Data Analyses for Small Samples and Non-Normal Data: Nonparametric Methods

Researchers regularly find themselves working with small data sets, especially for studies of practice interventions, the hallmark of social work research.  Similarly, their data sets may not meet the assumptions (e.g., normal distribution) required for the parametric techniques they were trained to use.  Yet most researchers receive little or no training in the techniques required to analyze these kinds of data properly – nonparametrics.  This educational gap leaves them without the tools to conduct suitable analyses of their data, or more importantly, the lack of exposure may constrain them from recognizing that nonparametric tools are available to them.  These researchers’ only option is to hope for robustness when they utilize parametric methods, despite their potential to guide them to the wrong conclusions.  In addition, because successful grant proposals may require believable pilot data, funding may hinge on the ability to show significant findings from small datasets.  Using parametric methods for data that do not meet the assumptions or have insufficient power can result in non-significant findings when they are actually present.  Conversely, researchers may find significant results that are an artifact of the inappropriate analytic technique.  Nonparametric strategies are often a solution for these issues.

This workshop, presented in clear and understandable language by the authors of an upcoming book on nonparametric analysis, will assist researchers in analyzing these kinds of data.  The workshop will be ideal for participants interested in easily identifying the appropriate test for their data and having access to systematic instructions to conduct the test and interpret the results.  A typical research scenario will illustrate each statistical method, and the step-by-step process for using SPSS will be provided. 

The workshop will begin with an overview of nonparametric analyses, the situations in which they can be useful, and the advantages of using nonparametrics.  A brief explanation of how nonparametrics differ from parametric analysis will be presented, along with a discussion of sample size and power.  Conceptual information about how, contrary to commonplace perceptions, nonparametric methods can be powerful and can provide useful, believable findings to answer research questions, will also be provided.  Important to the presentation will be a discussion of what constitutes a “small” sample and how to identify a non-normal distribution. 

Next, the presenters will systematically cover nonparametric techniques for one variable at various measurement levels (e.g., Binomial test, Chi-Square test, Kolmogorov-Smirnov test, Wilcoxon Signed-Rank test).  This will be followed by tests comparing two or more independent groups (e.g., Mann-Whitney U, Kruskal-Wallis, Spearman Rank-Order), and then tests comparing two or more related groups (e.g., McNemar’s, Marginal Homogeneity, Median Difference, Sign Test, Hodges-Lehman, Cochran’s Q, Kendall’s Coefficient of Concordance, Friedman’s 2-way ANOVA).  Lastly, tests that predict based on a set of independent variables will discussed (e.g., Theil’s Incomplete Method, Ordered Logistic Regression, Factorial Logistic Regression).

Participants should expect a rich exchange of ideas, along with specific examples and links to resources.  Materials and examples will be provided digitally during the workshop or upon request.  The presenters will allow time for both specific and general questions.