Graphical Analyses: Boxplots

The boxplot is a schematic graphical device for comparing the empirical distributions represented by batches of numbers [15]. For these data, the analytical method used (QXRD, OM-1, RR1-n) identifies the batches. This plot can be considered a visual one-way anova or t-test. The location of the distributions, their spread, and extremes are embedded in the graphical display. This allows meaningful comparison of distributional information through rapid assessment of the alignment or misalignment of median values and boxes, and differences in spread.

Important features of the boxplot are:

1. the width of the box is proportional to sample size,
2. the median value, used as an indicator of location because of its resistance to outliers, is identified by the X,
3. the interquartile range ("middle half") of the data are represented by the body of the box, and
4. the extremes (minimum and maximum) are represented by the ends of the straight lines projecting out of the box.

One important consideration for these data are that the QXRD box represents 36 numbers, while the RM certificate data (OM) represents only four numbers, and the round robin data (RR) represents just two numbers each. The boxes for the RR groups, with only two observations, have the upper line of the box equal to one data point, the other line equal to the other, and the X in the middle denotes the mean/median of the two observations.