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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