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07 - 11 - 2014
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## Comparison of two groups of data: Introduction

Criteria for the comparison of groups of data are chosen mainly depending on the distribution of data. For normally distributed data parametric methods are used, while for non-normally distributed – non-parametric.

Parametric methods are statistical methods which depend on the parameters of populations or probability distributions. Parametric tests are only applied for numerical data which are sampled from a population with an underlying normal distribution or whose distribution can be rendered normal by mathematical transformation. They mainly include t-tests and ANOVA (ANalysis Of VAriance).

Non-parametric methods require fewer assumptions about a population or probability distribution and because of this they are applicable in a wider range of situations – they can be used with qualitative data or with quantitative data when no assumption can be made about the population probability distribution.

Nonparametric tests in practice are less flexible and less powerful than parametric tests. Where it is possible to apply both parametric and nonparametric methods preference should be given to parametric ones because they tend to provide better precision. However, usually the majority of biomedical data have non-normal distribution and, therefore, require the use of nonparametric methods.

### Selection of criteria for statistical analysis of data (Adopted from http://www.microbiologybytes.com/statsbytes/univariate.html)

 Objective Parametric criteria Nonparametric criteria All types of data Description Exploratory data analysis (mean), plots Exploratory data analysis (median), plots Univariate data Comparison with a hypothetical distribution One sample t test Wilcoxon test, chi square goodness of fit Bivariate data Comparison of independent variables Unpaired t test Wilcoxon test (unpaired, = Mann-Whitney test), Fisher's test (for small groups) or Chi-square test of independence (for large groups) / Chi-square test of homogeneity (for large groups) Comparison of dependent variables Paired t test Wilcoxon test (paired) Measurement of association between variables Pearson correlation test Spearman correlation test Prediction from another variable Simple linear regression Nonparametric regression Multivariate data Comparison of 3 or more independent variables ANOVA Kruskal-Wallis test, Chi-square test of independence Comparison of 3 or more dependent variables Repeated measures ANOVA Friedman test