Page 42 - Clinical Small Animal Internal Medicine

10 Section 1 Evaluation and Management of the Patient

panel contains 30 different parameters to evaluate. Kolmogorov–Smirnov tests) and plots (for example, nor-
VetBooks.ir Although each separate parameter has a 5% probability of mal probability plots). Such tests assume data are nor-
mally distributed; rejection of the null hypothesis
being incorrect in a normal animal, when considering all
parameters the probability of at least one error rises to
normality.
78.5%. In other words, a veterinarian should be surprised indicates incompatibility with the null hypothesis of
if at least one parameter does not fall outside the refer- The problem with such tests is that they are notori-
ence range even in a healthy patient. ously inadequate to detect departures from normality
Another related problem arises when using screening when sample sizes are small. For example, consider the
tests with imperfect properties (false‐positive and ‐nega- following six data points: 100, 100, 80, 70, 50, 50. This is
tive results) in populations with low prevalences of ill- a U‐shaped distribution and so is clearly not normally
nesses. Even when the test properties are excellent, with distributed. Nevertheless, a Shapiro–Wilk test fails to
error rates less than 5%, if a disease is rare enough in a reject the null hypothesis that the data are normally dis-
population of patients being screened, there can para- tributed when α = 0.05 (P = 0.22), so if we relied on this
doxically be more false‐positive results than true‐posi- test result we would erroneously conclude that the sam-
tive results. This should be discomforting to veterinarians ple data derived from a population with a normal distri-
whose clinical decisionmaking depends on the veracity bution. Interestingly, if this dataset is doubled in size (n =
of diagnostic testing. 12), then the Shapiro–Wilk test would become signifi-
One approach to resolving this issue (apart from run- cant (P = 0.019) and the null hypothesis of normality
ning the test again to see if the result was aberrant) is to would be rejected.
use screening tests judiciously, reserving them for When sample sizes are small or when normality is an
patients with a heightened suspicion of actual illness. In untenable assumption, then alternative statistical tests
other words, clinical judgment and experience are as are sometimes available. These tests are called nonpara-
integral to the use and interpretation of diagnostic tests metric tests, because they do not assume that data follow
as contrasting the actual test results to reference ranges. a particular distribution, and hence are also known as
Such circumspection serves to elevate the likelihood of distribution‐free tests. Table 2.1 contains a list of the
illness in the patient being tested, or analogously the most commonly used nonparametric tests, as well as
prevalence of the illness in the population being screened. their equivalent parametric test (if one exists).
This will contribute to making fewer unjustified conclu- These tests have more statistical power (for example,
sions about abnormal results in otherwise healthy the ability to reject the null hypothesis when it is false)
patients. than parametric tests when data do not conform to a
parametric distribution (such as normality), and are
almost as powerful as parametric tests when the data
Parametric versus do conform to a parametric distribution. When the
Nonparametric Tests assumption of normality is questionable based on sta-
tistical tests or the sample size is too small for reliable
All statistical tests have assumptions underlying their use. testing, nonparametric tests are preferable whenever
Those that assume that data follow a particular probabil- possible.
ity distribution function (also known as the sampling
model) are called parametric tests (by virtue of the fact
that the functions have one or more parameters in them). Describing Data Distributions
Probably the most common distribution function used in
parametric statistical analyses is the normal distribution For data that are approximately normally distributed, it
(with two parameters: the mean and standard deviation). is customary to describe the center of the distribution
As noted earlier, Student’s two‐group t‐test assumes that with the sample average (i.e., mean), and to describe the
the data in each group are approximately normally dis- dispersion around the mean with either the standard
tributed. Other well‐known parametric tests also rely on deviation or the standard error of the mean (i.e., the
normality: the paired t‐test assumes the differences are standard deviation divided by the square root of the sam-
approximately normally distributed; analysis of variance ple size). When data are not normally distributed, how-
and least‐squares linear regression assume the model ever, it is generally advisable to describe the data with
residuals (the difference between observed and predicted statistics that do not assume a symmetric distribution
values) are approximately normally distributed. around the mean. Preferable measures to use include
How can a clinician know if data are normally distrib- medians, ranges, and percentiles of the data (for
uted? Various approaches exist, including distributional example, the 2.5th and 97.5th percentiles provide a 95%
tests (for example, Shapiro–Wilk, Shapiro–Francia, percentile‐based interval).