07 - 11 - 2014
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Nonparametric ANOVA

ANOVA for nonparametric variables in SPSS provides only limited capacities as there are no post hoc tests or paired comparisons of groups. Nonparametric ANOVA include two variants – for dependent variables (analogue of repeated measures ANOVA for parametric variables) and for independent variables (analogue of one-way parametric ANOVA).

Application of nonparametric ANOVA for dependent variables can be illustrated on the example with minimal inhibitory concentrations of essential oils (see Example 2), which was described in comparison of groups by nonparametric statistics.

Research question can be formulated as the following: Are there differences between minimal inhibitory concentrations (MICs) of tea tree oil alone, tea tree oil with gatifloxacin, thyme oil alone and thyme oil with gatifloxacin? We are going to compare four groups, therefore, usual nonparametric tests are not suitable.

To specify nonparametric ANOVA for dependent variables:

1) Click the Analyze menu, point to Nonparametric Tests, and select Related Samples… :

Nonparametric ANOVA for dependent variables

The Nonparametric Tests: Two or More Related Samples dialog box opens:

Selection of variables and options

2) In the Objective tab leave selected by default Automatically compare observed data to hypothesized and then click the Fields tab.

3) Select fields “Tea tree”, “Tea tree + Gati”, “Thyme” and “Thyme + Gati”:

Selection of variables

Сlick the transfer arrow button . The selected fields (variables) are moved to the Test Fields: list box.

4) Click the Settings tab. Leave selected by default Automatically choose the tests based on the data:

Selection of variables

5) Click the Run button. An Output Viewer window opens and shows statistics results.

In the Output Viewer window we see that for both species differences between 4 MICs are statistically significant. Criterion, which was chosen automatically, – Friedman’s 2-way ANOVA:

Results of multiple-group comparison

We can see that specifying nonparametric ANOVA for dependent variables (related samples) is totally the same like specifying comparison of two groups of dependent variables. The only difference is that software automatically chooses tests applicable for comparison of multiple groups (Friedman’s two-way ANOVA instead of Sign or Wilcoxon matched-pair signed-rank tests). Similar situation is with specifying nonparametric ANOVA for independent variables – procedure is totally the same, only automatically chosen criteria will be different (Kruskall-Wallis one-way ANOVA will be chosen).

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