# Non-Parametric Tests

## Introduction

While exploring quantitative data, it is of great importance to be able to choose proper statistical procedures and tests in order to attain appropriate results and draw correct conclusions (Forthofer, Lee, & Hernandez, 2007). This paper provides an analysis of the appropriateness of the use of a number of non-parametric tests in the study conducted by Clough et al. (2006). After explaining why the utilized tests were appropriate, an alternative test which could have been employed in this situation is suggested.

## Explanation of the Use of the Non-Parametric Test

In their article, Clough et al. (2006) describe the results of an analysis of data pertaining to the use of cannabis in an indigenous community in Australia. The data was collected twice (in 2001 and 2004) from two overlapping samples. In order to assess the data, the authors used the McNemar test for paired proportions, as well as the Wilcoxon signed rank test. These tests were used to estimate the changes in the use of marijuana, as well as the changes in the symptoms of misuse.

These tests were appropriate for the given situation due to the fact that it was required to compare whether the difference in the number of people who used cannabis was significant between the baseline and the follow-up in the same sample. It is apparent that the analyzed data was categorical (yes or no), so it would be impossible to use, for instance, a paired samples t-test, which compares means, whereas the use of the McNemar test for paired proportions is appropriate for nominal data with dichotomous variables (Field, 2013). Simultaneously, the Wilcoxon signed ranks test was used for pair-matched, non-nominal data, such as the symptoms of misuse in the same sample (Clough et al., 2006). This is also appropriate because it was needed to decide whether there was a significant difference in the symptoms between the baseline and the follow-up.

## A Possible Alternative Test and its Justification

Instead of the McNemar test, it was possible to use the test of marginal homogeneity (Field, 2013). It is stated that the test of marginal homogeneity is an extension of the McNemar test which allows for using variables that are dichotomous (like the McNemar test) or ordinal (unlike the McNemar test) (Field, 2013). For instance, it is possible to assess the difference in an ordinal variable in a sample prior to and after an intervention, or at the baseline and at the follow-up. Therefore, if the use of the McNemar test was appropriate for the given data, it is clear that the test of marginal homogeneity could also have been utilized, even though there was no need for it (Warner, 2013).

## Conclusion

Therefore, Clough et al. (2006) employed the McNemar test for paired proportions and the Wilcoxon signed rank test. The choice of the tests was appropriate due to the characteristics of the analyzed data. An alternative test which could have been used instead of the McNemar test for paired proportions is the test of marginal homogeneity, which is an extension of the McNemar test that can explore not only dichotomous nominal variables but also ordinal data.

## References

Clough, A. R., Lee, K. S. K., Cairney, S., Maruff, P., O’Reilly, B., d’Abbs, P., & Conigrave, K. M. (2006). Changes in cannabis use and its consequences over 3 years in a remote indigenous population in northern Australia. Addiction, 101(5), 696-705. Web.

Field, A. (2013). Discovering statistics using IBM SPSS Statistics (4th ed.). Thousand Oaks, CA: SAGE Publications.

Forthofer, R. N., Lee, E. S., & Hernandez, M. (2007). Biostatistics: A guide to design, analysis, and discovery (2nd ed.). Burlington, MA: Elsevier Academic Press.

Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: SAGE Publications.

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