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Graphical Display of Data
Graphs and charts are now a fundamental component of modern research and reporting. Today, researchers use many graphical means such as histograms, box plots, and scatterplots to better understand their data. Graphs are effective for displaying and summarizing large amounts of numerical data, and are useful for showing trends, patterns, and relationships between variables. Graphs and charts are also used to enhance reporting and communication. Graphical displays often provide vivid color and bring life to documents, while also simplifying complex narrative and data. This entry discusses the importance of graphs, describes common techniques for presenting data graphically, and provides information on creating effective graphical displays.
Importance of Graphs in Data Analysis and Reporting
In the conduct of research, researchers accumulate an enormous amount of data that requires analysis and interpretation in order to be useful. To facilitate this process, researchers use statistical software to generate various types of summary tables and graphical displays to better understand their data. Histograms, normal Q-Q plots, detrended Q-Q plots, and box plots are common graphs that are used to assess normality of data and identify outliers (i.e., extreme values) in the data. Such graphs are quite useful for identifying data anomalies that might require more in-depth study. Researchers also generate special graphs to ensure that important assumptions are not being violated when performing certain statistical tests (e.g., correlation, t test, analysis of variance [ANOVA]). For example, the residuals scatterplot and normal probability plot are useful for checking the assumptions of normality, linearity, and homoscedasticity, as well as identifying outliers.
Narrative and numerical data—no matter how well organized—are of little use if they fail to communicate information. However, many research papers and reports can be intimidating to the average person. Therefore, researchers need to find creative ways to present data so that they are sufficiently appealing to the average reader. Data that are presented in the form of charts and graphs are one way that researchers can make data more appealing; many people find graphs much easier to understand compared to narratives and tables. Effective graphical displays of data can undoubtedly simplify complex data, making it more comprehensible to the average reader. As the old clichè goes—a picture paints a thousand words.
Common Graphical Displays for Reporting
Bar Chart
Bar charts are one of the most commonly used techniques for presenting data and are considered to be one of the easiest diagrams to read and interpret. They are used to display frequency distributions for categorical variables. In bar chart displays, the value of the observation is proportional to the length of the bar; each category of the variable is represented by a separate bar; and the categories of the variable are generally shown along the horizontal axis, whereas the number of each category is shown on the vertical axis. Bar charts are quite versatile; they can be adapted to incorporate displays of both negative and positive data on the same chart (e.g., profits and losses across years). They are particularly useful for comparing groups and for showing changes over time. Bar charts should generally not contain more than 8–10 categories or they will become cluttered and difficult to read. When more than 10 categories are involved in data analysis, rotated bar charts or line graphs should be considered instead.
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