Under dimensioning techniques, we understand all techniques that place the entries in a two- or more dimensional space, rather than imposing a hierarchical, bifurcating structure like a dendrogram. All dimensioning techniques in BIONUMERICS provide great interactive features, making it possible to select, add or remove entries directly on the plot, display additional database information as colors or labels, relate groupings directly to discriminatory characters, etc.
BIONUMERICS offers a generalized and well-documented implementation of ANOVA (Analysis of Variance) and MANOVA (Multivariate Analysis of Variance) with comprehensive statistical analysis and validation testing tools. These very useful statistical methods allow you to investigate the relation between groups of entries and characters, as well as the significance of such groups. The groups can be clusters derived from a dendrogram, or any user-defined selections of entries (e.g., by origin, species, serotype …).
Multi-Dimensional Scaling (MDS), sometimes also called Principal Coordinates Analysis (PCoA), is a non-hierarchic grouping method. Rather than starting from the data set as Principal Components Analysis (PCA) does, MDS uses the similarity matrix as input, which has the advantage over PCA that it can be applied directly to pairwise-compared banding patterns.
Partition mapping analyzes the correspondences between two partitions (classifications) and produces a number of mapping rules that define the significantly pairing groups between the two sets. The BIONUMERICS partition mapping tool is very useful for analyzing the congruences and discrepancies between typing and classification techniques and for defining reliable and consistent groups on the basis of multiple classification methods.
Principal Components Analysis (PCA) starts directly from a character table to obtain non-hierarchic groupings in a multi-dimensional space. Any combination of components can be displayed in two or three dimensions. Discriminant analysis is very similar to PCA. The major difference is that PCA calculates the best discriminating components without foreknowledge about groups, whereas discriminant analysis calculates the best discriminating components (= discriminants) for groups that are defined by the user.
Basically being a type of neural network, a Self-Organizing Map (SOM) or Kohonen map is able to place many thousands of entries in a two-dimensional representation, according to overall relatedness. For complex data sets with large numbers of entries, SOM analysis can be the preferred grouping tool. An interesting option of a SOM is that unknown entries can be placed in an existing map with very little computing time, which offers a quick and easy-to-interpret classification tool. BIONUMERICS has been the first software to apply this exciting technique for biological data.
A number of parametric and non-parametric statistical tests can be performed in an easy and intuitive environment (Chi-square test, T-test, Wilcoxon signed-ranks test, Kruskal-Wallis test, ANOVA, Pearson correlation test, Spearmann rank-order test. Automatic display of available tests for each input data type. Kolgomorov-Smirnov test for normality. Clear significance reporting.