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Single response variable Response variable continuous Response variable non-continuous Correlations Linear and non-linear regression •General Linear Model: Ordinary least squares regression (OLS) •General Linear Model: Multiple regression •Robust regression •Generalized regression •Mixed model regression Multivariate approaches Goodness of Fit tests •Traditional correlation analyses (e.g. Pearson, Bray Curtis) •Non-parametric correlation (e.g. Spearman rank) Predictor variables continuous Multiple response variables Regression models •Logistic •Probit •Discriminant Function Analysis Data are continuous One sample test of empirical to known or statistical distributions •Kolmogorov-Smirnov test (KStest), Wilks Shapiro Two sample test: compare empirical distributions •Kolmogorov-Smirnov test (KStest) Predictor variables both continuous and categorical General Linear Model: • Analysis of Covariance (ANCOVA) Generalized Linear Modeling Logistic models T-test family •One sample •Two sample •Paired Predictor variables categorical General Linear Model: Analysis of variance (ANOVA) Contingency tables (comparisons of empirical distributions) •Chi square Data are categorical Mixed Models •Generalized Linear Model: Generalized Linear Modeling •Log-Linear modeling •Logistic regression •Other Maximum liklihood approaches Non-parametric approaches •Kruskal –Wallis •Wilcoxon matched pairs •Mann-Whitney test Goodness of fit test One sample test to known or statistical distributions •Chi square test MULTIVARIATE Multiple response variables Canonical Correlation analysis Predictor variables continuous Single or partial Mantel test RELATE procedure linking matrices OTHER USEFUL ANALYSES Resampling: exact p-values for testing with variables with complicated distributions General Additive Models: use of local smoothers to fit data. Great for fit - hard to use for hypothesis testing MANOVA Predictor variables categorical ANOSIM/SIMPER PERMANOVA Principal Component Analysis for continuous data Data Reduction approaches Ordination approaches Correspondence analysis for Categorical data Hierarchical Clustering K – Means Clustering Link-tree approaches Multidimensional scaling Partial Least Squares regression: useful for collinear predictor variables