Workflow and parameters used for the comparative statistical analysis of the platform 2CALM.

The figure depicts the flow diagram of the comparative analysis, including aggregation of parameters. In the first step, the sample data (full or bootstrap-resampled data of both samples) are clustered hierarchically for cluster dimensions (size) ranging from 10 nm– 1 000 nm. In the first level analysis of the pairwise resampled data, the Kolmogorov-Smirnov (KS)-/Wilcoxon (WX)-tests (relative density distribution/ curvature distribution) for each cluster dimension are performed. The KS- and WX-test results for comparison of cluster densities and curvatures of both (pairwise) samples are further aggregated using the t-norm-AND operator for all cluster dimensions. The results of p-value aggregation for density and curvature are once more aggregated, giving the average result of the comparison on the first statistical level. Next, the second statistical level analysis is performed. Here, the averaged density and curvature for each cluster dimension and resample are used to perform the mean-cross analysis between them. The mean-cross comparison uses KS-/WX-tests for a comparison between distributions of mean clusters density of all resamples from sample 1 and all individual density distributions of resamples from sample 2. Hence, an aggregation (t-norm AND operator) of the mean-cross KS/Wilcoxon-test results (p-values) for density and curvature for all cluster dimension gives a global p-value of similarity hypothesis. In parallel, in the second level analysis the K-/H-Ripley functions for all cluster dimensions are calculated. Hence, the mean-cross comparison on the K-/H-Ripley functions values, (same as for mean density/curvature distributions) is performed. The KS-/WX-Test results on comparison of the K-/H-Ripley function values are combined with t-norm AND, forming an additional set of parameters.

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