    pyplot.clf()
    for mark in mark_dict:
        y_list = [y_val + 10 for y_val in y_list]
        pyplot.plot(x_list, y_list, label=mark_dict[mark], marker=mark)

    pyplot.legend(loc="best", prop={'size':11})
    pyplot.savefig("markers.png")

def main():
    line_plot()

if "__main__" == __name__:
    main()

Answer 1

The Grammar of Graphics (2nd ed) by Wilkinson has a very little description about shape in Chapter 10, which discusses the following few concepts:

Morphing (technique used to vary shapes along continuous dimension). Here is the example taken from the book:

Another variant was also displayed:

However, Wilkinson comments such format as

"problematic [...] because it is not rotationally invariant. Shape must vary without affecting size, rotation, and other attributes. The graphics [above] could be used for representing negative and positive variation, but it is not clear that they would work as well as sized plus and minus signs."

Lastly, the following one shows categorical shape variation:

Which also agrees with many commonly used symbol scheme.

The biggest help of this section in the book, however, are two citations on relevant works:

Discriminating Strata in Scatterplots by Lewandowsky & Spence (PDF) actually carried out some experiment, showing scatterplots with different symbols to novice and expert. While the work does not recommend any scheme, it does suggest that "variations in shapes, amounts of fill, or use of discriminable letters can be used without great loss in accuracy."

Another one is A Model for Studying Dsiplay Methods of Statistical Graphics by Cleveland (URL), which investigates a lot more than just symbols, and should be able to provide a good foundation in this topic.