Box and whisker plots diagram with labeled parts: upper and lower whiskers, quartiles, and outliers. A key explains each term and shows quartiles as four sections of 25% each for clear data visualization.

The Basics

The box-and-whisker plots are very effective and easy to read. They summarize data much better than just a simple ‘average’, and provide a deeper insight into the distributional characteristics of a group of scores.

Here’s how they work

To begin with, scores are sorted. Then four equal-sized groups are made from the ordered scores. That is, 25% of all scores are placed in each group. The lines dividing the groups are called quartiles. The ‘inter-quartile range, aka the ‘middle box’, represents the middle 50% of scores for the group. Now for the whiskers- the upper and lower whiskers represent scores outside the middle 50%. Whiskers often (but not always) stretch over a wider range of scores than the middle quartile groups do.

Interpreting the Plots: Real-Life Example

Box and whisker plots comparing HOOS Overall scores pre-op and 3 months post-op show increased median and range post-op, with fewer outliers. The y-axis spans 0 to 100.

Here at CODE, we provide our clients with Box and Whisker plots on a regular basis. Below are several examples of Box and Whisker plots that display the Overall HOOS Scores for hip replacement patients. The HOOS score ranges from 0, which represents the greatest level of disability, to 100, which is the best possible score.

Example 1: this example displays the overall HOOS score for an individual provider’s patients Total Hip Replacement patients. The red plot represents the patients’ pre-op scores and the green 3-month post-op scores. The number of patients in each section of the graph is displayed across the top. So in this case, the pre-op plot represents 250 patients, and the post-op plot 200. The Y-axis is the PRO score- and HOOS is like basketball- the more points, the better- so 0 represents greatest disability, and 100 is a perfect score.

Example 2: In addition to the provider scores, it displays the data for all the THA patients within the practice. The providers’ data is the first plot, and the organization is the second. Rather than just using a simple line graph that shows the average score, which would pretty much be an overlapping line, this plot gives much more information about the distribution of the patients’ scores.

Example 3: This plot shows the pre and post-op scores for all of the providers within an organization.

Box and whisker plots compare HOOS Overall scores for Provider Pre-Op, Practice Pre-Op, Provider 3 Month Post-Op, and Practice 3 Month Post-Op; post-op groups display higher median scores and more outliers.
Box and whisker plots compare HOOS Overall scores for two provider groups in a group practice; left boxes are teal, right are blue. Each plot displays score distributions, medians, outliers, and horizontal lines marking key thresholds.

Box and Whiskers plots are much more valuable than using simple ‘averages’ or line graphs. They serve as a powerful tool for both individual providers and group practices.

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