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# Unadjusted Bivariate Two-Group Comparisons: When Simpler is Better

Vetter, Thomas, R., MD, MPH*; Mascha, Edward, J., PhD

doi: 10.1213/ANE.0000000000002636
General Articles: Special Article

Hypothesis testing involves posing both a null hypothesis and an alternative hypothesis. This basic statistical tutorial discusses the appropriate use, including their so-called assumptions, of the common unadjusted bivariate tests for hypothesis testing and thus comparing study sample data for a difference or association. The appropriate choice of a statistical test is predicated on the type of data being analyzed and compared. The unpaired or independent samples t test is used to test the null hypothesis that the 2 population means are equal, thereby accepting the alternative hypothesis that the 2 population means are not equal. The unpaired t test is intended for comparing dependent continuous (interval or ratio) data from 2 study groups. A common mistake is to apply several unpaired t tests when comparing data from 3 or more study groups. In this situation, an analysis of variance with post hoc (posttest) intragroup comparisons should instead be applied. Another common mistake is to apply a series of unpaired t tests when comparing sequentially collected data from 2 study groups. In this situation, a repeated-measures analysis of variance, with tests for group-by-time interaction, and post hoc comparisons, as appropriate, should instead be applied in analyzing data from sequential collection points. The paired t test is used to assess the difference in the means of 2 study groups when the sample observations have been obtained in pairs, often before and after an intervention in each study subject. The Pearson chi-square test is widely used to test the null hypothesis that 2 unpaired categorical variables, each with 2 or more nominal levels (values), are independent of each other. When the null hypothesis is rejected, 1 concludes that there is a probable association between the 2 unpaired categorical variables. When comparing 2 groups on an ordinal or nonnormally distributed continuous outcome variable, the 2-sample t test is usually not appropriate. The Wilcoxon-Mann-Whitney test is instead preferred. When making paired comparisons on data that are ordinal, or continuous but nonnormally distributed, the Wilcoxon signed-rank test can be used. In analyzing their data, researchers should consider the continued merits of these simple yet equally valid unadjusted bivariate statistical tests. However, the appropriate use of an unadjusted bivariate test still requires a solid understanding of its utility, assumptions (requirements), and limitations. This understanding will mitigate the risk of misleading findings, interpretations, and conclusions.

From the *Department of Surgery and Perioperative Care, Dell Medical School at the University of Texas at Austin, Austin, Texas

Departments of Quantitative Health Sciences and Outcomes Research, Cleveland Clinic, Cleveland, Ohio.

Accepted for publication October 4, 2017.

Funding: None.

The authors declare no conflicts of interest.

Address correspondence to Thomas R. Vetter, MD, MPH, Department of Surgery and Perioperative Care, Dell Medical School at the University of Texas at Austin, Health Discovery Bldg, Room 6.812, 1701 Trinity St, Austin, TX 78712. Address e-mail to thomas.vetter@austin.utexas.edu.

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