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  • Describe statistical tests used to evaluate differences among groups

  • Define statistically dependent (i.e., dependent or paired observations) samples and state how these affect the choice of a statistical test

  • Explain how the scale of measurement for the dependent variable influences the choice of a statistical test

  • Define nonparametric statistical methods and identify common nonparametric tests

  • Identify statistical tests to evaluate relationships between two continuous variables and between two ordinal variables


  • Analysis of variance (ANOVA)

  • Bivariate analyses

  • Chi-square test of homogeneity

  • Independent groups t-test

  • Kruskal-Wallis test

  • Negative relationship

  • Nonparametric methods

  • Paired t-test

  • Parametric methods

  • Pearson correlation coefficient

  • Positive relationship

  • Scatterplot

  • Sign test

  • Spearman rank correlation coefficient

  • Wilcoxon-Mann-Whitney test


One of the most common research designs encountered in biomedicine involves the comparison of outcomes in two groups. Typically, one group of patients will receive an experimental treatment and a second group receives a comparison treatment that may be a placebo, a second type of treatment, or usual care. Within pharmacy, the classic two-group study is a study comparing a drug treatment to placebo. The outcomes from each group are compared using a statistical test and conclusions are made regarding the efficacy of treatment based on the results of the statistical test.

The purpose of this chapter is to describe the most commonly used bivariate analyses,a including those used to compare groups, and to illustrate these techniques using small datasets. The chapter begins by describing the process of statistically comparing averages (or means) and then proportions between two independent groups. The situation of nonindependent groups, such as when a group of patients is measured at two different time points, is then discussed. Comparisons of the rank order of responses in two or more groups are also described, as is the calculation of the correlation between two variables. These statistical tests are described in the context of a case scenario. The chapter ends by reviewing the use and assumptions of the described statistical tests for comparing groups as shown with a flowchart.

aBivariate analysis is a term used to denote an analysis with just two variables. Some use the term univariate analysis to describe analysis of a single dependent variable, even though there may be multiple independent variables. Using this definition, some of the techniques discussed in this chapter, such as ANOVA and the t-test, may also be considered univariate techniques.


Consider the situation of a pharmacist-run community health center where services are provided to a substantial number of patients with Type II diabetes. Community health center pharmacists have worked with the local YWCA to provide exercise classes and make gym facilities available to their patients. They know that exercise should have a positive effect on patients with diabetes; that is, ...

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