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 method^{1} |
---|---|---|---|
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 |