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Table 2 Selection of important statistical methods suitable for the analysis of immunological data.

From: A guide to modern statistical analysis of immunological data

Example of research question Type of data [D: dependent, I: independent] Other data assumptions Statistical method1
Univariate techniques
Univariate group mean comparison techniques
Compare expression of a cytokine between two independent groups (e.g. treatment vs. control) D: continuous
I: categorical
Normal distribution homogeneity of variances t-test
  D: continuous or ordinal
I: categorical
  Mann Whitney-U test
Compare expression of a cytokine between two related groups (e.g. before and after treatment) D: continuous
I: categorical
Normal distribution, homogeneity of variances Paired t-test
  D: continuous or ordinal
I: categorical
  Wilcoxon rank sum test
Compare expression of a cytokine between three or more independent groups defined by one factor (e.g. treatments A, B, C) D: continuous
I: categorical
Normal distribution, homogeneity of variances One-way analysis of variance
  D: continuous or ordinal
I: categorical
  Kruskal Wallis – H test
Compare expression of a cytokine between three or more related groups (e.g. measurements 1, 2, and 3 weeks after treatment) D: continuous
I: categorical
Multivariate normal distribution, assumptions about covariance Repeated measurements analysis of variance
  D: continuous or ordinal
I: categorical
  Friedman's ANOVA
Correlation and regression analysis
Quantify association between two cytokines or a cytokine and another continuous variable D: continuous
I: continuous
Linear relationship, normality Pearson correlation coefficient
  D: continuous or ordinal
I: continuous or ordinal
Linear relationship Spearman rank correlation coefficient
Predicting expression of a cytokine by a continuous independent variable D: continuous
I: continuous
Specified relationship (e.g. linearity for linear regression), normal distribution (for parametric regression) Univariate regression
Multivariate techniques
Multivariate correlation and regression techniques
Quantify associations between two cytokines adjusted for the effect of a third continuous variable All variables: continuous Linear relationship, normality Partial correlation coefficient
Predicting a continuous outcome (e.g. a cytokine) by several continuous or categorical independent variables D: continuous
I: continuous, ordinal or categorical
Specified relationship (e.g. linearity for linear regression), normal distribution for parametric regression, No multi-collinearity Multiple regression
   Specified relationship, multi-collinearity Partial least squares regression
Quantifying the magnitude of correlation between two groups of continuous variables (e.g. Th1 and Th2 related cytokines) All variables: continuous   Canonical correlation analysis
Multivariate group mean comparison procedures
Compare cytokine expressions between three or more independent groups defined by two or more factors (e.g. treatment and gender) D: continuous
I: categorical
Normal distribution, homogeneity of variances Multi-way analysis of variance (ANOVA)
Simultaneously compare expressions of two or more cytokines between three or more independent groups defined by two or more factors D: continuous
I: categorical
Multivariate normal distribution, homogeneity of covariance matrices Multivariate analysis of variance (MANOVA)
Compare cytokine expressions between three or more related groups defined by two or more factors (e.g. measurements at different time points during a study and treatment) D: continuous
I: categorical
Multivariate normality, homogeneity of covariance matrices Multi-way repeated measurements analysis of variance
Grouping set of correlated cytokines to summary variables ("principal components") All variables: continuous High degree of multicollinearity Factor analysis/Principal components analysis
Grouping subjects in homogenous subgroups according to similar expression levels of two or more cytokines All variables: continuous Low degree of multicollinearity Cluster analysis
Classification procedures
Explaining or predicting group membership of two or more independent groups by cytokine levels D: categorical
I: continuous
Multivariate normal distribution, equal covariance matrices, low degree of multicollinearity Linear discriminant analysis
Explaining or predicting group membership of two independent groups by cytokine levels D: categorical
I: continuous, ordinal or categorical
  Logistic regression
Explaining or predicting group membership of three or more groups by cytokine levels D: categorical
I: continuous, ordinal or categorical
  Multinomial logistic regression
Advanced techniques for multiple relationships
Modelling multiple relationships between several immunological parameters and one or more outcome variables All variables: categorical, ordinal or continuous data Conceptual framework specifying the multiple relationships among the study variables Path analysis/Structural equation modelling
  1. 1All univariate and multivariate statistical approaches listed above can be implemented in general purpose statistical packages, e.g. among others S-PLUS® (Insightful Corporation, Seattle, WA), SAS® (SAS Institute Cary, NC, USA), SPSS® (Chicago: SPSS Inc.) or STATA® (StataCorp. Stata Statistical Software. College Station, TX: StataCorp LP). Path analysis/structural equation modelling can be implemented in STATA and SPSS that provide the extensions modules GLLAMM and AMOS, respectively, as well as in several special purpose software packages, e.g. among others LISREL® (Scientific Software International, Inc, IL, USA) or MX® (MCV, Department of Psychiatry, Richmond, VA, USA).