DISCUSSION: STATISTICAL ANALYSIS IN NURSING
Statistical Minute
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From the *Department of Anesthesiology, Amsterdam UMC, Vrije Universiteit
Amsterdam, Amsterdam, the Netherlands; and †Department of Surgery and
Perioperative Care, Dell Medical School at the University of Texas at Austin,
Austin, Texas.
Related Article, see p 1864
Nonparametric Statistical Methods in Medical
Research
Patrick Schober, MD, PhD, MMedStat,* and Thomas R. Vetter, MD, MPH†
Figure. Adapted text excerpt from the statistical methods section of
Wang et al1 and their Table 2. These authors used Mann-Whitney U
tests to compare patient self-reported NRS pain scores (the second-
ary outcome), which were not normally distributed, between their
chewing gum group (G Group) and the control group (C Group). NRS
indicates numeric rating scale.
KEY POINT: Nonparametric statistical tests can be a
useful alternative to parametric statistical tests when
the test assumptions about the data distribution are
not met.
Address correspondence to Patrick Schober, MD, PhD, MMedStat,
Department of Anesthesiology, Amsterdam UMC, Vrije Universiteit
Amsterdam, De Boelelaan 1117, 1081 HV Amsterdam, the Netherlands.
Address e-mail to [email protected].
these parameters—for example, on means and mean
differences between groups. In contrast, though the
exact definition varies in literature, nonparametric
methods generally do not assume a specific probabil-
ity distribution. While other nonparametric methods
exist, we focus here on the widely used rank-based
nonparametric tests. These methods use the ranks of
the data instead of their actual values and can basi-
cally be used for all data that can be ranked, includ-
ing ordinal data, discrete data (like counts), and
continuous data.
Nonparametric methods are commonly used
when data distribution assumptions of parametric
tests are not met. In practice, researchers often assess
whether the outcome variable is overall normally
distributed and use a nonparametric test when it is
not. It is worth noting, however, that rank-based non-
parametric tests:
• usually have slightly less power than paramet-
ric tests when the underlying distributional
assumptions of the parametric test are actually
met,
• often focus on hypothesis testing rather than
estimation of parameters of interest, and
• may not be available when more complex analy-
ses than simple within- or between-group com-
parisons are required.
It can thus be useful to consider whether a para-
metric test can be used despite apparently non-nor-
mally distributed outcome data. First, the normality
assumption does not necessarily apply to the depen-
dent variable itself but, for example, to the residuals
in a linear regression model. Second, some paramet-
ric tests like the t test can be relatively robust against
non-normality when the sample size is large. Third,
data transformations to approximate a normal distri-
bution can be considered. Fourth, when data follow
some other well-defined distribution (eg, Poisson
In this issue of Anesthesia & Analgesia, Wang et al1
report results of a trial of the effects of preopera-
tive gum chewing on sore throat after general anes-
thesia with a supraglottic airway device. The authors
used the Mann-Whitney U test—a nonparametric
test—to compare numerical rating scale pain scores
between the groups.
The majority of statistical methods—namely, para-
metric methods—is based on the assumption of a spe-
cific data distribution in the population from which
the data were sampled. This distribution is charac-
terized by ≥1 parameters, such as the mean and the
variance for the normal (Gaussian, “bell shaped”) dis-
tribution. Parametric methods commonly seek to esti-
mate population parameters and to test hypotheses on
1862 www.anesthesia-analgesia.org December 2020 • Volume 131 • Number 6
E StatiStical MiNute
December 2020 • Volume 131 • Number 6 www.anesthesia-analgesia.org 1863
distribution for count data), researchers can take
advantage of parametric methods designed for these
specific distributions.2
The Mann-Whitney U test (also known as the
Wilcoxon rank-sum test or Wilcoxon-Mann-Whitney
test) used by Wang et al1 (Figure) is the nonpara-
metric equivalent to the 2-sample t test to compare 2
independent groups. It tests the null hypothesis that
both groups come from populations with the same
distribution, specifically, whether randomly drawn
observations from one group are more likely to be
higher (or lower) than randomly drawn observations
from the other group.3 Contrary to common belief, the
Mann-Whitney U test does not compare the medians
between groups. This is only true under the assump-
tion that the distribution has the same shape in both
groups and differs only by its location. For >2 groups,
the Kruskal–Wallis test can be used as a nonparamet-
ric alternative to 1-way analysis of variance (ANOVA).
The Wilcoxon signed rank test is used to compare
2 paired (nonindependent) groups or 2 repeated
within-subject measurements, and this test assumes
that the distribution of the between-group differences
is symmetric. The Friedman test is the nonparametric
equivalent to 1-way repeated-measures ANOVA for
comparisons of >2 paired groups.4 For a nonparamet-
ric correlation analysis, Spearman rank correlation is
commonly used.5
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