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This overview about choosing the best type of graph for data frames the issue in terms of underlying statistical question. For instance, are you comparing values? Showing composition? Looking for trends? Interested in distribution? What you're trying to understand from your data can and should inform the type of graph you use to visualize and communicate the results.
This guide frames the decision of which chart type in terms of data type: numeric, categorical, mixed numeric and categorical, maps, network, or time series. Click through to read more about caveats associated with each type of chart.
Working with qualitative (i.e., non-numeric) data can pose a set of different issues. The Qualitative Chart Choser by Jennifer Lyons and Stephanie Evergreen frames chart choice by what "story" you want to tell with your data.
Selecting colors for a figure may seem like an inconsequential task and people often stick with the default color scale of whatever visualization tool they're using. This may not be the best choice, as misuse of color in data presentation may confuse the viewer and lead to misinterpretation of results. It is important to think through your color choices in order to best present your data and make the main points of a graph or chart easy for viewers to correctly figure out.
This interactive website helps users generate a usable color palette. Also check out the "single hue" and "divergent" choices. A similar website, Colorgorical, lets users specify hue, lightness, and other technical color characteristics when creating a color palette.
Another consideration is what if the person looking at the data visualization is colorblind? This website takes user-specified color input and displays what various colored graph types would look like to people with types of colorblindness.
A main point to consider is if your visualization is meant to be exploratory (something you are doing to get more familiar with your data) or explanatory (you know your result and want to communicate it to your audience). See here for additional examples of explanatory vs exploratory visuals.
This post by Nathan Yau of Flowing Data provides examples of good (and bad) charts, distilled into a handful of general rules for making charts. For instance, be mindful of the starting point of the y-axis on a chart so that data representation is truthful to the underlying data trends.
"Ten Simple Rules for Better Figures" by Rougier, Droettboom, and Bourne (2014) is a brief overview of "do" and "do not" advice for making effective scientific figures. The first rule? "Know your audience."