Boxplot
A boxplot is a graphical way of
summarizing the distribution of the scores of a group of patients.
Boxplots (often called "box and
whisker" plots) are a way of summarizing a distribution of
scores of a group of patients. By portraying the scores for more than one
group next to each other, one can frequently see the major trends in the
dataset.
The "box" in a boxplot shows
the median score as a line and the first (25th percentile) and third quartile
(75th percentile) of the score
distribution as the lower and upper parts of the box.
The median is the score at the 50%
percentile: half of all patients get a score higher than the median, and
50% get a score lower. It is the middle point in the distribution of
scores.
The 25th percentile is the point at
which 25% of the patients score lower (and 75% score higher). The 75th
percentile is the point at which 75% of the patients score lower (and 25%
score higher). Thus, the area in the "box" represents the middle
50% of the
patients.
The "whiskers" shown above
and below the boxes technically represent the largest and smallest
observed scores that are less than 1.5 box lengths from the end of the
box. In practice, these scores are about the lowest and highest values one
is likely to observe.
On very rare occasions, scores are
shown as open circles "o" or stars. These scores are ones that
are, respectively "very rare" and "exceedingly rare."
Such scores may represent very unusual patients or data processing errors.
In comparing the boxplots across
groups, a simple summary
is to say that the "box" area for one group is higher or lower
than that for another group. This comparison is analogous to saying that one group
tends to have higher scores than another. To the extent that the boxes do
not overlap, the groups are quite different from one another.
Formal statistical tests, of
course, are used to compare the groups to one another. As
a general rule-of-thumb for visual displays, if the degree of overlap is
less than 80% for moderately-sized samples, the differences will usually
prove to be statistically significant when a formal test is conducted.
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