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