Research for Evidence Based Practice

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 p.schober@amsterdamumc.nl.

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

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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

REFERENCES 1. Wang T, Wang Q, Zhou H, Huang S. Effects of preoperative

gum chewing on sore throat after general anesthesia with a supraglottic airway device: a randomized controlled trial. Anesth Analg. 2020;131:1864–1871.

2. Vetter TR, Schober P. Regression: the apple does not fall far from the tree. Anesth Analg. 2018;127:277–283.

3. Divine G, Norton HJ, Hunt R, Dienemann J. Statistical grand rounds: a review of analysis and sample size cal- culation considerations for Wilcoxon tests. Anesth Analg. 2013;117:699–710.

4. Schober P, Vetter TR. Repeated measures designs and anal- ysis of longitudinal data: if at first you do not succeed-try, try again. Anesth Analg. 2018;127:569–575.

5. Schober P, Vetter TR. Correlation analysis in medical research. Anesth Analg. 2020;130:332.