Statistics decision making flowchart

statistics-flowchart.txt

Compare means
* Two groups (control vs drug)
    * Same subjects measured twice (before/after)
        * Pairwise differences normal -> Paired t-test (parametric test)
        * Pairwise differences non-normal -> Wilcoxon matched pairs signed rank test (nonparametric test)
    * Each subject measured once
        * Each group normal and variances equal -> Unpaired t-test (parametric test)
        * Each group normal -> Unpaired t-test with Welch's correction (parametric test)
        * One or both groups non-normal -> Mann-Whitney test (nonparametric test)

* More than two groups (drug A vs drug B vs drug C)
    * One factor (drug)
        * Each subject measured more than once
            * Pass normality
                * Assume sphericity -> ANOVA or Mixed model (missing data)
                * Don't assume sphericity -> ANOVA or Mixed model (missing data) with G-G correction
            * Reject normality -> Friedman test (nonparametric test)
        * Each subject measured once
            * Pass normality and variances equal -> ANOVA (parametric test)
            * Pass normality -> Brown-Forsythe or Welch's ANOVA (parametric test)
            * Reject normality -> Kruskal-Wallis test (nonparametric test)

    * Two factors (drug, diet)
        * Each subject measured more than once
            * Pass normality
                * Assume sphericity -> ANOVA or Mixed model (missing data)
                * Don't assume sphericity -> ANOVA with G-G correction or Mixed model (missing data) with G-G correction
            * Reject normality -> Consider transformation
        * Each subject measured once
            * Pass normality -> ANOVA (parametric test)
            * Reject normality -> Consider transformation

    * Three factors (drug, diet, time)
        * Each subject measured more than once
            * Pass normality
                * Assume sphericity -> ANOVA or Mixed model (missing data)
                * Don't assume sphericity -> ANOVA with G-G correction or Mixed model (missing data) with G-G correction
            * Reject normality -> Consider transformation
        * Each subject measured once
            * Pass normality -> ANOVA (parametric test)
            * Reject normality -> Consider transformation

Relationship between X and Y
* Correlation (strength of relationship)
    * Pass normality -> Pearson correlation
    * Reject normality -> Spearman correlation
* Linear regression (slope)
    * Response is continuous -> Least squares regression
    * Response is a count -> Poisson regression
* Multiple regression (more than one X)
    * Response is continuous -> Least squares regression
    * Response is a count -> Poisson regression
* Nonlinear regression (dose-response) there are thousands of nonlinear models to choose from, need domain specific knowledge to choose something reasonable
    * Response continuous with no outliers -> use least squares regression to fit the nonlinear model you have selected
    * Response continuous with outliers -> use robust regression to fit the nonlinear model you have selected
    * Response is a count -> use Poisson regression to fit the nonlinear model you have selected

Categorical data
* 2x2 table
    * All expected cell counts at least 5 -> Chi-square test
    * Not all expected cell counts at least 5 -> Fisher's exact test
* 2xY table
    * Chi-square test

Survival analysis
* Kaplan-Meier

Sensitivity/Specificity
* ROC Curve