Description of continuous data using bar graphs: a misleading approach

Abstract

Introduction: With the ease provided by current computational programs, medical and scientifi c journals use bar graphs to describe continuous data. Methods: This manuscript discusses the inadequacy of bars graphs to present continuous data. Results: Simulated data show that box plots and dot plots are more-feasible tools to describe continuous data. Conclusions: These plots are preferred to represent continuous variables since they effectively describe the range, shape, and variability of observations and clearly identify outliers. By contrast, bar graphs address only measures of central tendency. Bar graphs should be used only to describe qualitative data.Keywords: Biostatistics. Descriptive statistics. Medical research.Over the decades, many authors have used bar graphs to describe continuous data (1) . The height of the bars in these graphs indicates a measure of central tendency (mean or median) of the data, while error bars describe a measure of dispersion (standard deviation) or precision (standard error). These graphs have become quite popular with the ease provided by some current computer programs. Despite their wide use, bar graphs have fostered a misleading approach to describe continuous data, while traditional tools such as box plots and dot plots are more suitable for this purpose. Bar graphs do not provide useful information about the behavior of data, such as skewness, range, and presence of atypical values (outliers). They only describe the position of the mean (or median) and dispersion around this measure.The box plot, also called box-and-whiskers plot, was introduced by the American mathematician John Wilder Tukey as a practical method to describe groups of numerical data based on their quartiles and extreme values (2) . When represented vertically, the box plot displays a rectangle (the box) whose base and top represent the position of the fi rst (Q1) and third (Q3) quartiles, respectively. A band inside the rectangle describes the second quartile (the median). The height of the rectangle then represents the inter-quartile range (IQR), and can be interpreted as a measure of data spread. To complete the graph, two vertical lines connect the third quartile to the highest value and the fi rst quartile to the lowest value. A practical method to detect potential outliers is to identify values above Q3 + 1.5 IQR and bellow Q1 -1.5 IQR in the plot. Outliers are represented by points (or other symbols), and vertical lines connect the third quartile to the highest point below Q3 + 1.5 IQR and the fi rst quartile to the lowest value above Q1 -1.5 IQR. This is the standard form of a box plot, but since its introduction by Tukey, many alternative forms have been proposed (3) (4) . The dot plot can be used to describe small sizes, since the box plot requires a sample size of at least 5 to be adequate.For example, we simulated data on a continuous variable with different means, dispersion, and skewness among three groups. For each group, we simulated samples of size n = 30. In the fi rst and sec...

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