A challenge for researchers is to present their findings so that it will be useable and understandable to the reader. Often visual representations assist the reader in understanding the findings, especially when groups are being compared. A box and whisker plot is a useful visual representation when (a) large numbers of observations are measured on an interval scale (the distance between points on the scale are equal, such as test scores, temperatures), (b) when two or more groups being compared, and (c) when the scores are not normally distributed.
The box and whisker plot (also called a box plot) allows immediate visualization of the center and spread of the scores. The statistics presented include the median (center) and two measures of spread or variability, the interquartile range and the overall range of scores. The components of the box and whisker plot are illustrated below.
The median represents the midpoint or the center of the scores. In calculating a median, scores are arranged in order of magnitude, and the middle number is the median. It is marked by the vertical line inside the box. For an odd number of data elements or scores, the median is the middle number. For an even number of scores, the median is computed as the mean of the middle two numbers. Thus, for the scores of (70, 72, 78, 84, 86, 88, 90), the median score is 84. For the scores of (70, 72, 78, 84, 86, 88, 90, 92), the median is the mean of the middle two numbers, 88 and 86. So, in this case, the median is 87. In a box and whisker plot, the median is represented by the vertical line inside the box.
The interquartile range is a measure of spread or dispersion. It is the difference between the 75th percentile or the third quartile (called Q3) and the 25th percentile or first quartile (called Q1). The formula for the interquartile range is therefore Q3 - Q1. To calculate Q3, take the median of the upper half of the data. To calculate Q1, take the median of the lower half of the data. In a box and whisker plot, the ends of the box represent the lower and upper quartiles.
The range is a measure of dispersion and represents the difference between the lowest and highest scores in the data set. The range is calculated by subtracting the smallest score from the largest score. In a box and whisker plot, the whiskers are the two lines outside the box that extend to the highest and lowest data scores.
In the article by Giangregorio, a box plot (Figure 1) is used to visually display the osteoporosis knowledge findings for the different professional categories. This allows for a quick comparison of the median, interquartile range, and range for the different professional categories.
One can see from the box and whisker plot summarizing the osteoporosis data that the dieticians had the highest median score (18) followed by pharmacists, technologists, physical therapists, nurses, OTA/PTAs, and then OTs. By examining the position of the median score in the box, it can be seen that sometimes the median is in the center of the box (as with nursing), indicating equal dispersion of scores on either side of the median, or the median can be off-centered (as with technologists), indicating smaller variability in one of the quartiles. In examining the technologists group, the median score was 15. The second quartile scores had little variability all with scores of 14 or 15. The third quartile scores had greater variability with scores ranging from 15 to 18.
Looking at the representation of the dispersion findings, it can be seen that there was no variability in scores for the pharmacist group (median 16). Smaller dispersion was seen for the dietician group (interquartile range of 1 and total range of 2) and physical therapists (interquartile range from 13 to 15 (2) and total range from 11 to 16 (range of 5)). Nursing had the largest range from 6 to 20 (range of 14) with the interquartile range or 50% of scores between 11 and 15.
The box and whisker plot is an effective way to present the findings from this study and allows the reader to quickly compare the professional categories findings.