Page 44 - Clinical Small Animal Internal Medicine

12 Section 1 Evaluation and Management of the Patient

observed value. This underscores the point that when means and standard deviations) and for identifying out-
VetBooks.ir data do not conform to a particular parametric distribu- liers that may represent data errors.
Another common error arises when replicate meas-
tion, it is preferable to use a method of describing the
data that does not depend on specifying a particular
This arises, for example, when two or more treatments
distribution. urements are taken from the same patient over time.
Graphically representing such data is likewise inappro- are successively tested in patients with before/after com-
priate when using bar charts based on means and error parisons, or when monitoring blood values over time. As
bars using standard deviations or standard errors. One mentioned earlier, n replicate measurements taken from
indispensable way of graphically portraying such data is a single individual cannot be treated as equivalent to sin-
through the use of a box and whiskers plot, as shown for gle measurements coming from n different individuals.
the data above in Figure 2.2. Figure 2.3 illustrates this principle by examining before/
The advantage of such graphs is that they are con- after measurements taken on five patients at different
structed based only the data, and not on any distribu- times. Both panel 1 (left) and panel 2 (right) contain the
tional assumptions (such as normality). The lower and identical 10 points but panel 1 ignores the pairing within
upper ends of the box correspond to the 25th and 75th individuals, and a regression line fitted to the 10 points
percentiles respectively; the horizontal line within the suggests a negative correlation between the measure-
box corresponds to the 50th percentile (i.e., the median), ments over time. Panel 2, in contrast, links the before/after
the bars (i.e., the “whiskers”) above and below the box pairs within individuals and an entirely different picture
contain all data above and below 1.5 times the vertical emerges: every individual’s values actually increased over
width of the box (i.e., the interquartile range), and the time. Ignoring such pairing not only obscures actual
individual points beyond the whiskers represent effects but also in cases such as this suggests a paradoxical
extreme (outlying) values. Figure 2.2 reinforces the reversal of effects. Therefore, in studies where two or
observation from the histogram that the data are more measurements are taken from the same patients
skewed towards higher values, which causes the mean over time, it is important to not combine the patients’ val-
to be larger than the median. This type of plot is also ues at individual time points through the use of histo-
valuable in assessing symmetry of a data distribution grams, boxplots, or other graphical representations. Panel
(asymmetric distributions should not be described with B is often called a “spaghetti plot” because it can, with
larger numbers of individuals, take on an appearance of
many intertwined lines across two or more times.

25
Measures of Association and Effect

20 As noted earlier, the construct and interpretation of the
P‐value is unsatisfying, if not bewildering to consumers
of statistical analyses who are not well versed in their
subtleties. The preoccupation with statistical testing in
Data value 15 the medical literature should presumably be subordinate
to and supplanted by a more favorable inclination
towards estimation: the mathematical calculation of sta-
10
tistics that measure the magnitude of differences and
associations in data. The imperative for this is no more
evident than in the often seen but erroneous exposition
5 that “no differences were found from a set of analyses
because none were statistically significant.”
Among the most common intuitively appealing meas-
0 ures of association are those conjoined from descriptive
measures of prevalence and incidence.
Figure 2.2 Box and whiskers plot for data shown in Figure 2.1.
Lower and upper ends of the box represent the 25th and 75th
percentiles, respectively; the orange line within the box equals the Prevalence
50th percentile (median), the bars (“whiskers”) above and below Prevalence represents the proportion of individuals in a
the box contain all data above and below 1.5 times the
interquartile range, and individual points beyond the whiskers population who, at a single point or restricted period of
represent outliers. time, possess a health characteristic of interest, as in