SOCR Choice of Statistical Test

Study Design				Hypotheses Parameters Test Statistics			SOCR Tools
Dependent Variables		Independent Variables		Hypotheses Parameters Test Statistics			SOCR Tools
Number	Type & Assumptions	Number	Type	Hypotheses	Parameter	Statistical Tests	Demos	Analyses
1	continuous normal	None (1 population)	N/A	H_o:μ=0 H_a:μ≠0	mean	one-sample T-test		Analyses
	continuous non-normal			H_o:m=m_o H_a:m≠m_o	median	one-sample median, Sign-test
	categorical			H_o:p=p_o H_a:p≠p_o	proportions	χ² goodness-of-fit, binomial test	Binomial Coin Exper
	categorical			Survival Analysis		Kaplan-Meier		Analyses
	normal	1 (2 independent populations)	2 categories	H_o:μ_o=μ₁ H_a:μ_o≠μ₁	mean	2 independent sample T-test		Analyses
	non-normal			H_o:m=m_o H_a:m≠m_o	medians	Mann Whitney, Wilcoxon rank sum test, Two-Sample Median Test		Analyses
	categorical			H_o:p=p_o H_a:p≠p_o	proportions	χ² test Fisher's Exact test		Analyses
	normal	None (1 population measured twice) or 1 (2 paired populations)	N/A or categorical	H_o:μ_o=μ₁ H_a:μ_o≠μ₁	means	paired T-test		Analyses
	non-normal			H_o:m=m_o H_a:m≠m_o	medians	Wilcoxon signed ranks test		Analyses
	categorical			H_o:p=p_o H_a:p≠p_o	proportions	McNemar, χ² test		Analyses
	normal	1 (≥3 populations)	categorical	H_o:μ_o=...=μ_k H_a:μ_i≠μ_j	means	one-way ANOVA		Analyses
	non-normal			H_o:m_o=...=m_k H_a:m_i≠m_j	medians	Kruskal Wallis		Analyses
	categorical			H_o:p_o=...=p_k H_a:p_i≠p_j	proportions	χ² test		Analyses
	normal	≥2 (e.g., 2-way ANOVA)	categorical	H_o:a_oμ_o+...+a_kμ_k=0 H_a:a_oμ_o+...+a_kμ_k≠0	means	Factorial ANOVA
	non-normal			TBD	medians	Friedman test
	categorical			TBD	proportions	log-linear, logistic regression
	normal	None (1 population measured ≥3 times)	N/A	TBD	means	Repeated measures ANOVA
	normal	1	continuous	TBD		correlation, simple linear regression		Analyses
	non-normal		continuous			non-parametric correlation
	categorical		categorical or continuous			logistic regression
	categorical		continuous			discriminant analysis
	normal	≥2	continuous			multiple linear regression
	non-normal
	categorical					logistic regression
	normal		mixed categorical & continuous			ANCOVA, GML
	non-normal
	categorical					logistic regression
2	normal	≥2	categorical			MANOVA
≥2	normal	≥2	continuous			multivariate multiple linear regression
2 sets of ≥2	normal	0	N/A			canonical correlation
≥2	normal	0	N/A			factor analysis
Power Analysis							Power Applet