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Table 1 Statistical approaches for interdependence analysis of immunological markers dependent on the scale of measurement

From: Applied immuno-epidemiological research: an approach for integrating existing knowledge into the statistical analysis of multiple immune markers

Scale of measurement Bivariate methods Multivariate methods
Binomial (e.g. positive, negative) Contingency table; tests: Chi-square or Fisher’s exact test; association measure: phi coefficient, Yule’s Q Multilayer contingency table, classification trees
Nominal (e.g. Th1, Th2, or T-Reg) Contingency table; tests: chi-square or Fisher’s exact test; association measure: contingency coefficient Multilayer contingency tables, correspondence analysis, classification trees
Ordinal (e.g. low, medium, high) Contingency table; tests: chi-square or Fisher’s exact test, tau test; association measure: Spearman-Rank correlation, Kendall’s Tau or Goodman and Kruskal’s γ Multilayer contingency tables, correspondence analysis, classification trees
Continuous (non-normal distributed) Scatter Plots; test: Spearman-Rank Correlation, criteria: Kendall’s Tau or Goodman and Kruskal’s γ Factor analytic techniques: e.g. principal component analysis
Continuous (normal distributed) Scatter Plots; test and association measure: Pearson correlation coefficient Factor analytic techniques: e.g. principal component analysis
  1. Rules of thumb for quantifying the strength of association based on the magnitude of association measures (e.g. Goodman and Kruskal’s γ): no association: 0 < |γ| < = 0.25, weak: 0.25 < |γ| < 0.50, moderate: 0.50 < |γ| < = 0.75, strong: |γ| > 0.75